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+# A GOOD IMAGE GENERATOR IS WHAT YOU NEED FOR HIGH-RESOLUTION VIDEO SYNTHESIS
+
+Yu Tian1∗, Jian $\mathbf { R e n } ^ { 2 }$ , Menglei Chai2, Kyle Olszewski2, Xi Peng3,   
+Dimitris N. Metaxas1, Sergey Tulyakov2   
+1Rutgers University, 2Snap Inc., 3University of Delaware   
+{yt219, dnm}@cs.rutgers.edu,   
+{jren, mchai, kolszewski, stulyakov}@snapchat.com
+
+# ABSTRACT
+
+Image and video synthesis are closely related areas aiming at generating content from noise. While rapid progress has been demonstrated in improving imagebased models to handle large resolutions, high-quality renderings, and wide variations in image content, achieving comparable video generation results remains problematic. We present a framework that leverages contemporary image generators to render high-resolution videos. We frame the video synthesis problem as discovering a trajectory in the latent space of a pre-trained and fixed image generator. Not only does such a framework render high-resolution videos, but it also is an order of magnitude more computationally efficient. We introduce a motion generator that discovers the desired trajectory, in which content and motion are disentangled. With such a representation, our framework allows for a broad range of applications, including content and motion manipulation. Furthermore, we introduce a new task, which we call cross-domain video synthesis, in which the image and motion generators are trained on disjoint datasets belonging to different domains. This allows for generating moving objects for which the desired video data is not available. Extensive experiments on various datasets demonstrate the advantages of our methods over existing video generation techniques. Code will be released at https://github.com/snap-research/MoCoGAN-HD.
+
+# 1 INTRODUCTION
+
+Video synthesis seeks to generate a sequence of moving pictures from noise. While its closely related counterpart—image synthesis—has seen substantial advances in recent years, allowing for synthesizing at high resolutions (Karras et al., 2017), rendering images often indistinguishable from real ones (Karras et al., 2019), and supporting multiple classes of image content (Zhang et al., 2019), contemporary improvements in the domain of video synthesis have been comparatively modest. Due to the statistical complexity of videos and larger model sizes, video synthesis produces relatively low-resolution videos, yet requires longer training times. For example, scaling the image generator of Brock et al. (2019) to generate $2 5 6 \times 2 5 6$ videos requires a substantial computational budget1. Can we use a similar method to attain higher resolutions? We believe a different approach is needed.
+
+There are two desired properties for generated videos: (i) high quality for each individual frame, and (ii) the frame sequence should be temporally consistent, i.e. depicting the same content with plausible motion. Previous works (Tulyakov et al., 2018; Clark et al., 2019) attempt to achieve both goals with a single framework, making such methods computationally demanding when high resolution is desired. We suggest a different perspective on this problem. We hypothesize that, given an image generator that has learned the distribution of video frames as independent images, a video can be represented as a sequence of latent codes from this generator. The problem of video synthesis can then be framed as discovering a latent trajectory that renders temporally consistent images. Hence, we demonstrate that (i) can be addressed by a pre-trained and fixed image generator, and (ii) can be achieved using the proposed framework to create appropriate image sequences.
+
+To discover the appropriate latent trajectory, we introduce a motion generator, implemented via two recurrent neural networks, that operates on the initial content code to obtain the motion representation. We model motion as a residual between continuous latent codes that are passed to the image generator for individual frame generation. Such a residual representation can also facilitate the disentangling of motion and content. The motion generator is trained using the chosen image discriminator with contrastive loss to force the content to be temporally consistent, and a patch-based multi-scale video discriminator for learning motion patterns. Our framework supports contemporary image generators such as StyleGAN2 (Karras et al., 2019) and BigGAN (Brock et al., 2019).
+
+We name our approach as MoCoGAN-HD (Motion and Content decomposed GAN for HighDefinition video synthesis) as it features several major advantages over traditional video synthesis pipelines. First, it transcends the limited resolutions of existing techniques, allowing for the generation of high-quality videos at resolutions up to $1 0 2 4 \times 1 0 2 4$ . Second, as we search for a latent trajectory in an image generator, our method is computationally more efficient, requiring an order of magnitude less training time than previous video-based works (Clark et al., 2019). Third, as the image generator is fixed, it can be trained on a separate high-quality image dataset. Due to the disentangled representation of motion and content, our approach can learn motion from a video dataset and apply it to an image dataset, even in the case of two datasets belonging to different domains. It thus unleashes the power of an image generator to synthesize high quality videos when a domain (e.g., dogs) contains many high-quality images but no corresponding high-quality videos (see Fig. 4). In this manner, our method can generate realistic videos of objects it has never seen moving during training (such as generating realistic pet face videos using motions extracted from images of talking people). We refer to this new video generation task as cross-domain video synthesis. Finally, we quantitatively and qualitatively evaluate our approach, attaining state-of-the-art performance on each benchmark, and establish a challenging new baseline for video synthesis methods.
+
+# 2 RELATED WORK
+
+Video Synthesis. Approaches to image generation and translation using Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have demonstrated the ability to synthesize high quality images (Radford et al., 2016; Zhang et al., 2019; Brock et al., 2019; Donahue & Simonyan, 2019; Jin et al., 2021). Built upon image translation (Isola et al., 2017; Wang et al., 2018b), works on video-to-video translation (Bansal et al., 2018; Wang et al., 2018a) are capable of converting an input video to a high-resolution output in another domain. However, the task of high-fidelity video generation, in the unconditional setting, is still a difficult and unresolved problem. Without the strong conditional inputs such as segmentation masks (Wang et al., 2019) or human poses (Chan et al., 2019; Ren et al., 2020) that are employed by video-to-video translation works, generating videos following the distribution of training video samples is challenging. Earlier works on GANbased video modeling, including MDPGAN (Yushchenko et al., 2019), VGAN (Vondrick et al., 2016), TGAN (Saito et al., 2017), MoCoGAN (Tulyakov et al., 2018), ProgressiveVGAN (Acharya et al., 2018), TGANv2 (Saito et al., 2020) show promising results on low-resolution datasets. Recent efforts demonstrate the capacity to generate more realistic videos, but with significantly more computation (Clark et al., 2019; Weissenborn et al., 2020). In this paper, we focus on generating realistic videos using manageable computational resources. LDVDGAN (Kahembwe & Ramamoorthy, 2020) uses low dimensional discriminator to reduce model size and can generate videos with resolution up to $5 1 2 \times 5 1 2$ , while we decrease training cost by utilizing a pre-trained image generator. The high-quality generation is achieved by using pre-trained image generators, while the motion trajectory is modeled within the latent space. Additionally, learning motion in the latent space allows us to easily adapt the video generation model to the task of video prediction (Denton et al., 2017), in which the starting frame is given (Denton & Fergus, 2018; Zhao et al., 2018; Walker et al., 2017; Villegas et al., 2017b;a; Babaeizadeh et al., 2017; Hsieh et al., 2018; Byeon et al., 2018), by inverting the initial frame through the generator (Abdal et al., 2020), instead of training an extra image encoder (Tulyakov et al., 2018; Zhang et al., 2020).
+
+Interpretable Latent Directions. The latent space of GANs is known to consist of semantically meaningful vectors for image manipulation. Both supervised methods, either using human annotations or pre-trained image classifiers (Goetschalckx et al., 2019; Shen et al., 2020), and unsupervised methods (Jahanian et al., 2020; Plumerault et al., 2020), are able to find interpretable directions for image editing, such as supervising directions for image rotation or background removal (Voynov &
+
+![](images/1d51f6cbf295d027c9a3cd793ca8bdc6862f3cbdc3e68b27dcb8f2dd21f8b26d.jpg)  
+Figure 1: Left: Given an initial latent code $\mathbf { z } _ { 1 }$ , a trajectory $\epsilon _ { t }$ , and a PCA basis $\mathbf { V }$ , the motion generator $G _ { \mathrm { M } }$ encodes $\mathbf { z } _ { 1 }$ using $\mathrm { L S T M _ { \mathrm { e n c } } }$ to get the initial hidden state and uses $\mathrm { L S T M _ { d e c } }$ to estimate hidden states for future frames. The image generator $G _ { \mathrm { I } }$ synthesizes images using the predicted latent codes. The discriminator $D _ { \mathrm { { V } } }$ is trained on both real and generated video sequences. Right: For each generated video, the first and subsequent frames are sent to an image discriminator $D _ { \mathrm { I } }$ . An encoder-like network $F$ calculates the features of synthesized images used to compute the contrastive loss ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ with positive (same image content, but different augmentation, shown in blue) and negative pairs (different image content and augmentation, shown in red).
+
+Babenko, 2020; Shen & Zhou, 2020). We further consider the motion vectors in the latent space. By disentangling the motion trajectories in an unsupervised fashion, we are able to transfer the motion information from a video dataset to an image dataset in which no temporal information is available.
+
+Contrastive Representation Learning is widely studied in unsupervised learning tasks (He et al., 2020; Chen et al., 2020a;b; Henaff et al., 2020; L ´ owe et al., 2019; Oord et al., 2018; Misra & Maaten, ¨ 2020). Related inputs, such as images (Wu et al., 2018) or latent representations (Hjelm et al., 2019), which can vary while training due to data augmentation, are forced to be close by minimizing differences in their representation during training. Recent work (Park et al., 2020) applies noisecontrastive estimation (Gutmann & Hyvarinen, 2010) to image generation tasks by learning the ¨ correspondence between image patches, achieving performance superior to that attained when using cycle-consistency constraints (Zhu et al., 2017; Yi et al., 2017). On the other hand, we learn an image discriminator to create videos with coherent content by leveraging contrastive loss (Hadsell et al., 2006) along with an adversarial loss (Goodfellow et al., 2014).
+
+# 3 METHOD
+
+In this section, we introduce our method for high-resolution video generation. Our framework is built on top of a pre-trained image generator (Karras et al., 2020a;b; Zhao et al., 2020a;b), which helps to generate high-quality image frames and boosts the training efficiency with manageable computational resources. In addition, with the image generator fixed during training, we can disentangle video motion from image content, and enable video synthesis even when the image content and the video motion come from different domains.
+
+More specifically, our inference framework includes a motion generator $G _ { \mathrm { M } }$ and an image generator $G _ { \mathrm { I } }$ . $G _ { \mathrm { M } }$ is implemented with two LSTM networks (Hochreiter & Schmidhuber, 1997) and predicts the latent motion trajectory $\mathbf { Z } = \left\{ \mathbf { z } _ { 1 } , \mathbf { z } _ { 2 } , \cdots , \mathbf { z } _ { n } \right\}$ , where $n$ is the number of frames in the synthesized video. The image generator $G _ { \mathrm { I } }$ can thus synthesize each individual frame from the motion trajectory. The generated video sequence $\tilde { \mathbf { v } }$ is given by $\tilde { \mathbf { v } } = \{ \tilde { \mathbf { x } } _ { 1 } , \tilde { \mathbf { x } } _ { 2 } , \cdots , \tilde { \mathbf { x } } _ { n } \}$ . For each synthesized frame $\tilde { \mathbf { x } } _ { t }$ , we have $\tilde { \mathbf { x } } _ { t } = G _ { \mathrm { I } } ( \mathbf { z } _ { t } )$ for $t = 1 , 2 , \cdots , n$ . We also define the real video clip as $\mathbf { v } = \{ \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \cdots , \mathbf { x } _ { n } \}$ and the training video distribution as $p _ { v }$ .
+
+To train the motion generator $G _ { \mathrm { M } }$ to discover the desired motion trajectory, we apply a video discriminator to constrain the generated motion patterns to be similar to those of the training videos, and an image discriminator to force the frame content to be temporally consistent. Our framework is illustrated in Fig. 1. We describe each component in more detail in the following sections.
+
+# 3.1 MOTION GENERATOR
+
+The motion generator $G _ { \mathrm { M } }$ predicts consecutive latent codes using an input code $\mathbf { z } _ { 1 } \in { \mathcal { Z } }$ , where the latent space $\mathcal { Z }$ is also shared by the image generator. For BigGAN (Brock et al., 2019), we sample $\mathbf { z } _ { 1 }$ from the normal distribution $p _ { z }$ . For StyleGAN2 (Karras et al., 2020b), $p _ { z }$ is the distribution after the multi-layer perceptron (MLP), as the latent codes within this distribution can be semantically disentangled better than when using the normal distribution (Shen et al., 2020; Zhu et al., 2020).
+
+Formally, $G _ { \mathrm { M } }$ includes an LSTM encoder $\mathrm { L S T M _ { \mathrm { e n c } } }$ , which encodes $\mathbf { z } _ { 1 }$ to get the initial hidden state, and a LSTM decoder $\mathrm { L S T M _ { d e c } }$ , which estimates $n - 1$ continuous hidden states recursively:
+
+$$
+\begin{array} { c } { { { \bf h } _ { 1 } , { \bf c } _ { 1 } = \mathrm { L S T M } _ { \mathrm { e n c } } ( { \bf z } _ { 1 } ) , } } \\ { { { \bf h } _ { t } , { \bf c } _ { t } = \mathrm { L S T M } _ { \mathrm { d e c } } ( \epsilon _ { t } , ( { \bf h } _ { t - 1 } , { \bf c } _ { t - 1 } ) ) , t = 2 , 3 , \cdots , n , } } \end{array}
+$$
+
+where $\mathbf { h }$ and c denote the hidden state and cell state respectively, and $\epsilon _ { t }$ is a noise vector sampled from the normal distribution to model the motion diversity at timestamp $t$ .
+
+Motion Disentanglement. Prior work (Tulyakov et al., 2018) applies $\mathbf { h } _ { t }$ as the motion code for the frame to be generated, while the content code is fixed for all frames. However, such a design requires a recurrent network to estimate the motion while preserving consistent content from the latent vector, which is difficult to learn in practice. Instead, we propose to use a sequence of motion residuals for estimating the motion trajectory. Specifically, we model the motion residual as the linear combination of a set of interpretable directions in the latent space (Shen & Zhou, 2020; Hark ¨ onen ¨ et al., 2020). We first conduct principal component analysis (PCA) on $m$ randomly sampled latent vectors from $\mathcal { Z }$ to get the basis $\mathbf { V }$ . Then, we estimate the motion direction from the previous frame $\mathbf { z } _ { t - 1 }$ to the current frame $\mathbf { z } _ { t }$ by using $\mathbf { h } _ { t }$ and $\mathbf { V }$ as follows:
+
+$$
+\mathbf { z } _ { t } = \mathbf { z } _ { t - 1 } + \lambda \cdot \mathbf { h } _ { t } \cdot \mathbf { V } , t = 2 , 3 , \cdots , n ,
+$$
+
+where the hidden state ${ \mathbf h } _ { t } \in [ - 1 , 1 ]$ , and $\lambda$ controls the step given by the residual. With Eqn. 1 and Eqn. 2, we have $G _ { \mathrm { M } } ( \mathbf { z } _ { 1 } ) = \left\{ \mathbf { z } _ { 1 } , \mathbf { z } _ { 2 } , \cdots , \mathbf { z } _ { n } \right\}$ , and the generated video $\tilde { \mathbf { v } }$ is given as $\tilde { { \textbf { v } } } =$ $G _ { \mathrm { I } } ( G _ { \mathrm { M } } ( \mathbf { z } _ { 1 } ) )$ .
+
+Motion Diversity. In Eqn. 1, we introduce a noise vector $\epsilon _ { t }$ to control the diversity of motion. However, we observe that the LSTM decoder tends to neglect the $\epsilon _ { t }$ , resulting in motion mode collapse, meaning that $G _ { \mathrm { M } }$ cannot capture the diverse motion patterns from training videos and generate distinct videos from one initial latent code with similar motion patterns for different sequences of noise vectors. To alleviate this issue, we introduce a mutual information loss ${ \mathcal { L } } _ { \mathrm { m } }$ to maximize the mutual information between the hidden vector $\mathbf { h } _ { t }$ and the noise vector $\epsilon _ { t }$ . With $\mathrm { s i m } ( \mathbf { u } , \mathbf { v } ) = \mathbf { u } ^ { T } \mathbf { v } / \left\| \mathbf { u } \right\| \left\| \mathbf { v } \right\|$ denoting the cosine similarity between vectors $\mathbf { u }$ and $\mathbf { v }$ , we define ${ \mathcal { L } } _ { \mathrm { m } }$ as follows:
+
+$$
+\mathcal { L } _ { \mathrm { m } } = \frac { 1 } { n - 1 } \sum _ { t = 2 } ^ { n } \sin ( H ( \mathbf { h } _ { t } ) , \epsilon _ { t } ) ,
+$$
+
+where $H$ is a 2-layer MLP that serves as a mapping function.
+
+Learning. To learn the appropriate parameters for the motion generator $G _ { \mathrm { M } }$ , we apply a multi-scale video discriminator $D _ { \mathrm { { V } } }$ to tell whether a video sequence is real or synthesized. The discriminator is based on the architecture of PatchGAN (Isola et al., 2017). However, we use 3D convolutional layers in $D _ { \mathrm { { V } } }$ , as they can model temporal dynamics better than 2D convolutional layers. We divide input video sequence into small 3D patches, and classify each patch as real or fake. The local responses for the input sequence are averaged to produce the final output. Additionally, each frame in the input video sequence is conditioned on the first frame, as it falls into the distribution of the pre-trained image generator, for more stable training. We thus optimize the following adversarial loss to learn $G _ { \mathrm { M } }$ and $D _ { \mathrm { { V } } }$ :
+
+$$
+\mathcal { L } _ { D _ { \mathrm { V } } } = \mathbb { E } _ { { \mathbf { v } } \sim p _ { v } } \left[ \log D _ { \mathrm { v } } ( { \mathbf { v } } ) \right] + \mathbb { E } _ { { \mathbf { z } } _ { 1 } \sim p _ { z } } \left[ \log ( 1 - D _ { \mathrm { V } } ( G _ { \mathrm { I } } ( G _ { \mathrm { M } } ( { \mathbf { z } } _ { 1 } ) ) ) ) \right] .
+$$
+
+# 3.2 CONTRASTIVE IMAGE DISCRIMINATOR
+
+As our image generator is pre-trained, we may use an image generator that is trained on a given domain, e.g. images of animal faces (Choi et al., 2020), and learn the motion generator parameters using videos from a different domain, such as videos of human facial expressions (Nagrani et al.,
+
+2017). With Eqn. 4 alone, however, we lack the ability to explicitly constrain the generated images $\tilde { \mathbf { x } } _ { t \mid t > 1 }$ to possess similar quality and content as the first image $\tilde { \mathbf { x } } _ { 1 }$ , which is sampled from the image space of the image generator and thus has high fidelity. Hence, we introduce a contrastive image discriminator $D _ { \mathrm { I } }$ , which is illustrated in Fig. 1, to match both image quality and content between $\tilde { \mathbf { x } } _ { 1 }$ and $\tilde { \mathbf { x } } _ { t \mid t > 1 }$ .
+
+Quality Matching. To increase the perceptual quality, we train $D _ { \mathrm { I } }$ and $G _ { \mathrm { M } }$ adversarially by forwarding $\tilde { \mathbf { x } } _ { t }$ into the discriminator $D _ { \mathrm { I } }$ and using $\tilde { \mathbf { x } } _ { 1 }$ as real sample and $\tilde { \mathbf { X } } _ { t \mid t > 1 }$ as the fake sample.
+
+$$
+\mathcal { L } _ { D _ { 1 } } = \mathbb { E } _ { \mathbf { z } _ { 1 } \sim p _ { z } } \left[ \log D _ { \mathrm { I } } ( G _ { \mathrm { I } } ( \mathbf { z } _ { 1 } ) ) \right] + \mathbb { E } _ { \mathbf { z } _ { 1 } \sim p _ { z } , \mathbf { z } _ { t } \sim G _ { \mathrm { M } } ( \mathbf { z } _ { 1 } ) | t > 1 } \left[ \log ( 1 - D _ { \mathrm { I } } ( G _ { \mathrm { I } } ( \mathbf { z } _ { t } ) ) ) \right] .
+$$
+
+Content Matching. To learn content similarity between frames within a video, we use the image discriminator as a feature extractor and train it with a form of contrastive loss known as InfoNCE (Oord et al., 2018). The goal is that pairs of images with the same content should be close together in embedding space, while images containing different content should be far apart.
+
+Given a minibatch of $N$ generated videos $\{ \tilde { \mathbf { v } } ^ { ( 1 ) } , \tilde { \mathbf { v } } ^ { ( 2 ) } , \cdots , \tilde { \mathbf { v } } ^ { ( N ) } \}$ , we randomly sample one frame $t$ from each video: $\{ \tilde { \mathbf { x } } _ { t } ^ { ( 1 ) } , \tilde { \mathbf { x } } _ { t } ^ { ( 2 ) } , \cdot \cdot \cdot , \tilde { \mathbf { x } } _ { t } ^ { ( N ) } \}$ , and make two randomly augmented versions $( \tilde { \mathbf { x } } _ { t } ^ { ( i a ) } , \tilde { \mathbf { x } } _ { t } ^ { ( i b ) } )$ for each frame $\tilde { \mathbf { x } } _ { t } ^ { ( i ) }$ , resulting in $2 N$ samples. $( \tilde { \mathbf { x } } _ { t } ^ { ( i a ) } , \tilde { \mathbf { x } } _ { t } ^ { ( i b ) } )$ are positive pairs, as they share the same content. $( \tilde { \mathbf { x } } _ { t } ^ { ( i \cdot ) } , \tilde { \mathbf { x } } _ { t } ^ { ( j \cdot ) } )$ are all negative pairs for $i \neq j$ .
+
+Let $F$ be an encoder network, which shares the same weights and architecture of $D _ { \mathrm { I } }$ , but excluding the last layer of $D _ { \mathrm { I } }$ and including a 2-layer MLP as a projection head that produces the representation of the input images. We have a contrastive loss function ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ , which is the cross-entropy computed across $2 N$ augmentations as follows:
+
+$$
+\mathcal { L } _ { \mathrm { c o n t r } } = - \sum _ { i = 1 } ^ { N } \sum _ { \alpha = a } ^ { b } \log \frac { \exp ( \sin ( F ( \tilde { \mathbf { x } } _ { t } ^ { ( i a ) } ) , F ( \tilde { \mathbf { x } } _ { t } ^ { ( i b ) } ) ) / \tau ) } { \sum _ { j = 1 } ^ { N } \sum _ { \beta = a } ^ { b } \mathbb { 1 } _ { [ j \neq i ] } ( \exp ( \sin ( F ( \tilde { \mathbf { x } } _ { t } ^ { ( i \alpha ) } ) , F ( \tilde { \mathbf { x } } _ { t } ^ { ( j \beta ) } ) ) / \tau ) } ,
+$$
+
+where $\sin ( \cdot , \cdot )$ is the cosine similarity function defined in Eqn. 3, $\mathbb { 1 } _ { [ j \neq i ] } \in \{ 0 , 1 \}$ is equal to 1 iff $j \neq i$ , and $\tau$ is a temperature parameter empirically set to 0.07. We use a momentum decoder mechanism similar to that of MoCo (He et al., 2020) by maintaining a memory bank to delete the oldest negative pairs and update the new negative pairs. We apply augmentation methods including translation, color jittering, and cutout (DeVries & Taylor, 2017) on synthesized images. With the positive and negative pairs generated on-the-fly during training, the discriminator can effectively focus on the content of the input samples.
+
+The choice of positive pairs in Eqn. 6 is specifically designed for cross-domain video synthesis, as videos of arbitrary content from the image domain is not available. In the case that images and videos are from the same domain, the positive and negative pairs are easier to obtain. We randomly select and augment two frames from a real video to create positive pairs sharing the same content, while the negative pairs contain augmented images from different real videos.
+
+Aside from ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ , we also adopt the feature matching loss (Wang et al., 2018b) ${ \mathcal { L } } _ { \mathrm { f } }$ between the generated first frame and other frames by changing the $L _ { 1 }$ regularization to cosine similarity.
+
+Full Objective. The overall loss function for training motion generator, video discriminator, and image discriminator is thus defined as:
+
+$$
+\operatorname* { m i n } _ { G _ { \mathrm { M } } } ( \operatorname* { m a x } _ { D _ { \mathrm { V } } } \mathcal { L } _ { D _ { \mathrm { V } } } + \operatorname* { m a x } _ { D _ { \mathrm { I } } } \mathcal { L } _ { D _ { \mathrm { I } } } ) + \operatorname* { m a x } _ { G _ { \mathrm { M } } } ( \lambda _ { \mathrm { m } } \mathcal { L } _ { \mathrm { m } } + \lambda _ { \mathrm { f } } \mathcal { L } _ { \mathrm { f } } ) + \operatorname* { m i n } _ { D _ { \mathrm { I } } } ( \lambda _ { \mathrm { c o n t r } } \mathcal { L } _ { \mathrm { c o n t r } } )
+$$
+
+where $\lambda _ { \mathrm { m } }$ , $\lambda _ { \mathrm { c o n t r } }$ , and $\lambda _ { \mathrm { f } }$ are hyperparameters to balance losses.
+
+# 4 EXPERIMENTS
+
+In this section, we evaluate the proposed approach on several benchmark datasets for video generation. We also demonstrate cross-domain video synthesis for various image and video datasets.
+
+# 4.1 VIDEO GENERATION
+
+We conduct experiments on three datasets including UCF-101 (Soomro et al., 2012), FaceForensics (Rossler et al., 2018), and Sky Time-lapse (Xiong et al., 2018) for unconditional video synthesis. ¨ We use StyleGAN2 as the image generator. Training details can be found in Appx. B.
+
+Table 1: IS and FVD on UCF-101.   
+
+<table><tr><td>Method</td><td>IS (↑)</td><td>FVD (↓)</td></tr><tr><td>VGAN</td><td>8.31 ± .09</td><td></td></tr><tr><td>TGAN</td><td>11.85 ± .07</td><td></td></tr><tr><td>MoCoGAN</td><td>12.42 ± .07</td><td></td></tr><tr><td>ProgressiveVGAN</td><td>14.56 ± .05</td><td></td></tr><tr><td>LDVD-GAN</td><td>22.91 ± .19</td><td></td></tr><tr><td>TGANv2</td><td>26.60 ± .47</td><td>1209 ± 28</td></tr><tr><td>DVD-GAN</td><td>27.38 ± .53</td><td>=</td></tr><tr><td>Ours</td><td>33.95 ± .25</td><td>700 ± 24</td></tr></table>
+
+Table 2: FVD, ACD, and Human Preference on FaceForensics.   
+
+<table><tr><td>Method</td><td>FVD (↓)</td><td>ACD (↓)</td></tr><tr><td>GT</td><td>9.02</td><td>0.2935</td></tr><tr><td>TGANv2 Ours</td><td>58.03 53.26</td><td>0.4914 0.3300</td></tr><tr><td></td><td></td><td></td></tr><tr><td>Method</td><td>Human Preference</td><td>(%)</td></tr><tr><td>Ours /TGANv2</td><td></td><td>73.6 / 26.4</td></tr></table>
+
+UCF-101 is widely used in video generation. The dataset includes 13, 320 videos of 101 sport categories. The resolution of each video is $3 2 0 \times 2 4 0$ . To process the data, we crop a rectangle with size of $2 4 0 \times 2 4 0$ from each frame in a video and resize it to $2 5 6 \times 2 5 6$ . We train the motion generator to predict 16 frames. For evaluation, we report Inception Score (IS) (Saito et al., 2020) on 10, 000 generated videos and Fr´echet Video Distance (FVD) (Unterthiner et al., 2018) on 2, 048 videos. The classifier used to calculate IS is a C3D network (Tran et al., 2015) that is trained on the Sports-1M dataset (Karpathy et al., 2014) and fine-tuned on UCF-101, which is the same model used in previous works (Saito et al., 2020; Clark et al., 2019).
+
+The quantitative results are shown in Tab. 1. Our method achieves state-of-the-art results for both IS and FVD, and outperforms existing works by a large margin. Interestingly, this result indicates that a well-trained image generator has learned to represent rich motion patterns, and therefore can be used to synthesize high-quality videos when used with a well-trained motion generator.
+
+FaceForensics is a dataset containing news videos featuring various reporters. We use all the images from 704 training videos, with a resolution of $2 5 6 \times 2 5 6$ , to learn an image generator, and sequences of 16 consecutive frames to train motion generator. Note that our network can generate even longer continuous sequences, e.g. 64 frames (Fig. 12 in Appx.), though only 16 frames are used for training.
+
+We show the FVD between generated and real video clips (16 frames in length) for different methods in Tab. 2. Additionally, we use the Average Content Distance (ACD) from MoCoGAN (Tulyakov et al., 2018) to evaluate the identity consistency for these human face videos. We calculate ACD values over 256 videos. We also report the two metrics for ground truth (GT) videos. To get FVD of GT videos, we randomly sample two groups of real videos and compute the score. Our method achieves better results than TGANv2 (Saito et al., 2020). Both methods have low FVD values, and can generate complex motion patterns
+
+![](images/009d321d03f84d81cb9272a74b4285a7fff0d1fa52834fcf57e94097294ed8e9.jpg)  
+Figure 2: Example generated videos from a model trained on FaceForensics. We can generate natural and photo-realistic videos with various motion patterns, such as eye blink and talking. Four examples show frames 2, 7, 11, and 16.
+
+close to the real data. However, the much lower ACD value of our approach, which is close to GT, demonstrates that the videos it synthesizes have much better identity consistency than the videos from TGANv2. Qualitative examples in Fig. 2 illustrate different motions patterns learned from the dataset. Furthermore, we perform perceptual experiments using Amazon Mechanical Turk (AMT) by presenting a pair of videos from the two methods to users and asking them to select a more realistic one. Results in Tab. 2 indicate our method outperforms TGANv2 in $7 3 . 6 \%$ of the comparisons.
+
+Sky Time-Lapse is a video dataset consisting of dynamic sky scenes, such as moving clouds. The number of video clips for training and testing is 35, 392 and 2, 815, respectively. We resize images to $1 2 8 \times 1 2 8$ and train the model to generate 16 frames. We compare our methods with the two recent approaches of MDGAN (Xiong et al., 2018) and DTVNet (Zhang et al., 2020), which are specifically designed for this dataset. In Tab. 3, we report the FVD for all three methods. It is clear that our approach significantly outperforms the others. Example sequences are shown in Fig. 3.
+
+Following DTVNet (Zhang et al., 2020), we evaluate the proposed model for the task of video prediction. We use the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) (Wang et al., 2004) as evaluation metrics to measure the frame quality at the pixel level and the structural similarity between synthesized and real video frames. Evaluation is performed on the testing set. We select the first frame $\mathbf { x } _ { 1 }$ from each video clip and project it to the latent space of the image generator (Abdal et al., 2020) to get $\hat { \mathbf { z } } _ { 1 }$ . We use $\hat { \mathbf { z } } _ { 1 }$ as the starting latent code for motion generator to get 16 latent codes, and interpolate them to get 32 latent codes to synthesize a video sequence, where the first frame is given by $G _ { \mathrm { I } } ( \hat { \bf z } _ { 1 } )$ . For a fair comparison, we also use $G _ { \mathrm { I } } ( \hat { \bf z } _ { 1 } )$ as the starting frame for MDGAN and DTVNet to calculate the metrics with ground truth videos. In addition, we calculate the PSNR and SSIM between $\mathbf { x } _ { 1 }$ and $G _ { \mathrm { I } } ( \hat { \bf z } _ { 1 } )$ as the upper bound for all methods, which we denote as Up-B. Tab. 3 shows the video prediction results, which demonstrate that our method’s performance is superior to those of MDGAN and DTVNet. Interestingly, by simply interpolating the motion trajectory, we can easily generate longer video sequence, e.g. from 16 to 32 frames, while retaining high quality.
+
+Table 3: Evaluation on Sky Time-lapse for video synthesis and prediction.   
+
+<table><tr><td>Method</td><td>FVD (↓)</td><td>PSNR (↑)</td><td>SSIM (↑)</td></tr><tr><td>Up-B</td><td>1</td><td>25.367</td><td>0.781</td></tr><tr><td>MDGAN</td><td>840.95</td><td>13.840</td><td>0.581</td></tr><tr><td>DTVNet</td><td>451.14</td><td>21.953</td><td>0.531</td></tr><tr><td>Ours</td><td>77.77</td><td>22.286</td><td>0.688</td></tr></table>
+
+![](images/e2a803672b70bf1b3a1b61ee267e94d5b0a9b41de7977e03b19b1449e7d3eb79.jpg)  
+Figure 3: Sample generated frames at several time steps $\mathbf { \rho } ( t )$ for the Sky Time-lapse dataset.
+
+![](images/6ea4cb0bfae791a923a6b9dadc2f96d39c0ed245967d5bbd678103fcd228f383.jpg)  
+Figure 4: Example sequences for cross-domain video generation. First Row: (FFHQ, VoxCeleb). Second Row: (LSUN-Church, TLVDB). Third Row: (AFHQ-Dog, VoxCeleb). Fourth Row: (AnimeFaces, VoxCeleb). Images in the first and second rows have a resolution of $2 5 6 \times 2 5 6$ , while the third and fourth rows have a resolution of $5 1 2 \times 5 1 2$ .
+
+# 4.2 CROSS-DOMAIN VIDEO GENERATION
+
+To demonstrate how our approach can disentangle motion from image content and transfer motion patterns from one domain to another, we perform several experiments on various datasets. More specifically, we use the StyleGAN2 model, pre-trained on the FFHQ (Karras et al., 2019), AFHQDog (Choi et al., 2020), AnimeFaces (Branwen, 2019), and LSUN-Church (Yu et al., 2015) datasets, as the image generators. We learn human facial motion from VoxCeleb (Nagrani et al., 2020) and time-lapse transitions in outdoor scenes from TLVDB (Shih et al., 2013). In these experiments, a pair such as (FFHQ, VoxCeleb) indicates that we synthesize videos with image content from FFHQ and motion patterns from VoxCeleb. We generate videos with a resolution of $2 5 6 \times 2 5 6$ and $1 0 2 4 \times 1 0 2 4$ for FFHQ, $5 1 2 \times 5 1 2$ for AFHQ-Dog and AnimeFaces, and $2 5 6 \times 2 5 6$ for LSUN-Church. Qualitative examples for (FFHQ, VoxCeleb), (LSUN-Church, TLVDB), (AFHQ-Dog, VoxCeleb), and (AnimeFaces, VoxCeleb) are shown in Fig. 4, depicting high-quality and temporally consistent videos (more videos, including results with BigGAN as the image generator, are shown in the Appendix).
+
+We also demonstrate how the motion and content are disentangled in Fig. 5 and Fig. 6, which portray generated videos with the same identity but performing diverse motion patterns, and the same motion applied to different identities, respectively. We show results from (AFHQ-Dog, VoxCeleb) (first two rows) and (AnimeFaces, VoxCeleb) (last two rows) in these two figures.
+
+![](images/09659f6861048e5e0134752c50211a917651a84a057589302fb57f579616201b.jpg)  
+Figure 5: The first and second row (also the third and fourth row) share the same initial content code but with different motion codes.
+
+![](images/52bc42e59b25ba73ffc31e42a584757750dcc1cbb3d55b7b1ac10dc667e8de59.jpg)  
+Figure 6: The first and second row (also the third and fourth row) share the same motion code but with different content codes.
+
+# 4.3 ABLATION ANALYSIS
+
+We first report IS and FVD in Tab. 4 for UCF-101 using the following methods: w/o Eqn. 2 uses $\mathbf { z } _ { t } =$ $\mathbf { h } _ { t }$ instead of estimating the residual as in Eqn. 2; w/o $D _ { \mathrm { I } }$ omits the contrastive image discriminator $D _ { \mathrm { I } }$ and uses the video discriminator $D _ { \mathrm { { V } } }$ only for learning the motion generator; w/o $D _ { \mathrm { { V } } }$ omits $D _ { \mathrm { V } }$ during training; and Full-128 and $F u l l { - } 2 5 6$ indicate that we generate videos using our full method with resolutions of $1 2 8 \times 1 2 8$ and $2 5 6 \times 2 5 6$ , respectively. We resize frames for all methods to $1 2 8 \times 1 2 8$ when calculating IS and FVD. The full method outperforms all others, proving the importance of each module for learning temporally consistent and high-quality videos.
+
+We perform further analysis of our cross-domain video generation on (FFHQ, VoxCeleb). We compare our full method $( F u l l )$ with two variants. w/o ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ denotes that we omit the contrastive loss (Eqn. 6) from $D _ { \mathrm { I } }$ , and w/o ${ \mathcal { L } } _ { \mathrm { m } }$ indicates that we omit the mutual information loss (Eqn. 3) for the motion generator. The results in Tab. 5 demonstrate that ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ is beneficial for learning videos with coherent content, as employing ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ results in lower ACD values and higher human preferences. ${ \mathcal { L } } _ { \mathrm { m } }$ also contributes to generating higher quality videos by mitigating motion synchronization. To validate the motion diversity, we show pairs of 9 randomly generated videos from the two methods to users and ask them to choose which one has superior motion diversity, including rotations and facial expressions. User preference suggests that using ${ \mathcal { L } } _ { \mathrm { m } }$ increases motion diversity.
+
+Table 4: Ablation study on UCF-101.   
+
+<table><tr><td>Method</td><td>IS (↑)</td><td>FVD (↓)</td></tr><tr><td>w/o Eqn. 2</td><td>28.20</td><td>790.87</td></tr><tr><td>w/o D1</td><td>33.22</td><td>796.67</td></tr><tr><td>w/o Dv</td><td>33.84</td><td>867.43</td></tr><tr><td>Full-128</td><td>32.36</td><td>838.09</td></tr><tr><td>Full-256</td><td>33.95</td><td>700.00</td></tr></table>
+
+Table 5: Ablation study on (FFHQ, VoxCeleb).   
+
+<table><tr><td>Method</td><td>w/o Lcontr</td><td>w/o Lm</td><td>Full</td></tr><tr><td>ACD (↓)</td><td>0.5328</td><td>0.5158</td><td>0.4353</td></tr><tr><td>Method</td><td></td><td>Human Preference (%)</td><td></td></tr><tr><td>Full vs w/o Lcontr Full vs w/o Lm</td><td></td><td>68.3 / 31.7 64.4 / 35.6</td><td></td></tr></table>
+
+# 4.4 LONG SEQUENCE GENERATION
+
+Due to the limitation of computational resources, we train MoCoGAN-HD to synthesize 16 consecutive frames. However, we can generate longer video sequences during inference by applying the following two ways.
+
+Motion Generator Unrolling. For motion generator, we can run the LSTM decoder for more steps to synthesize long video sequences. In Fig. 7, we show a synthesized video example of 64 frames using the model trained on the FaceForensics dataset. Our method is capable to synthesize videos with more frames than the number of frames used for training.
+
+![](images/eb58dda6e71eb8437862ac9901d8339ddc7f246564f649044df7a6980983a46f.jpg)  
+Figure 7: The generation of a 64-frame video using a model trained with 16-frame on FaceForensics.
+
+Motion Interpolation. We can do interpolation on the motion trajectory directly to synthesize long videos. Fig. 8 shows an interpolation example of 32-frame on (AFHQ-Dog, VoxCeleb) dataset.
+
+![](images/516b6dbf38791c9a04fa97dffd0f9fd5c0d80ee72907af4bbb938ef7aa66bd6c.jpg)  
+Figure 8: The generation of a 32-frame video on (AFHQ-Dog, VoxCeleb) by doing the interpolation on motion trajectory.
+
+# 5 CONCLUSION
+
+In this work, we present a novel approach to video synthesis. Building on contemporary advances in image synthesis, we show that a good image generator and our framework are essential ingredients to boost video synthesis fidelity and resolution. The key is to find a meaningful trajectory in the image generator’s latent space. This is achieved using the proposed motion generator, which produces a sequence of motion residuals, with the contrastive image discriminator and video discriminator. This disentangled representation further extends applications of video synthesis to content and motion manipulation and cross-domain video synthesis. The framework achieves superior results on a variety of benchmarks and reaches resolutions unattainable by prior state-of-the-art techniques.
+
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+# A ADDITIONAL DETAILS FOR THE FRAMEWORK
+
+# A.1 ADDITIONAL DETAILS FOR THE MOTION GENERATOR
+
+To use StyleGAN2 (Karras et al., 2020b) as the image generator, we randomly sample $1 , 0 0 0 , 0 0 0$ latent codes from the input space $\mathcal { Z }$ and send them to the 8-layer MLPs to get the latent codes in the space of $\mathcal { W }$ . Each latent code is a 512-dimension vector. We perform PCA on these 1, 000, 000 latent codes and select the top 384 principal components to form the matrix $\mathbf { V } \in \mathbb { R } ^ { 3 8 4 \times 5 1 2 }$ , which is used to model the motion residuals in Eqn. 2. The LSTM encoder and the LSTM decoder in the motion generator both have an input size of 512 and a hidden size of 384. The noise vector $\epsilon _ { t }$ in Eqn. 1 is also a 512-dimension vector, and the network $H$ in Eqn. 3 is a 2-layer MLPs with 512 hidden units in each of the two fully-connected layers.
+
+For BigGAN (Brock et al., 2019), we sample the latent code directly from the space of $\mathcal { Z }$
+
+A.2 ADDITIONAL DETAILS FOR THE DISCRIMINATORS
+
+# A.2.1 VIDEO DISCRIMINATOR
+
+The input images for the video discriminator $D _ { \mathrm { { V } } }$ are processed at two scales. We downsample the output images from the image generator to the resolution of $1 2 8 \times 1 2 8$ and $6 4 \times 6 4$ . For indomain video synthesis, the input sequences for $D _ { \mathrm { { V } } }$ have the shape of $6 \times ( n - 1 ) \times 1 2 8 \times 1 2 8$ and $6 \times ( n - 1 ) \times \mathbf { \bar { 6 4 } } \times 6 4$ , where $n$ is the sequence length used for training. For each of the $( n - 1 )$ subsequent frames, we concatenate the RGB channels of both the first frame and that subsequent frame, resulting in a 6-channel input. For cross-domain video synthesis, the input sequences for $D _ { \mathrm { { V } } }$ have the shape of $3 \times n \times 1 2 8 \times 1 2 8$ and $3 \times n \times 6 4 \times 6 4$ , as the concatenation of the first frame will make the discriminator aware the domain gaps. Details for $D _ { \mathrm { { V } } }$ are shown in Tab. 6.
+
+Table 6: The network architecture for video discriminator.   
+
+<table><tr><td>Operation</td><td>Kernel</td><td>Strides</td><td># Channels</td><td>Norm Type</td><td>Nonlinearity</td></tr><tr><td>Conv3d</td><td>4×4</td><td>2</td><td>64</td><td></td><td>Leaky ReLU (0.2)</td></tr><tr><td>Conv3d</td><td>4×4</td><td>2</td><td>128</td><td>InstanceNorm3d</td><td>Leaky ReLU (0.2)</td></tr><tr><td>Conv3d</td><td>4×4</td><td>2</td><td>256</td><td>InstanceNorm3d</td><td>Leaky ReLU (0.2)</td></tr><tr><td>Conv3d</td><td>4×4</td><td>1</td><td>512</td><td>InstanceNorm3d</td><td>Leaky ReLU (0.2)</td></tr><tr><td>Conv3d</td><td>4×4</td><td>1</td><td>1</td><td>=</td><td>=</td></tr></table>
+
+# A.2.2 IMAGE DISCRIMINATOR
+
+The image discriminator $D _ { \mathrm { I } }$ has an architecture based on that of the $\mathrm { B i g G A N }$ discriminator, except that we remove the self-attention layer. The feature extractor $F$ used for contrastive learning has the same architecture as $D _ { \mathrm { I } }$ , except that it does not include the last layer of $D _ { \mathrm { I } }$ but has two additional fully connected (FC) layers as the projection head. The number of hidden units for these two FC layers are both 256.
+
+Here we describe in more detail the image augmentation and memory bank techniques used for conducting contrastive learning.
+
+Image Augmentation. We perform data augmentation on images to create positive and negative pairs. We normalize the images to $[ - 1 , 1 ]$ and apply the following augmentation techniques.
+
+• Affine. We augment each image with an affine transformation defined with three random parameters: rotation $\alpha _ { r } \in \mathcal { U } ( \bar { - } 1 8 0 , 1 8 0 )$ , translation $\alpha _ { t } \in \mathcal { U } ( - 0 . 1 , 0 . 1 )$ , and scale $\alpha _ { s } \in$ $\mathcal { U } ( 0 . 9 5 , 1 . 0 5 )$ .   
+• Brightness. We add a random value $\alpha _ { b } \sim \mathcal { U } ( - 0 . 5 , 0 . 5 )$ to all channels of each image.   
+• Color. We add a random value $\alpha _ { c } \sim \mathcal { U } ( - 0 . 5 , 0 . 5 )$ to one randomly-selected channel of each image.
+
+• Cutout (DeVries & Taylor, 2017). We mask out pixels in a random subregion of each image to 0. Each subregion starts at a random point and with size $( \alpha _ { m } H , \alpha _ { m } W )$ , where $\alpha _ { m } \sim \mathcal { U } ( 0 , 0 . 2 5 )$ and $( H , W )$ is the image resolution.
+
+• Flipping. We horizontally flip the image with the probability of 0.5.
+
+Memory Bank. It has been shown that contrastive learning benefits from large batch-sizes and negative pairs (Chen et al., 2020b). To increase the number of negative pairs, we incorporate the memory mechanism from MoCo (He et al., 2020), which designates a memory bank to store negative examples. More specifically, we keep an exponential moving average of the image discriminator, and its output of fake video frames are buffered as negative examples. We use a memory bank with a dictionary size of 4, 096.
+
+# B MORE DETAILS FOR EXPERIMENTS
+
+Image Generators. We train the unconditional StyleGAN2 models from scratch on the UCF-101, FaceForensics, Sky Time-lapse, and AFHQ-Dog datasets. We train the image generators with the official Tensorflow code2 and select the checkpoints that obtain the best Fr´echet inception distance (FID) (Heusel et al., 2017) score to be used as the image generators. The FID score of each image generator is shown in Table 7. For FFHQ, AnimeFaces, and LSUN-Church, we simply use the released pre-trained models.
+
+We also train an unconditional BigGAN model on the FFHQ dataset using the public PyTorch code3.   
+We train a model with resolution $1 2 8 \times 1 2 8$ and select the last checkpoint as the image generator.
+
+Table 7: FID of our trained StyleGAN2 models on different datasets.   
+
+<table><tr><td></td><td>UCF-101</td><td>FaceForensics</td><td>Sky Time-lapse</td><td>AFHQ-Dog</td></tr><tr><td>FID</td><td>45.63</td><td>10.99</td><td>10.80</td><td>7.85</td></tr></table>
+
+Training Time. We train each image generator for UCF-101, FaceForensics, Sky Time-lapse, and AFHQ-Dog in less than 2 days using 8 Tesla V100 GPUs. For FFHQ, AnimeFaces, and LSUNChurch, we use the released models with no training cost. The training time for video generators ranges from $1 . 5 \sim 3$ days depending on the datasets (Due to the memory issue, the training for generating videos with resolution of $1 , 0 2 4 \times 1 , 0 2 4$ was done on 8 Quadro RTX 8000, with 5 days). The total training time for all the datasets is $1 . 5 \sim 5$ days and the estimated cost for training on Google Cloud is $\$ 0.78 \sim \ S 2.3 K$ .
+
+Implementation Details. We implement our experiments with PyTorch 1.3.1 and also tested them with PyTorch 1.6. We use the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 0.0001 for $G _ { \mathrm { M } }$ , $D _ { \mathrm { { V } } }$ , and $D _ { \mathrm { I } }$ in all experiments. In Eqn. 2, we set $\lambda = 0 . 5$ for conventional video generation tasks and use a smaller $\lambda = 0 . 2$ for cross-domain video generation, as it improves the content consistency. In Eqn. 7, we set $\lambda _ { \mathrm { m } } = \lambda _ { \mathrm { c o n t r } } = \lambda _ { \mathrm { f } } = 1$ . Grid searching on these hyper-parameters could potentially lead to a performance boost. For TGANv2, we use the released code4 to train the models on UCF-101 and FaceForensics using 8 Tesla V100 with 16GB of GPU memory.
+
+Video Prediction. For video prediction, we predict consecutive frames, given the first frame $\mathbf { x }$ from a test video clip as the input. We find the inverse latent code $\hat { \bf z } _ { 1 }$ for $\mathbf { x } _ { 1 }$ by minimizing the following objective:
+
+$$
+\hat { \mathbf { z } } _ { 1 } = \underset { \hat { \mathbf { z } } _ { 1 } } { \arg \operatorname* { m i n } } \left\| \mathbf { x } _ { 1 } - G _ { \mathrm { I } } ( \hat { \mathbf { z } } _ { 1 } ) \right\| _ { 2 } + \lambda _ { \mathrm { v g g } } \left\| F _ { \mathrm { v g g } } ( \mathbf { x } _ { 1 } ) - F _ { \mathrm { v g g } } ( G _ { \mathrm { I } } ( \hat { \mathbf { z } } _ { 1 } ) ) \right\| _ { 2 } ,
+$$
+
+where $\lambda _ { \mathrm { v g g } }$ is the weight for perceptual loss (Johnson et al., 2016), $F _ { \mathrm { v g g } }$ is the VGG feature extraction model (Simonyan $\&$ Zisserman, 2014). We set $\lambda _ { \mathrm { v g g } } = 1$ and optimize Eqn. 8 for $2 0 , 0 0 0$ iterations. We take $\hat { \mathbf { z } } _ { 1 }$ as the input to our model for video prediction.
+
+AMT Experiments. We present more details on the AMT experiments for different experimental settings and datasets. For each experiment, we run 5 iterations to get the averaged score.
+
+• FaceForensics, Ours vs TGANv2. We randomly select 300 videos from each method and ask users to select the better one from a pair of videos. • Sky Time-lapse, Ours vs DTVNet. We compare our method with DTVNet on the video prediction task. The testing set of Sky Time-lapse dataset includes 2, 815 short video clips. Considering that many of these video clips share similar content and are sampled from 148 long videos, we select 148 short videos with different content for testing. For these videos, we perform inversion (Eqn. 8) on the first frame to get the latent code and generate videos. For DTVNet, we use the first frame directly as input to produce their results. We ask users to chose the one with better video quality from a pair of videos generated by our method and DTVNet. The results shown in Tab. 8 demonstrate the clear advantage of our approach.
+
+Table 8: Human evaluation experiments on Sky Time-lapse dataset.   
+
+<table><tr><td>Method</td><td>Human Preference (%)</td></tr><tr><td>Ours /DTVNet</td><td>77.3 / 22.7</td></tr></table>
+
+• FFHQ, Full vs w/o ${ \mathcal { L } } _ { \mathrm { c o n t r } }$ . We randomly sample 200 videos generated by each method and ask users to select the more realistic one from a pair of videos.
+
+• FFHQ, Full vs w/o ${ \mathcal { L } } _ { \mathrm { m } }$ . For each method, we use the same content code $\mathbf { z } _ { 1 }$ to generate 9 videos with different motion trajectories, and organize them into a $3 \times 3$ grid. To conduct AMT experiments, we randomly generate $5 0 3 \times 3$ videos for each method and ask users to choose the one with higher motion diversity from a pair of videos.
+
+Cross-Domain Video Generation. We provide more details on the image and video datasets.
+
+• Image Datasets:
+
+– FFHQ (Karras et al., 2019) consists of 70, 000 high-quality face images at $1 0 2 4 \times 1 0 2 4$ resolution with considerable variation in terms of age, ethnicity, and background.   
+– AFHQ-Dog (Choi et al., 2020) contains 5, 239 high-quality dog images at $5 1 2 \times 5 1 2$ resolution with both training and testing sets.   
+– AnimeFaces (Branwen, 2019) includes 2, 232, 462 anime face images at $5 1 2 \times 5 1 2$ resolution.   
+– LSUN-Church (Yu et al., 2015) includes 126, 227 in-the-wild church images at $2 5 6 \times$ 256 resolution.
+
+• Video Datasets:
+
+– VoxCeleb (Nagrani et al., 2020) consists of 22, 496 short clips of human speech, extracted from interview videos uploaded to YouTube.   
+– TLVDB (Shih et al., 2013) includes 463 time-lapse videos, covering a wide range of landscapes and cityscapes.
+
+For the video datasets, we randomly select 32 consecutive frames from training videos and select every other frame to form a 16-frame sequence for training.
+
+# C MORE VIDEO RESULTS
+
+In this section, we provide more qualitative video results generated by our approach. We show the thumbnail from each video in the figures. Full resolution videos are in the supplementary material. We also provide an HTML page to visualize these videos.
+
+UCF-101. In Fig. 9, we show videos generated by our approach on the UCF-101 dataset.
+
+FaceForensics. In Fig. 10, we show the generated videos for FaceForensics. In Fig. 11 and Fig. 12, we show that our approach can generate long consecutive results, 32 and 64 frames respectively, even when trained with 16-frame clips. In Fig. 13, we demonstrate that our approach can generate diverse motion patterns using the same content code. In Fig. 14, we apply the same motion codes with different content to get the synthesized videos.
+
+Sky Time-lapse. Fig. 15 shows the generated videos for the Sky Time-lapse dataset.
+
+(FFHQ, VoxCeleb). Fig. 16, Fig. 17, and Fig. 18 present the generated videos that have motion patterns from VoxCeleb and content from FFHQ, with resolutions of $1 2 8 \times 1 2 8$ , $2 5 6 \times 2 5 6$ , and $1 0 2 4 \times 1 0 2 4$ , respectively. We use BigGAN as the generator for Fig. 16 and StyleGAN2 for Fig. 17 and Fig. 18.
+
+(AFHQ-Dog, VoxCeleb). Fig. 19 presents the generated videos that have motion patterns from VoxCeleb and content from AFHQ-Dog. The videos have a resolution of $5 1 2 \times 5 1 2$ . In Fig. 20, we show the interpolation between every two frames to get longer sequences.
+
+(AnimeFaces, VoxCeleb). Fig. 21 shows the generated videos that have motion patterns from VoxCeleb and content from AmimeFaces. The videos have a resolution of $5 1 2 \times 5 1 2$ .
+
+(LSUN-Church, TLVDB). Fig. 22 presents the generated videos that have time-lapse changing style from TLVDB and content from LSUN-Church.
+
+![](images/656422d8a2df210e3146707dcdb12fde3649bcd3fcf93f62ecdf145702a17967.jpg)  
+Figure 9: Example videos generated by our approach on the UCF-101 dataset.
+
+![](images/c5ff5419633d0644e0e341a7d75db48338d2b5671868858be71bd04e7c6153c9.jpg)  
+Figure 10: Example videos generated by our approach on the FaceForensics dataset.
+
+![](images/761d1c674d9ee743520b4d034eacf7d8346b26568f13046f11ddbba719fa7f2f.jpg)  
+Figure 11: The generated videos on the FaceForensics dataset consisting of 32 frames.
+
+![](images/4ad635a60c3aa8237ade234971f9517c9b4f08c1ac26fe96e7b8da092a2e4e05.jpg)  
+Figure 12: The generated videos on the FaceForensics dataset consisting of 64 frames.
+
+![](images/ad012a7a8f176597f32f4e1311158d969b6df2f4076ace43e878320dae39797c.jpg)  
+Figure 13: Each row is synthesized using the same content code to generate diverse motion patterns. Please see the corresponding supplementary video for a better illustration.
+
+![](images/4003a2aba6d19b3fe338880c8b3e5c746593f5f9594f7bc953b40b71f3a38c3c.jpg)  
+Figure 14: Each row is synthesized with the same motion trajectory but different content codes. Please see the corresponding supplementary video for a better illustration.
+
+![](images/b09b8b7b2442b49f813aef812bf5318c58277beb10c2652b3353bffd59871d25.jpg)  
+Figure 15: Example videos generated by our approach on the Sky Time-lapse dataset. The videos have a resolution of $1 2 8 \times 1 2 8$ .
+
+![](images/4c1fdaa7a976b8b57c81778061255328995263d4c5ebb109c4052315586de727.jpg)  
+Figure 16: Cross-domain video generation for (FFHQ, Vox). The videos have a resolution of $1 2 8 \times 1 2 8$ .
+
+![](images/56cc49b5a03b5c0cbe43a035e35986744b62a7d970b623473e8d5733feee46b7.jpg)  
+Figure 17: Cross-domain video generation for (FFHQ, Vox). The videos have a resolution of $2 5 6 \times 2 5 6$ .
+
+![](images/183d0acfc91549f201c5ccdfaeca4ec1e9c5528883c01ff6f7b227665552e808.jpg)  
+Figure 18: Cross-domain video generation for (FFHQ, Vox). The videos have a resolution of $1 0 2 4 \times 1 0 2 4$ .
+
+![](images/fe517c17c7bcd4684ef59d85cc5e690d7dbd7a3e30efb2733313cb7f8d5680ac.jpg)  
+Figure 19: Cross-domain video generation for (AFHQ-Dog, Vox). The videos have a resolution of $5 1 2 \times 5 1 2$ .
+
+![](images/7b9c9e6c87fcefbc321f30d0b5fe95a91ed52cda550800332e0721ca28cdd274.jpg)  
+Figure 20: Cross-domain video generation for (AFHQ-Dog, Vox). We interpolate every two frames to get 32 sequential frames. The videos have a resolution of $5 1 2 \times 5 1 2$ .
+
+![](images/407cf308e90a25e7054af47caa2195e530ebe7e2c0eadad7146c7c49c8fcb5ff.jpg)  
+Figure 21: Cross-domain video generation for (AnimeFaces, Vox). The videos have a resolution of $5 1 2 \times 5 1 2$ .
+
+![](images/e8e559630390e3cf2b0fa67b36c8a27d2dd8d927cedb590947e66c71c6b98aae.jpg)  
+Figure 22: Cross-domain video generation for (LSUN-Church, TLVDB). The videos have a resolution of $2 5 6 \times 2 5 6$ .
+
+# D MORE ABLATION ANALYSIS FOR MUTUAL INFORMATION LOSS ${ \mathcal { L } } _ { \mathrm { m } }$
+
+In addition to Tab. 5, we perform another ablation experiment to show how mutual information loss ${ \mathcal { L } } _ { \mathrm { m } }$ improves motion diversity by considering the following setting. We random sample a content code $z _ { 1 } \in { \mathcal { Z } }$ and use it as an input to synthesize 100 videos, where each video contains 16 frames. We average the generated 100 videos (they share the same first frame) to get one meanvideo, which contains 16 frames. For example, for the last frame in the mean-video, it is obtained by averaging all the last frames from the 100 generated videos. We also calculate the per-pixel standard deviation (std) for each averaged frame in the mean-video. More blurry frames and higher per-pixel std indicate the 100 synthetic videos contain more diverse motion.
+
+We evaluate the settings of $F u l l$ and w/o ${ \mathcal { L } } _ { \mathrm { m } }$ (without using the mutual information loss) by running the above experiments for 50 times, e.g., sampling $z _ { 1 }$ for 50 times. Across the 50 trials, for Full model, the mean and std of the per-pixel std for the $1 6 ^ { t h }$ frame (the last frame in a generated video) is $0 . 2 3 3 \pm 0 . 0 3 6$ , which is significantly higher than that of the w/o ${ \mathcal { L } } _ { \mathrm { m } }$ model $( 0 . 1 2 6 \pm 0 . 0 2 5 )$ . In Fig. 23, we show 8 examples of the last frame from the mean-video and the images with per-pixel std (See supplementary material for the whole videos). Our Full model has more diverse motion as the averaged frame is more blurry and the per-pixel std is higher. Note that StyleGAN2 enables noise inputs for extra randomness, we disable it in this ablation study.
+
+![](images/51c0580023dc8299a096d24d1d17147ffce9571574f91afc09ee116a73dc2d59.jpg)  
+Figure 23: Row 1 and 3: The last frame of the mean-video and per-pixel std of w/o ${ \mathcal { L } } _ { \mathrm { m } }$ model. Row 2 and 4: The last frame of the mean-video and per-pixel std of the Full model. The Full model has a more blurry mean-video and higher per-pixel std, which indicates more diverse motion.
+
+# E LIMITATIONS
+
+Our framework requires a well-trained image generator for frame synthesis. In order to synthesize high-quality and temporally coherent videos, an ideal image generator should satisfy two requirements: R1. The image generator should synthesize high-quality images, otherwise the video discriminator can easily tell the generated videos as the image quality is different from the real videos. R2. The image generator should be able to generate diverse image contents to include enough motion modes for sequence modeling.
+
+Example of R1. UCF-101 is a challenging dataset even for the training of an image generator. In Tab. 7, the StyleGAN2 model trained on UCF-101 has FID 45.63, which is much worse than the others. We hypothesis the reason is that UCF-101 dataset has many categories, but within each category, it includes relatively a small amount of videos and these videos share very similar content. Such observation is also discussed in DVDGAN (Clark et al., 2019). Although we can achieve state-of-the-art performance on UCF-101 dataset, the quality of the generated videos is not as good as other datasets (Fig. 9), and the quality of synthesized videos is still not close to real videos.
+
+Example of R2. We test our method on BAIR Robot Pushing Dataset (Ebert et al., 2017). We train a $6 4 \times 6 4$ StyleGAN2 image generator with using the frames from BAIR videos. The image generator has FID as 6.12. Based on the image generator, we train a video generation model that can synthesize 16 frames. An example of synthesized video is shown in Fig. 24 (more videos are in the supplementary materials). We can see our method can successfully model shadow changing, the robot arm moving, but it struggles to decouple the robot arm from some small objects in the background, which we show analysis follows.
+
+![](images/e0a325556e98c9afa069fb37200cb4337e35330e735c2c25f0a85677a8bc04eb.jpg)  
+Figure 24: A synthesized video using BAIR dataset. Note the background changing of the first frame (upper-left) and the last frame (bottom-right).
+
+# E.1 ANALYSIS OF THE INFORMATION CONTAINED IN PCA COMPONENTS.
+
+Inspired by previous work (Hark ¨ onen et al., 2020), we further investigate the latent space of the ¨ image generator by considering the information contained in each PCA component. Fig. 25 shows the percentage of total variance captured by top PCA components. The image generator on BAIR compresses most of the information on a few components. Specially, the top $2 0 \mathrm { P C A }$ components captures $8 5 \%$ of the variance. In contrast, the latent space of the image generator trained on FFHQ (and FFHQ 1024 for high-resolution image synthesis) uses $1 0 0 ~ \mathrm { P C A }$ components to capture $8 5 \%$ information. This implies the BAIR generator models the dataset in a low-dimension space, and such generator increases the difficulty for fully disentangling all the objects in images for manipulation.
+
+![](images/713dfec61ead66f47ab290bc97279a7013cf407f42be55df1cb69d2350749654.jpg)  
+Figure 25: Percentage of variations captured by top PCA components on different models.
+
+Moreover, we visualize the video synthesis results by moving along the top $2 0 ~ \mathrm { P C A }$ components. Let $V _ { i }$ denote the $i ^ { t h }$ PCA component. Given content code $z _ { 1 }$ , we synthesize a 5-frame video clip by using the following sequence as input: $\left\{ z _ { 1 } - 2 V _ { i } , z _ { 1 } - V _ { i } , z _ { 1 } , z _ { 1 } + V _ { i } , z _ { 1 } + 2 V _ { i } \right\}$ . In Fig. 26, we show the video synthesis results by moving along the top $2 0 ~ \mathrm { P C A }$ directions. It can be seen that: 1) changing the later components (the $8 ^ { t h }$ and later rows) of BAIR only make small changes; 2) the first 7 components of BAIR have entangled semantic meaning, while the components in FFHQ have more disentangled meaning ( $2 ^ { n d }$ row, rotation; $2 0 ^ { t h }$ row, smile). This indicates the image generator of BAIR may not cover enough (disentangled) motion modes, and it might be hard for the motion generator to fully disentangle all the contents and motion with only a few dominating PCA components, while for the image generator trained on FFHQ, it is much easier for disentangling foreground and background.
+
+![](images/621309b8d0cfc18d02ea6eb4d0907fd0b2ba1236fa9d88914060e90d5d238210.jpg)  
+Figure 26: Visualization of top 20 principle components of BAIR (left) and FFHQ (right).
+
+![](images/16867bbe72a5c0478477b3900f51e5bedb8d081ccc14e71cbb70cf69c80d4340.jpg)

parse/train/BJxh2j0qYm/BJxh2j0qYm_content_list.json

@@ -0,0 +1,1516 @@
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+    {
+        "type": "text",
+        "text": "Dynamic Channel Pruning: Feature Boosting and Suppression ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Xitong Gao $\\bot$ ∗, Yiren Zhao $^ 2$ ∗, Lukasz Dudziak $^ 3$ , Robert Mullins4, Cheng-zhong $\\mathbf { X u } ^ { \\mathrm { 5 } }$ ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Shenzhen Institutes of Advanced Technology, Shenzhen, China   \n2,3,4 University of Cambridge, Cambridge, UK   \n5 University of Macau, Macau, China   \n1 xt.gao@siat.ac.cn, 2 yaz21@cam.ac.uk ",
+        "bbox": [
+            184,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Making deep convolutional neural networks more accurate typically comes at the cost of increased computational and memory resources. In this paper, we reduce this cost by exploiting the fact that the importance of features computed by convolutional layers is highly input-dependent, and propose feature boosting and suppression (FBS), a new method to predictively amplify salient convolutional channels and skip unimportant ones at run-time. FBS introduces small auxiliary connections to existing convolutional layers. In contrast to channel pruning methods which permanently remove channels, it preserves the full network structures and accelerates convolution by dynamically skipping unimportant input and output channels. FBS-augmented networks are trained with conventional stochastic gradient descent, making it readily available for many state-of-the-art CNNs. We compare FBS to a range of existing channel pruning and dynamic execution schemes and demonstrate large improvements on ImageNet classification. Experiments show that FBS can respectively provide $5 \\times$ and $2 \\times$ savings in compute on VGG-16 and ResNet-18, both with less than $0 . 6 \\%$ top-5 accuracy loss. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+            588
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "State-of-the-art vision and image-based tasks such as image classification (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; He et al., 2016), object detection (Ren et al., 2017; Huang et al., 2017) and segmentation (Long et al., 2015) are all built upon deep convolutional neural networks (CNNs). While CNN architectures have evolved to become more efficient, the general trend has been to use larger models with greater memory utilization, bandwidth and compute requirements to achieve higher accuracy. The formidable amount of computational resources used by CNNs present a great challenge in the deployment of CNNs in both cost-sensitive cloud services and low-powered edge computing applications. ",
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+    {
+        "type": "text",
+        "text": "One common approach to reduce the memory, bandwidth and compute costs is to prune over-parameterized CNNs. If performed in a coarse-grain manner this approach is known as channel pruning (Ye et al., 2018; He et al., 2017; Liu et al., 2017; Wen et al., 2016). Channel pruning evaluates channel saliency measures and removes all input and output connections from unimportant channels— generating a smaller dense model. A saliency-based pruning method, however, has threefold disadvantages. Firstly, by removing channels, the capabilities of CNNs are permanently lost, and the resulting CNN may never regain its accuracy for difficult inputs for which the removed channels were responsible. Secondly, despite the fact that channel pruning may drastically shrink model size, without careful design, computational resources cannot be effectively reduced in a CNN without a detrimental impact on its accuracy. Finally, the saliency of a neuron is not static, which can be illustrated by the feature visualization in Figure 1. Here, a CNN is shown a set of input images, certain channel neurons in a convolutional output may get highly excited, whereas another set of images elicit little response from the same channels. This is in line with our understanding of CNNs that neurons in a convolutional layer specialize in recognizing distinct features, and the relative importance of a neuron depends heavily on the inputs. ",
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+    {
+        "type": "text",
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+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The above shortcomings prompt the question: why should we prune by static importance, if the importance is highly input-dependent? Surely, a more promising alternative is to prune dynamically depending on the current input. A dynamic channel pruning strategy allows the network to learn to prioritize certain convolutional channels and ignore irrelevant ones. Instead of simply reducing model size at the cost of accuracy with pruning, we can accelerate convolution by selectively computing only a subset of channels predicted to be important at run-time, while considering the sparse input from the preceding convolution layer. In effect, the amount of cached activations and the number of read, write and arithmetic operations used by a well-designed dynamic model can be almost identical to an equivalently sparse statically pruned one. In addition to saving computational resources, a dynamic model preserves all neurons of the full model, which minimizes the impact on task accuracy. ",
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose feature boosting and suppression (FBS) to dynamically amplify and suppress output channels computed by the convolutional layer. Intuitively, we can imagine that the flow of information of each output channel can be amplified or restricted under the control of a “valve”. This allows salient information to flow freely while we stop all information from unimportant channels and skip their computation. Unlike pruning statically, the valves use features from the previous layer to predict the saliency of output channels. With conventional stochastic gradient descent (SGD) methods, the predictor can learn to adapt itself by observing the input and output features of the convolution operation. ",
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+    {
+        "type": "text",
+        "text": "FBS introduces tiny auxiliary connections to existing convolutional layers. The minimal overhead added to the existing model is thus negligible when compared to the potential speed up provided by the dynamic sparsity. Existing dynamic computation strategies in CNNs (Lin et al., 2017; Odena et al., 2017; Bolukbasi et al., 2017) produce on/off pruning decisions or execution path selections. Training them thus often resorts to reinforcement learning, which in practice is often computationally expensive. Even though FBS similarly use non-differentiable functions, contrary to these methods, the unified losses are still wellminimized with conventional SGD. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We apply FBS to a custom CIFAR-10 (Krizhevsky et al., 2014) classifier and popular CNN models such as VGG-16 (Simonyan & Zisserman, 2015) and ResNet-18 (He et al., 2016) trained on the ImageNet dataset (Deng et al., 2009). Empirical results show that under the same speed-ups, FBS can produce models with validation accuracies surpassing all other channel pruning and dynamic conditional execution methods examined in the paper. ",
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+    {
+        "type": "image",
+        "img_path": "images/ec163895e99a91029cb698a9a91ed95b476b1369b23dfb25f76e0587a202b687.jpg",
+        "image_caption": [
+            "Figure 1: When images from the ImageNet validation dataset are shown to a pre-trained ResNet-18 (He et al., 2016), the outputs from certain channel neurons may vary drastically. The top rows in (a) and (b) are found respectively to greatly excite neurons in channels 114 and 181 of layer block 3b/conv2, whereas the bottom images elicit little activation from the same channel neurons. The number below each image indicate the maximum values observed in the channel before adding the shortcut and activation. Finally, (c) shows the distribution of maximum activations observed in the first 20 channels. "
+        ],
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+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "2.1 Structured Sparsity ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since LeCun et al. (1990) introduced optimal brain damage, the idea of creating more compact and efficient CNNs by removing connections or neurons has received significant attention. Early literature on pruning deep CNNs zero out individual weight parameters (Hassibi et al., 1994; Guo et al., 2016). This results in highly irregular sparse connections, which were notoriously difficult for GPUs to exploit. This has prompted custom accelerator solutions that exploit sparse weights (Parashar et al., 2017; Han et al., 2016). Although supporting both sparse and dense convolutions efficiently normally involves some compromises in terms of efficiency or performance. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Alternatively, recent work has thus increasingly focused on introducing structured sparsity (Wen et al., 2016; Ye et al., 2018; Alvarez & Salzmann, 2016; Zhou et al., 2016), which can be exploited by GPUs and allows custom accelerators to focus solely on efficient dense operations. Wen et al. (2016) added group Lasso on channel weights to the model’s training loss function. This has the effect of reducing the magnitude of channel weights to diminish during training, and remove connections from zeroed-out channels. To facilitate this process, Alvarez & Salzmann (2016) additionally used proximal gradient descent, while Li et al. (2017) and He et al. (2018a) proposed to prune channels by thresholds, i.e. they set unimportant channels to zero, and fine-tune the resulting CNN. The objective to induce sparsity in groups of weights may present difficulties for gradient-based methods, given the large number of weights that need to be optimized. A common approach to overcome this is to solve (He et al., 2017) or learn (Liu et al., 2017; Ye et al., 2018) channel saliencies to drive the sparsification of CNNs. He et al. (2017) solved an optimization problem which limits the number of active convolutional channels while minimizing the reconstruction error on the convolutional output. Liu et al. (2017) used Lasso regularization on channel saliencies to induce sparsity and prune channels with a global threshold. Ye et al. (2018) learned to sparsify CNNs with an iterative shrinkage/thresholding algorithm applied to the scaling factors in batch normalization. There are methods (Luo et al., 2017; Zhuang et al., 2018) that use greedy algorithms for channel selection. Huang et al. (2018) and He et al. (2018b) adopted reinforcement learning to train agents to produce channel pruning decisions. PerforatedCNNs, proposed by Figurnov et al. (2016), use predefined masks that are model-agnostic to skip the output pixels in convolutional layers. ",
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+    {
+        "type": "text",
+        "text": "2.2 Dynamic Execution ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In a pruned model produced by structured sparsity methods, the capabilities of the pruned neurons and connections are permanently lost. Therefore, many propose to use dynamic networks as an alternative to structured sparsity. During inference, a dynamic network can use the input data to choose parts of the network to evaluate. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Convolutional layers are usually spatially sparse, i.e. their activation outputs may contain only small patches of salient regions. A number of recent publications exploit this for acceleration. Dong et al. (2017) introduced low-cost collaborative layers which induce spatial sparsity in cheap convolutions, so that the main expensive ones can use the same sparsity information. Figurnov et al. (2017) proposed spatially adaptive computation time for residual networks (He et al., 2016), which learns the number of residual blocks required to compute a certain spatial location. Almahairi et al. (2016) presented dynamic capacity networks, which use the gradient of a coarse output’s entropy to select salient locations in the input image for refinement. Ren et al. (2018) assumed the availability of $a$ priori spatial sparsity in the input image, and accelerated the convolutional layer by computing non-sparse regions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "There are dynamic networks that make binary decisions or multiple choices for the inference paths taken. BlockDrop, proposed by Wu et al. (2018), trains a policy network to skip blocks in residual networks. Liu & Deng (2018) proposed conditional branches in deep neural networks (DNNs), and used Q-learning to train the branching policies. Odena et al. (2017) designed a DNN with layers containing multiple modules, and decided which module to use with a recurrent neural network (RNN). Lin et al. (2017) learned an RNN to adaptively prune channels in convolutional layers. The on/off decisions commonly used in these networks cannot be represented by differentiable functions, hence the gradients are not well-defined. Consequently, the dynamic networks above train their policy functions by reinforcement learning. There exist, however, methods that workaround such limitations. Shazeer et al. (2017) introduced sparsely-gated mixture-of-experts and used a noisy ranking on the backpropagate-able gating networks to select the expensive experts to evaluate. Bolukbasi et al. (2017) trained differentiable policy functions to implement early exits in a DNN. Hua et al. (2018) learned binary policies that decide whether partial or all input channels are used for convolution, but approximate the gradients of the non-differentiable policy functions with continuous ones. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "3 Feature Boosting and Suppression ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We start with a high-level illustration (Figure 2) of how FBS accelerates a convolutional layer with batch normalization (BN). The auxiliary components (in red) predict the importance of each output channel based on the input features, and amplify the output features accordingly. Moreover, certain output channels are predicted to be entirely suppressed (or zero-valued as represented by $\\varTheta$ ), such output sparsity information can advise the convolution operation to skip the computation of these channels, as indicated by the dashed arrow. It is notable that the expensive convolution can be doubly accelerated by skipping the inactive channels from both the input features and the predicted output channel saliencies. The rest of this section provides detailed explanation of the components in Figure 2. ",
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+        "img_path": "images/00841c99e6441664d8e5cf5e76ee9ffd57468d400db2d18166279b67b9b3218e.jpg",
+        "image_caption": [
+            "Figure 2: A high level view of a convolutional layer with FBS. By way of illustration, we use the $l ^ { \\mathrm { t h } }$ layer with 8-channel input and output features, where channels are colored to indicate different saliencies, and the white blocks $( \\boxed { \\mathcal { Q } } )$ represent all-zero channels. "
+        ],
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+    {
+        "type": "text",
+        "text": "3.1 Preliminaries ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "For simplicity, we consider a deep sequential batch-normalized (Ioffe & Szegedy, 2015) CNN with $L$ convolutional layers, i.e ${ \\bf \\therefore } \\ { \\bf x } _ { L } = F ( { \\bf x } _ { 0 } ) = f _ { L } \\left( \\cdot \\cdot \\cdot f _ { 2 } ( f _ { 1 } ( { \\bf x } _ { 0 } ) \\right) \\cdot \\cdot \\cdot { \\bf \\cdot } ) $ , where the $l ^ { \\mathrm { t h } }$ layer $f _ { l } : \\mathbb { R } ^ { C _ { l - 1 } \\times H _ { l - 1 } \\times W _ { l - 1 } } \\to \\mathbb { R } ^ { C _ { l } \\times H _ { l } \\times W _ { l } }$ computes the features $\\mathbf { x } _ { l } \\in \\mathbb { R } ^ { C _ { l } \\times H _ { l } \\times W _ { l } }$ , which comprise of $C _ { l }$ channels of features with height $H _ { l }$ and width $W _ { l }$ . The $l ^ { \\mathrm { t h } }$ layer is thus defined as: ",
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+    {
+        "type": "equation",
+        "img_path": "images/a5e81b45c2e5279220decb2960ae82304dc8ac1381af1eac6978be4b60fddd7b.jpg",
+        "text": "$$\nf _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) = ( \\gamma _ { l } \\cdot \\mathsf { n o r m } \\left( \\mathsf { c o n v } _ { l } \\left( \\mathbf { x } _ { l - 1 } , \\pmb { \\theta } _ { l } \\right) \\right) + \\beta _ { l } ) _ { + } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Here, additions $( + )$ and multiplications $( \\cdot )$ are element-wise, $( \\mathbf { z } ) _ { + } = \\operatorname* { m a x } \\left( \\mathbf { z } , 0 \\right)$ denotes the ReLU activation, $\\gamma _ { l } , \\beta _ { l } \\in \\mathbb { R } ^ { C _ { l } }$ are trainable parameters, norm $\\mathbf { \\rho } ( \\mathbf { z } )$ normalizes each channel of features $\\mathbf { z }$ across the population of $\\mathbf { z }$ , with $\\mu _ { \\mathbf { z } } , \\pmb { \\sigma } _ { \\mathbf { z } } ^ { 2 } \\in \\mathbb { R } ^ { C _ { l } }$ respectively containing the population mean and variance of each channel, and a small $\\epsilon$ prevents division by zero: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/d5b447fe1f9ab3851f17298f5661a2b9783c3e1643bb592babfcaf96be7294fe.jpg",
+        "text": "$$\n\\mathsf { n o r m } \\left( \\mathbf { z } \\right) = \\frac { \\mathbf { z } - \\mu _ { \\mathbf { z } } } { \\sqrt { \\pmb { \\sigma } _ { \\mathbf { z } } ^ { 2 } + \\epsilon } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            421,
+            853,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Additionally, convl $\\left( \\mathbf { x } _ { l - 1 } , \\pmb { \\theta } _ { l } \\right)$ computes the convolution of input features using the weight tensor $\\pmb { \\theta } _ { l } \\in \\mathbb { R } ^ { C ^ { l } \\times C ^ { l - 1 } \\times k ^ { 2 } }$ , where $k$ −is the kernel size. Specifically, FBS concerns the ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "optimization of convl $\\left( \\mathbf { x } _ { l - 1 } , \\pmb { \\theta } _ { l } \\right)$ functions, as a CNN spends the majority of its inference time in them, using $k ^ { 2 } C _ { l - 1 } C _ { l } H _ { l } W _ { l }$ multiply-accumulate operations (MACs) for the $l ^ { \\mathrm { t h } }$ layer. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Designing a Dynamic Layer ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Consider the following generalization of a layer with dynamic execution: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/148fc840c3f70274c29e506d264467ff7460fb6969aec714a824a1c88c42e750.jpg",
+        "text": "$$\n\\hat { f } \\left( \\mathbf { x } , \\cdots \\right) = f \\left( \\mathbf { x } , \\pmb { \\theta } , \\cdots \\right) \\cdot \\pi \\left( \\mathbf { x } , \\pmb { \\phi } , \\cdots \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $f$ and $\\pi$ respectively use weight parameters $\\pmb { \\theta }$ and $\\phi$ and may have additional inputs, and compute tensors of the same output shape, denoted by $\\mathbf { F }$ and $\\mathbf { G }$ . Intuitively, the expensive $\\mathbf { F } ^ { [ \\mathbf { i } ] }$ can always be skipped for any index i whenever the cost-effective $\\mathbf { G } ^ { [ \\mathbf { i } ] }$ evaluates to $\\mathbf { 0 }$ . Here, the superscript [i] is used to index the $\\mathbf { i } ^ { \\mathrm { t h } }$ slice of the tensor. For example, if we have features $\\mathbf { F } \\in \\mathbb { R } ^ { C \\times H \\times W }$ containing $C$ channels of $H$ -by- $W$ features, $\\mathbf { F } ^ { \\left\\lfloor c \\right\\rfloor } \\in \\mathbb { R } ^ { H \\times W }$ retrieves the $c ^ { \\mathrm { t h } }$ feature image. We can further sparsify and accelerate the layer by adding, for instance, a Lasso on $\\pi$ to the total loss, where $\\mathbb { E } _ { \\mathbf { x } } \\left[ \\mathbf { z } \\right]$ is the expectation of $\\mathbf { z }$ over $\\mathbf { x }$ : ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c5126d08b6fc83037d16757c2f44b50932a7a5d6f4814c740d9d1edcdc3b65b9.jpg",
+        "text": "$$\n\\mathcal { R } \\left( \\mathbf { x } \\right) = \\mathbb { E } _ { \\mathbf { x } } \\left[ \\left. \\pi \\left( \\mathbf { x } , \\phi , \\cdot \\cdot \\cdot \\right) \\right. _ { 1 } \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Despite the simplicity of this formulation, it is however very tricky to design $\\hat { f }$ properly. Under the right conditions, we can arbitrarily minimize the Lasso while maintaining the same output from the layer by scaling parameters. For example, in low-cost collaborative layers (Dong et al., 2017), $f$ and $\\pi$ are simply convolutions (with or without ReLU activation) that respectively have weights $\\pmb { \\theta }$ and $\\phi$ . Since $f$ and $\\pi$ are homogeneous functions, one can always halve $\\phi$ and double $\\pmb { \\theta }$ to decrease (4) while the network output remains the same. In other words, the optimal network must have $\\| \\phi \\| _ { \\infty }  0$ , which is infeasible in finiteprecision arithmetic. For the above reasons, Dong et al. (2017) observed that the additional loss in (4) always degrades the CNN’s task performance. Ye et al. (2018) pointed out that gradient-based training algorithms are highly inefficient in exploring such reparameterization patterns, and channel pruning methods may experience similar difficulties. Shazeer et al. (2017) avoided this limitation by finishing $\\pi$ with a softmax normalization, but (4) can no longer be used as the softmax renders the $\\ell ^ { 1 }$ -norm, which now evaluates to 1, useless. In addition, similar to sigmoid, softmax (without the cross entropy) is easily saturated, and thus may equally suffer from vanishing gradients. Many instead design $\\pi$ to produce on/off decisions and train them with reinforcement learning as discussed in Section 2. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 Feature Boosting and Suppression with Channel Saliencies ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Instead of imposing sparsity on features or convolutional weight parameters (e.g. Wen et al. (2016); Alvarez & Salzmann (2016); Li et al. (2017); He et al. (2018a)), recent channel pruning methods (Liu et al., 2017; Ye et al., 2018) induce sparsity on the BN scaling factors $\\gamma _ { l }$ . Inspired by them, FBS similarly generates a channel-wise importance measure. Yet contrary to them, instead of using the constant BN scaling factors $\\gamma _ { l }$ , we predict channel importance and dynamically amplify or suppress channels with a parametric function $\\pi ( \\mathbf { x } _ { l - 1 } )$ dependent on the output from the previous layer $\\mathbf x l - 1$ . Here, we propose to replace the layer definition $f _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right)$ for each of $l \\in [ 1 , L ]$ with $\\hat { f } _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right)$ which employs dynamic channel pruning: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5f953ace8e7057ee36bbac655d277ec023143bca8cc253e94cefb266b1eafda4.jpg",
+        "text": "$$\n\\hat { f } _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) = \\left( \\pi _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) \\cdot \\left( \\mathsf { n o r m } \\left( \\mathsf { c o n v } _ { l } \\left( \\mathbf { x } _ { l - 1 } , \\pmb { \\theta } _ { l } \\right) \\right) + \\beta _ { l } \\right) \\right) _ { + } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where a low-overhead policy $\\pi _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right)$ evaluates the pruning decisions for the computationally demanding conv $\\left( \\mathbf { x } _ { l - 1 } , \\pmb { \\theta } _ { l } \\right)$ : ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d4391126f318377c5c691c52cdf4a62e404586d778f0d6d9d430f78feae54441.jpg",
+        "text": "$$\n\\pi _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) = \\mathsf { w t a } _ { \\lceil d C _ { l } \\rceil } \\left( g _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here, ${ \\mathsf { w t a } } _ { k } ( { \\mathbf { z } } )$ is a $k$ -winners-take-all function, i.e. it returns a tensor identical to $\\mathbf { z }$ , except that we zero out entries in $\\mathbf { z }$ that are smaller than the $k$ largest entries in absolute magnitude. In other words, $\\mathsf { w t a } _ { \\lceil d C _ { l } \\rceil } \\bigl ( g _ { l } \\bigl ( \\mathbf { x } _ { l - 1 } \\bigr ) \\bigr )$ provides a pruning strategy that computes only $\\lceil d C _ { l } \\rceil$ most salient channels predicted by $g _ { l } ( \\mathbf { x } _ { l - 1 } )$ , and suppresses the remaining channels with zeros. In Section 3.4, we provide a detailed explanation of how we design a cheap $g _ { l } ( \\mathbf { x } _ { l - 1 } )$ that learns to predict channel saliencies. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "It is notable that our strategy prunes $C _ { l } - \\lceil d C _ { l } \\rceil$ least salient output channels from $l ^ { \\mathrm { t h } }$ layer, where the density $d \\in ] 0 , 1 ]$ can be varied to sweep the trade-off relationship between performance and accuracy. Moreover, pruned channels contain all-zero values. This allows the subsequent $( l + 1 ) ^ { \\mathrm { t h } }$ layer to trivially make use of input-side sparsity, since all-zero features can be safely skipped even for zero-padded layers. Because all convolutions can exploit both input- and output-side sparsity, the speed-up gained from pruning is quadratic with respect to the pruning ratio. For instance, dynamically pruning half of the channels in all layers gives rise to a dynamic CNN that uses approximately $\\frac { 1 } { 4 }$ of the original MACs. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Theoretically, FBS does not introduce the reparameterization discussed in Section 3.2. By batch normalizing the convolution output, the convolution kernel $\\theta _ { l }$ is invariant to scaling. Computationally, it is more efficient to train. Many alternative methods use nondifferentiable $\\pi$ functions that produce on/off decisions. In general, DNNs with these policy functions are incompatible with SGD, and resort to reinforcement learning for training. In contrast, (6) allows end-to-end training, as wta is a piecewise differentiable and continuous function like ReLU. Srivastava et al. (2015) suggested that in general, a network is easier and faster to train for complex tasks and less prone to catastrophic forgetting, if it uses functions such as wta that promote local competition between many subnetworks. ",
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "3.4 Learning to Predict Channel Saliencies ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This section explains the design of the channel saliency predictor $g _ { l } ( \\mathbf { x } _ { l - 1 } )$ . To avoid significant computational cost in $g _ { l }$ , we subsample $\\mathbf x _ { l - 1 }$ by reducing the spatial dimensions of each channel to a scalar using the following function $\\mathsf { s s } : \\mathbb { R } ^ { C \\times H \\times W } \\to \\mathbb { R } ^ { C }$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/2845eb3bcac471f9806f1825040737099fae7e499736be72550837824ca65e14.jpg",
+        "text": "$$\n\\mathfrak { s s } \\left( \\mathbf { x } _ { l - 1 } \\right) = \\frac { 1 } { H W } \\left[ \\mathfrak { s } \\left( \\mathbf { x } _ { l - 1 } ^ { [ 1 ] } \\right) \\ \\mathfrak { s } \\left( \\mathbf { x } _ { l - 1 } ^ { [ 2 ] } \\right) \\ \\cdot \\ \\cdot \\ \\mathfrak { s } \\left( \\mathbf { x } _ { l - 1 } ^ { [ C ] } \\right) \\right] ,\n$$",
+        "text_format": "latex",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathsf { s } \\left( \\mathbf { x } _ { l - 1 } ^ { [ c ] } \\right)$ reduces the $c ^ { \\mathrm { t h } }$ channel of $\\mathbf { z }$ to a scalar using, for instance, the $\\ell ^ { 1 }$ -norm $\\| \\mathbf { x } _ { l - 1 } ^ { [ c ] } \\| _ { 1 }$ , $\\ell ^ { 2 }$ -norm, $\\ell ^ { \\infty }$ -norm, or the variance of $\\mathbf { x } _ { l - 1 } ^ { [ c ] }$ . The results in Section 4 use the $\\ell ^ { 1 }$ - −  − norm by default, which is equivalent to global average pooling for the ReLU activated $\\mathbf x l - 1$ . We then design $g _ { l } ( \\mathbf { x } _ { l - 1 } )$ − to predict channel saliencies with a fully connected layer following −the subsampled activations $\\mathsf { s s } \\left( \\mathbf { x } _ { l - 1 } \\right)$ , where $\\phi _ { l } \\in \\mathbb { R } ^ { C ^ { l } \\times C ^ { l - 1 } }$ is the weight tensor of the layer: ",
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+    {
+        "type": "equation",
+        "img_path": "images/0c241dfa0c8176e014e3a262478c7cb963c59d80d082bba0a1654dcd3913636d.jpg",
+        "text": "$$\ng _ { l } \\left( \\mathbf { x } _ { l - 1 } \\right) = \\left( \\mathsf { s s } \\left( \\mathbf { x } _ { l - 1 } \\right) \\phi _ { l } + \\pmb { \\rho } _ { l } \\right) _ { + } .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "We generally initialize $\\rho _ { l }$ with $1$ and apply He et al. (2015)’s initialization to $\\phi _ { l }$ . Similar to how Liu et al. (2017) and Ye et al. (2018) induced sparsity in the BN scaling factors, we regularize all layers with the Lasso on $g _ { l } ( \\mathbf { x } _ { l - 1 } )$ : $\\begin{array} { r l } {  { \\lambda \\sum _ { l = 1 } ^ { L } \\mathbb { E } _ { \\mathbf { x } } [  g _ { l } ( \\mathbf { x } _ { l - 1 } )  _ { 1 } ] } \\quad } & { { } } \\end{array}$ in the total loss, where $\\lambda = 1 0 ^ { - 8 }$ in our experiments. ",
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+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We ran extensive experiments on CIFAR-10 (Krizhevsky et al., 2014) and the ImageNet ILSVRC2012 (Deng et al., 2009), two popular image classification datasets. We use MCifarNet (Zhao et al., 2018), a custom 8-layer CNN for CIFAR-10 (see Appendix A for its structure), using only 1.3 M parameters with 91.37% and 99.67% top-1 and top-5 accuracies respectively. M-CifarNet is much smaller than a VGG-16 on CIFAR-10 (Liu et al., 2017), which uses $2 0 \\mathrm { M }$ parameters and only $2 . 2 9 \\%$ more accurate. Because of its compactness, our CNN is more challenging to accelerate. By faithfully reimplementing Network Slimming (NS) (Liu et al., 2017), we closely compare FBS with NS under various speedup constraints. For ILSVRC2012, we augment two popular CNN variants, ResNet-18 (He et al., 2016) and VGG-16 (Simonyan & Zisserman, 2015), and provide detailed accuracy/MACs trade-off comparison against recent structured pruning and dynamic execution methods. ",
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+        "type": "text",
+        "text": "Our method begins by first replacing all convolutional layer computations with (5), and initializing the new convolutional kernels with previous parameters. Initially, we do not suppress any channel computations by using density $d = 1$ in (6) and fine-tune the resulting network. For fair comparison against NS, we then follow Liu et al. (2017) by iteratively decrementing the overall density $d$ of the network by 10% in each step, and thus gradually using fewer channels to sweep the accuracy/performance trade-off. The difference is that NS prunes channels by ranking globally, while FBS prunes around $1 - d$ of each layer. ",
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+    {
+        "type": "text",
+        "text": "4.1 CIFAR-10 ",
+        "text_level": 1,
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+        "img_path": "images/bf0b69083c0580f998d0a893355ef98d28a82ea3f6269d64ac066bec0980aa44.jpg",
+        "image_caption": [
+            "Figure 3: Experimental results on M-CifarNet. We compare in (a) the accuracy/MACs trade-off between FBS, NS and FBS $^ +$ NS. The baseline is emphasized by the circle $\\bigcirc$ . The heat map in (b) reveals the individual probability of skipping a channel for each channel ( $x$ -axis), when an image of a category ( $y$ -axis) is shown to the network with $d = 1$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "By respectively applying NS and FBS to our CIFAR-10 classifier and incrementally increasing sparsity, we produce the trade-off relationships between number of operations (measured in MACs) and the classification accuracy as shown in Figure 3a. FBS clearly surpasses NS in its ability to retain the task accuracy under an increasingly stringent computational budget. Besides comparing FBS against NS, we are interested in combining both methods, which demonstrates the effectiveness of FBS if the model is already less redundant, i.e. it cannot be pruned further using NS without degrading the accuracy by more than $1 \\%$ . The composite method (NS+FBS) is shown to successfully regain most of the lost accuracy due to NS, producing a trade-off curve closely matching FBS. It is notable that under the same $9 0 . 5 0 \\%$ accuracy constraints, FBS, NS+FBS, and NS respectively achieve $3 . 9 3 \\times$ , $3 . 2 2 \\times$ , and $1 . 1 9 \\times$ speed-up ratios. Conversely for a $2 \\times$ speed-up target, they respectively produce models with accuracies not lower than $9 1 . 5 5 \\%$ , $9 0 . 9 0 \\%$ and $8 7 . 5 4 \\%$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 3b demonstrates that our FBS can effectively learn to amplify and suppress channels when dealing with different input images. The 8 heat maps respectively represent the channel skipping probabilities of the 8 convolutional layers. The brightness of the pixel at location $( x , y )$ denotes the probability of skipping the $x ^ { \\mathrm { t h } }$ channel when looking at an image of the $y ^ { \\mathrm { t h } }$ category. The heat maps verify our belief that the auxiliary network learned to predict which channels specialize to which features, as channels may have drastically distinct probabilites of being used for images of different categories. The model here is a M-CifarNet using FBS with $d = 0 . 5$ , which has a top-1 accuracy of $9 0 . 5 9 \\%$ (top-5 $9 9 . 6 5 \\%$ ). Moreover, channels in the heat maps are sorted so the channels that are on average least frequently evaluated are placed on the left, and channels shaded in stripes are never evaluated. The network in Figure 3b is not only approximately $4 \\times$ faster than the original, by removing the unused channels, we also reduce the number of weights by 2.37 $\\times$ . This reveals that FBS naturally subsumes channel pruning strategies such as NS, as we can simply prune away channels that are skipped regardless of the input. It is notable that even though we specified a universal density $d$ , FBS learned to adjust its dynamicity across all layers, and prune different ratios of channels from the convolutional layers. ",
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+    {
+        "type": "text",
+        "text": "4.2 ImageNet ILSVRC2012 Classification ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "By applying FBS and NS respectively to ResNet-18, we saw that the ILSVRC2012 validation accuracy of FBS consistently outperforms NS under different speed-up constraints (see Appendix B for the implementation details and trade-off curves). For instance, at $d = 0 . 7$ , it utilizes only 1.12 G MACs (1.62 $\\times$ fewer) to achieve a top-1 error rate of $3 1 . 5 4 \\%$ , while NS requires 1.51 G MACs (1.21 $\\times$ fewer) for a similar error rate of $3 1 . 7 0 \\%$ . When compared across recent dynamic execution methods examined in Table 1, FBS demonstrates simultaneously the highest possible speed-up and the lowest error rates. It is notable that the baseline accuracies for FBS refer to a network that has been augmented with the auxiliary layers featuring FBS but suppress no channels, i.e. $d = 1$ . We found that this method brings immediate accuracy improvements, an increase of $1 . 7 3 \\%$ in top-1 and $0 . 4 6 \\%$ in top-5 accuracies, to the baseline network, which is in line with our observation on M-CifarNet. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "In Table 2, we compare different structured pruning and dynamic execution methods to FBS for VGG-16 (see Appendix B for the setup). At a speed-up of 3.01 $\\times$ , FBS shows a minimal increase of $0 . 4 4 \\%$ and $0 . 0 4 \\%$ in top-1 and top-5 errors respectively. At $5 . 2 3 \\times$ speed-up, it only degrades the top-1 error by $1 . 0 8 \\%$ and the top-5 by $0 . 5 9 \\%$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Not only does FBS use much fewer MACs, it also demonstrates significant reductions in bandwidth and memory requirements. In Table 3, we observe a large reduction in the number of memory accesses in single image inference as we simply do not access suppressed weights and activations. Because these memory operations are often costly DRAM accesses, minimizing them leads to power-savings. Table 3 further reveals that in diverse application scenarios such as low-end and cloud environments, the peak memory usages by the optimized models are much smaller than the originals, which in general improves cache utilization. ",
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+    {
+        "type": "table",
+        "img_path": "images/11ed0f7e7bff5d8e71385b7dd1e3c28cd4c86b19dc585dbb84be567cd66d8696.jpg",
+        "table_caption": [
+            "Table 1: Comparisons of error rates of the baseline and accelerated ResNet-18 models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Dynamic</td><td colspan=\"2\">Baseline</td><td colspan=\"2\">Accelerated</td><td rowspan=\"2\">MAC saving</td></tr><tr><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td></tr><tr><td>Soft Filter Pruning (He et al., 2018a)</td><td></td><td>29.72</td><td>10.37</td><td>32.90</td><td>12.22</td><td>1.72×</td></tr><tr><td>Network Slimming (Liu et al. (20l7),our implementation)</td><td></td><td>31.02</td><td>11.32</td><td>32.79</td><td>12.61</td><td>1.39×</td></tr><tr><td>Discrimination-aware Channel Pruning (Zhuang et al., 2018)</td><td></td><td>30.36</td><td>11.02</td><td>32.65</td><td>12.40</td><td>1.89×</td></tr><tr><td>Low-cost Collaborative Layers (Dong et al., 2017)</td><td></td><td>30.02</td><td>10.76</td><td>33.67</td><td>13.06</td><td>1.53×</td></tr><tr><td>Channel Gating Neural Networks (Hua et al., 2018)</td><td>广</td><td>30.98</td><td>11.16</td><td>32.60</td><td>12.19</td><td>1.61×</td></tr><tr><td>Feature Boosting and Suppression (FBS)</td><td>√</td><td>29.29</td><td>10.32</td><td>31.83</td><td>11.78</td><td>1.98×</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a30499804c9aaa32a945e132031566db4e3c504b15a6291e42256c2dab0a4226.jpg",
+        "table_caption": [
+            "Table 2: Comparisons of top-5 error rate increases for VGG-16 on ILSVRC2012 validation set under 3 $\\times$ , 4 $\\times$ and $5 \\times$ speed-up constraints. The baseline has a $1 0 . 1 \\%$ top-5 error rate. Results from He et al. (2017) only show numbers with one digit after the decimal point. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Dynamic</td><td>△ top-5 errors 3× 4×</td><td></td><td>(%) 5×</td></tr><tr><td>Filter Pruning (Li et al. (20l7),reproduced by He et al. (2017))</td><td rowspan=\"10\"></td><td></td><td>8.6</td><td>14.6</td></tr><tr><td>Perforated CNNs (Figurnov et al., 2016)</td><td>3.7</td><td>5.5</td><td></td></tr><tr><td>Network Slimming (Liu et al. (20i7),our implementation)</td><td>1.37</td><td>3.26</td><td>5.18</td></tr><tr><td>Runtime Neural Pruning (Lin et al., 2017)</td><td>2.32</td><td>3.23</td><td>3.58</td></tr><tr><td>Channel Pruning (He et al., 2017)</td><td>0.0</td><td>1.0</td><td>1.7</td></tr><tr><td>AutoML for Model Compression (He et al., 2018b)</td><td></td><td></td><td>1.4</td></tr><tr><td>ThiNet-Conv (Luo et al., 2017)</td><td>0.37</td><td></td><td></td></tr><tr><td>Feature Boosting and Suppression (FBS)</td><td></td><td>0.04 0.52</td><td>0.59</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Total Memory Accesses</td><td colspan=\"2\">PeakMemory Usage</td></tr><tr><td>Weights</td><td>Activations</td><td>Edge (1 image)</td><td>Cloud (128 images)</td></tr><tr><td>VGG-16</td><td>56.2MB</td><td>86.5MB</td><td>24.6MB</td><td>3.09GB</td></tr><tr><td>VGG-16 3×</td><td>23.9 MB (2.35x)</td><td>40.8MB (2.12×)</td><td>9.97MB (2.47×)</td><td>1.24 GB (2.47×)</td></tr><tr><td>ResNet-18</td><td>44.6MB</td><td>17.8MB</td><td>9.19MB</td><td>0.47 GB</td></tr><tr><td>ResNet-18 2×</td><td>20.5MB (2.18×)</td><td>12.3 MB (1.45×)</td><td>4.68MB (1.96x)</td><td>0.31GB (1.49×)</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 3: Comparisons of the memory accesses and peak memory usage of the ILSVRC2012 classifiers with FBS respectively under $3 \\times$ and $2 \\times$ inference speed-ups. The Weights and Activations columns respectively show the total amount of weight and activation accesses required by all convolutions for a single image inference. The Peak Memory Usage columns show the peak memory usages with different batch sizes. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In summary, we proposed feature boosting and suppression that helps CNNs to achieve significant reductions in the compute required while maintaining high accuracies. FBS fully preserves the capabilities of CNNs and predictively boosts important channels to help the accelerated models retain high accuracies. We demonstrated that FBS achieves around 2 $\\times$ and $5 \\times$ savings in computation respectively on ResNet-18 and VGG-16 within $0 . 6 \\%$ loss of top-5 accuracy. Under the same performance constraints, the accuracy gained by FBS surpasses all recent structured pruning and dynamic execution methods examined in this paper. In addition, it can serve as an off-the-shelf technique for accelerating many popular CNN networks and the fine-tuning process is unified in the traditional SGD which requires no algorithmic changes in training. Finally, the implementation of FBS and the optimized networks are fully open source and released to the public1. ",
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+    },
+    {
+        "type": "text",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            250,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work is supported in part by the National Key R&D Program of China (No.   \n2018YFB1004804), the National Natural Science Foundation of China (No. 61806192).   \nWe thank EPSRC for providing Yiren Zhao his doctoral scholarship. ",
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+    },
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+    {
+        "type": "text",
+        "text": "A Details of M-CifarNet on CIFAR-10 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            101,
+            578,
+            118
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For the CIFAR-10 classification task, we use M-CifarNet, a custom designed CNN, with less than 1.30 M parameters and takes 174 M MACs to perform inference for a 32-by-32 RGB image. The architecture is illustrated in Table 4, where all convolutional layers use $3 \\times 3$ kernels, the Shape column shows the shapes of each layer’s features, and pool7 is a global average pooling layer. ",
+        "bbox": [
+            174,
+            150,
+            825,
+            219
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We trained M-CifarNet (see Appendix A) with a 0.01 learning rate and a 256 batch size. We reduced the learning rate by a factor of $1 0 \\times$ for every 100 epochs. To compare FBS against NS fairly, every model with a new target MACs budget were consecutively initialized with the previous model, and trained for a maximum of 300 epochs, which is enough for all models to converge to the best obtainable accuracies. For NS, we follow Liu et al. (2017) and start training with an $\\ell ^ { 1 }$ -norm sparsity regularization weighted by $1 0 ^ { - 5 }$ on the BN scaling factors. We then prune at 150 epochs and fine-tune the resulting network without the sparsity regularization. ",
+        "bbox": [
+            174,
+            227,
+            823,
+            338
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We additionally employed image augmentation procedures from Krizhevsky et al. (2012) to preprocess each training example. Each CIFAR-10 example was randomly horizontal flipped and slightly perturbed in the brightness, saturation and hue. ",
+        "bbox": [
+            176,
+            345,
+            823,
+            387
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 4 additionally provides further comparisons of layer-wise compute costs between FBS, NS, and the composition of the two methods (NS $^ +$ FBS). It is notable that the FBS column has two different output channel counts, where the former is the number of computed channels for each inference, and the latter is the number of channels remaining in the layer after removing the unused channels. ",
+        "bbox": [
+            176,
+            395,
+            823,
+            464
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/49f0d2ac37b6f0ae27c27e2d86e51da64f151d9a24b34197f9ae4f56785fa80d.jpg",
+        "table_caption": [
+            "Table 4: The network structure of M-CifarNet for CIFAR-10 classification. In addition, we provide a detailed per-layer MACs comparison between FBS, NS, and the composition of them (NS+FBS). We minimize the models generated by the three methods while maintaining a classification accuracy of at least $9 0 . 5 \\%$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Layer</td><td>Shape</td><td colspan=\"4\">Number of MACs (Output Channels) Original NS FBS</td></tr><tr><td>convo</td><td>30 × 30</td><td></td><td></td><td>893k</td><td>NS+FBS</td></tr><tr><td>conv1</td><td>30 × 30</td><td>1.5 M (64)</td><td>1.3M (52) 27.0M (64)</td><td>(32/62) 8.4M (32/42)</td><td>860k (32) 10.2M (39)</td></tr><tr><td>conv2</td><td>15 ×15</td><td>33.2M (64)</td><td></td><td>4.2M</td><td>5.9M</td></tr><tr><td></td><td>15×15</td><td>16.6M (128)</td><td>15.9 M (123)</td><td>(64/67) 8.3M</td><td>（74 11.6 M</td></tr><tr><td>conv3</td><td>15 ×15</td><td>33.2M (128)</td><td>31.9M (128)</td><td>(64/79)</td><td>（77）</td></tr><tr><td>conv4 conv5</td><td>8×8</td><td>33.2M (128) 14.1M</td><td>33.1M (128) 13.4M (182)</td><td>8.3M (64/83)</td><td>12.1M (77)</td></tr><tr><td>conv6</td><td>8×8</td><td>(192) (192)</td><td>11.6 M (111)</td><td>3.6 M (96/128)</td><td>4.9M (110) 4.3M (67)</td></tr><tr><td>conv7</td><td>8×8</td><td>21.2M 21.2M</td><td>12.3 M</td><td>5.4M (96/152)</td><td></td></tr><tr><td>pool7</td><td></td><td>(192)</td><td>(192)</td><td>5.4 M (96/96)</td><td>4.5M (116)</td></tr><tr><td>fc</td><td>1×1 1×1</td><td>1.9k (10)</td><td>1.9k (10)</td><td>960 (10)</td><td>1.1k (10)</td></tr><tr><td></td><td></td><td>174.3M</td><td>146.5M</td><td></td><td></td></tr><tr><td>Total Saving</td><td></td><td>1</td><td>1.19×</td><td>44.3M 3.93×</td><td>54.2M 3.21×</td></tr></table>",
+        "bbox": [
+            207,
+            503,
+            794,
+            723
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Figure 4 shows how the skipping probabilites heat maps of the convolutional layer conv4 evolve as we fine-tune FBS-augmented M-CifarNet. The network was trained for 12 epochs, and we saved the model at every epoch. The heat maps are generated with the saved models in sequence, where we apply the same reordering to all heat map channels with the sorted result from the first epoch. It can be observed that as we train the network, the channel skipping probabilites become more pronounced. ",
+        "bbox": [
+            173,
+            839,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/0ac2dbb3a50aafe67f3efd4e38811dfbcd9c7c0d1019acfb820610f3f0cc6d8a.jpg",
+        "image_caption": [
+            "Figure 4: The training history of a convolutional layer conv4 in M-CifarNet. The history is visualized by the 12 skipping probabilites heat maps, where the heights denote the 10 categories in CIFAR-10, and channels in conv4 occupy the width. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            344,
+            107,
+            658,
+            392
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B Details of the ILSVRC2012 classifiers ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            474,
+            602,
+            492
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "ILSVRC2012 classifiers, i.e. ResNet-18 and VGG-16, were trained with a procedure similar to Appendix A. The difference was that they were trained for a maximum of 35 epochs, the learning rate was decayed for every 20 epochs, and NS models were all pruned at 15 epochs. For image preprocessing, we additionally cropped and stretched/squeezed images randomly following Krizhevsky et al. (2012). ",
+        "bbox": [
+            174,
+            506,
+            825,
+            577
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Since VGG-16 is computationally intensive with over 15 G MACs, We first applied NS on VGG-16 to reduce the computational and memory requirements, and ease the training of the FBS-augmented variant. We assigned a $1 \\%$ budget in top-5 accuracy degradation and compressed the network using NS, which gave us a smaller VGG-16 with $2 0 \\%$ of all channels pruned. The resulting network is a lot less redundant, which almost halves the compute requirements, with only 7.90 G MACs remaining. We then apply FBS to the well-compressed network. ",
+        "bbox": [
+            174,
+            583,
+            825,
+            680
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Residual networks (He et al., 2016), such as ResNet-18, adopt sequential structure of residual blocks: $\\mathbf { x } _ { b } = K \\left( \\mathbf { x } _ { b - 1 } \\right) + F \\left( \\mathbf { x } _ { b - 1 } \\right)$ , where $\\mathbf { x } _ { b }$ is the output of the $b ^ { \\mathrm { t h } }$ block, $K$ is either an identity function or a downsampling convolution, and $F ^ { \\prime }$ consists of a sequence of convolutions. For residual networks, we directly apply FBS to all convolutional layers, with a difference in the way we handle the feature summation. Because the $\\left( b + 1 \\right) ^ { \\mathrm { t h } }$ block receives as input the sum of the two features with sparse channels $K \\left( \\mathbf { x } _ { b - 1 } \\right)$ and $F \\left( \\mathbf { x } _ { b - 1 } \\right)$ , a certain channel of this sum is treated as sparse when the same channels in both features are simultaneously sparse. ",
+        "bbox": [
+            174,
+            686,
+            825,
+            801
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 compares the accuracy/performance trade-off curves between FBS and NS for ResNet-18. ",
+        "bbox": [
+            174,
+            808,
+            821,
+            835
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/03cc25e4465c9126a92eedc919885878b989aaaa077f60070dd89df8fb2e157e.jpg",
+        "image_caption": [
+            "Figure 5: The accuracy/performance trade-off comparison between NS and FBS for ResNet18 on the ImageNet ILSVRC2012 validation set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            282,
+            367,
+            710,
+            616
+        ],
+        "page_idx": 13
+    }
+]

parse/train/BfPzZSype5M/BfPzZSype5M.md

@@ -0,0 +1,262 @@
+# RMM: Reinforced Memory Management for Class-Incremental Learning
+
+Yaoyao Liu1 Bernt Schiele1 Qianru Sun2
+
+1Max Planck Institute for Informatics, Saarland Informatics Campus 2School of Computing and Information Systems, Singapore Management University {yaoyao.liu, schiele}@mpi-inf.mpg.de qianrusun@smu.edu.sg
+
+# Abstract
+
+Class-Incremental Learning (CIL) [40] trains classifiers under a strict memory budget: in each incremental phase, learning is done for new data, most of which is abandoned to free space for the next phase. The preserved data are exemplars used for replaying. However, existing methods use a static and ad hoc strategy for memory allocation, which is often sub-optimal. In this work, we propose a dynamic memory management strategy that is optimized for the incremental phases and different object classes. We call our method reinforced memory management (RMM), leveraging reinforcement learning. RMM training is not naturally compatible with CIL as the past, and future data are strictly non-accessible during the incremental phases. We solve this by training the policy function of RMM on pseudo CIL tasks, e.g., the tasks built on the data of the 0-th phase, and then applying it to target tasks. RMM propagates two levels of actions: Level-1 determines how to split the memory between old and new classes, and Level-2 allocates memory for each specific class. In essence, it is an optimizable and general method for memory management that can be used in any replaying-based CIL method. For evaluation, we plug RMM into two top-performing baselines (LUCIR $^ +$ AANets and POD $+ .$ AANets [30]) and conduct experiments on three benchmarks (CIFAR-100, ImageNet-Subset, and ImageNet-Full). Our results show clear improvements, e.g., boosting POD $+ .$ AANets by $3 . 6 \%$ , $4 . 4 \%$ , and $1 . 9 \%$ in the 25-Phase settings of the above benchmarks, respectively. The code is available at https://class-il.mpi-inf.mpg.de/rmm/.
+
+# 1 Introduction
+
+Ideally, AI systems should be adaptive to ever-changing environments—where the data are continuously observed by sensors. Their models should be capable of learning new concepts from data while maintaining the ability to recognize previous ones. In practice, the systems often have constrained memory budgets because of which most of the historical data have to be abandoned [20]. However, deep-learning-based AI systems, when continuously updated using new data and limited historical data, often suffer from catastrophic forgetting, as the updates can override knowledge acquired from previous data [33, 34, 39].
+
+To encourage research on the forgetting problem, Rebuffi et al. [40] defined a standard protocol of class-incremental learning (CIL) for image classification, where the training data of different object classes come in phases. In each phase, the classifier is evaluated on all classes observed so far. As the total memory size is limited [40], CIL systems abandon the majority of the data and only preserve a small number of exemplars, e.g., 20 exemplars per class, which will be used for replaying in subsequent phases. Replaying usually happens for multiple epochs [13, 18, 30, 40], so both the old class exemplars and new class data need to be stored in the limited memory. Existing CIL methods allocate memory between the old and new classes in an arbitrary and static fashion, e.g., 20 per old class vs. 1, 300 per new class for the ImageNet-Full dataset. This causes a serious imbalance between the old and new classes and can exacerbate the problem of catastrophic forgetting.
+
+![](images/fb925de9131e5e29d0397072250f83a2fbcecb9ae91b493cab1ae5477fb7b21f.jpg)  
+Figure 1: (a) Existing CIL methods [18, 30, 40] allocate memory between old and new classes in an arbitrary and frozen way, causing the data imbalance between old and new classes and exacerbating the catastrophic forgetting of old knowledge in the learned model. (b) Our proposed method— Reinforced Memory Management (RMM)—is able to learn the optimal and class-specific memory sizes in different incremental phases. Please note we use orange, blue, and green dots to denote the samples observed in the (i-1)-th, $i$ -th, and $( i { + } 1 )$ -th phases, respectively.
+
+To address this, we propose to learn an optimal memory management policy for each incremental phase with continuously reinforced model performance and call our method reinforced memory management (RMM). Detailed actions include 1) allocating the memory between the existing (old) and the coming (new) data for each phase, and 2) specifying the memory for each old class according to its recognition difficulty before abandoning any of its data. To this end, we leverage reinforcement learning [26–28, 51, 59] and design a new policy function to contain two sub-functions that propagate two levels of actions in a hierarchical way. Level-1 function determines how to split memory between the old and new data. Its output action is then inputted into the Level-2 function to determine how to allocate memory for each old class. The overall objective of the function is to maximize the cumulative evaluation accuracy across all incremental phases. However, this is not naturally compatible with the standard protocol of CIL [40] where neither past nor future data are accessible for evaluation. To tackle this issue, we propose to pre-train the function on pseudo CIL tasks and then adopt it in the learning process of our target task. In principle, we can build such pseudo tasks using any available categorical data, e.g., the data in the 0-th phase of the target CIL task or the data from another dataset. Even though this is a non-stationary reinforcement learning problem, we can regard the pseudo and target CIL tasks as a sequence of stationary tasks and train the policy function to exploit the dependencies between these consecutive tasks. Such continuous adaptation in non-stationary environments is feasible based on the empirical analysis given in [2].
+
+Technically, we propose the following method to guarantee the transferability of policy functions between pseudo and target CIL tasks. We take a Level-1 action based on the ratio of the number of new classes to the total number of classes observed so far. A lower (higher) ratio will result in weakening the stability (plasticity) of the classification model. Then, we take a Level-2 action for each individual class conditioned on both the Level-1 action and the training entropy of that class. A higher entropy denotes a more difficult class, leading to more memory allocated to the class. For evaluation, we conduct extensive CIL experiments by plugging RMM into two top-performing methods (LUCIR $+ .$ AANets, POD $^ { + }$ AANets) and testing them on three benchmarks (CIFAR-100, ImageNet-Subset, and ImageNet-Full). Our results show the clear and consistent superiority of RMM, e.g., it boosts the state-of-the-art POD $+$ AANets by $3 . 6 \%$ , $4 . 4 \%$ , and $1 . 9 \%$ in the 25-Phase settings of the above benchmarks, respectively.
+
+Our technical contribution is three-fold. 1) A hierarchical reinforcement learning algorithm called RMM to manage the memory in a way that can be conveniently modified through incremental phases and for different classes. 2) A pseudo task generation strategy that requires only in-domain available data (small-scale) or cross-domain datasets (large-scale), relieving the data incompatibility between reinforcement learning and class-incremental learning. 3) Extensive experiments, visualization, and interpretation for RMM in three CIL benchmarks and using two top models as baselines.
+
+# 2 Related Work
+
+Incremental Learning [22, 36, 48, 53, 58] continuously updates the model using data coming in a sequence of phases. Similar tasks are also referred to as continual learning [12, 32] and lifelong learning [3, 9]. Recent papers are either task-incremental learning—each phase corresponds to a task (dataset) that contains new data of all seen classes [7, 10, 19, 29, 43, 47, 57], or classincremental learning (CIL)—each phase contains data of a new set of classes, i.e., classes are unseen [4, 6, 18, 25, 31, 37, 40, 41, 49, 52, 55–57]. This paper is concerned with CIL. The key challenge of CIL is the forgetting problem—older classes are forgotten in later phases. Existing methods tackling this can be divided into three categories: memory-based, regularization-based, and network-architecture-based [11, 35]. Memory-based methods preserved a small subset of the old class data (exemplars) to replay the model on them (together with the new class data), in order to relieve the forgetting of the old classes. Some work [18, 40] proposed heuristic strategies to select more representative exemplars from the old class data, and others [31, 47] tried to generate exemplars in optimizable frameworks. None of them changed the allocation of memory for different classes, i.e., all used an arbitrary and static scheme for memory allocation. Regularization-based methods introduce regularization terms in the loss function to consolidate previous knowledge when training the model on new data. The key idea is to enforce predicted label logits [29, 40], features maps [13, 18], or the topology in the feature space [49] of the new model to be close to that of the previous model. Network-architecture-based methods aim to design “incremental network architectures”. Some work [45, 54] gradually extended the network capacity for new data, while others proposed to freeze partial network parameters [1, 30] to preserve the knowledge of the old classes.
+
+Reinforcement Learning defines an agent that needs to decide its actions in an unknown environment by maximizing the expected cumulative reward. It has been widely applied to many optimization problems, e.g., neural architecture search [54, 59] and neural machine translation [38, 46]. Reinforcement learning has also been introduced to solve incremental learning problems. Xu et al. [54] proposed to increase convolution filters once a new task arrives and optimize the increased number by reinforcement learning. Gao et al. [14] proposed an improved version that makes the minimal expansion of the network, reducing memory and computing overheads. Veniat et al. [50] introduced a modular architecture, where each module represents a different atomic skill, and used the REINFORCE algorithm [51] to optimize it. Huang et al. [21] combined reinforcement learning with Net2Net [8] and designed a NAS-based CIL method. In our work, we also use the REINFORCE algorithm [51], but differ in three aspects. First, we are the first to optimize memory allocation for CIL in a reinforced way. Second, we learn the policy functions on generated pseudo CIL tasks, where we can access both past, and future data (for each incremental phase) and thus are able to compute the cross-phase (long-term) rewards. In contrast, the related work [14, 54] could use only current-phase data to estimate a short-term reward. Third, our reinforcement learning has a hierarchical structure that specially fits the nature of the data stream in the CIL settings.
+
+# 3 Preliminaries
+
+Class-Incremental Learning (CIL) usually assumes $( N { + } 1 )$ learning phases: an initial phase and $N$ incremental phases during which the number of classes gradually increases till the maximum [13, 18, 20, 31]. We assume that total memory $\mathcal { M }$ is bounded and fixed for all incremental phases [40]. $\mathcal { M }$ is used to store the exemplars and new coming data as both kinds of data need to be loaded repeatedly during training epochs. In the initial (0-th) phase, data $\mathcal { D } _ { 0 }$ , containing the training samples of $\mathcal { C } _ { 0 }$ classes, are used to learn the initial classification model $\Theta _ { 0 }$ . In the $i$ -th incremental phase, we split $\mathcal { M }$ into two dynamic partitions: the exemplar memory $\mathcal { M } _ { \mathrm { o l d } }$ and new data memory $M _ { \mathrm { n e w } }$ . We select $\mathcal { E } _ { t }$ as representative samples of the data seen in the $t$ -th phase, and denote total exemplars $\mathcal { E } _ { 0 } \sim \mathcal { E } _ { i - 1 }$ shortly as $\mathcal { E } _ { 0 : i - 1 }$ . We save $\mathcal { E } _ { 0 : i - 1 }$ into $\mathcal { M } _ { \mathrm { o l d } }$ and free $M _ { \mathrm { n e w } }$ . Then, we observe new data that contain $\mathcal { C } _ { i }$ new classes. We randomly load new data into $M _ { \mathrm { n e w } }$ until $M _ { \mathrm { n e w } }$ is full, and all the other new data are discarded. We denote the loaded new data as $\mathcal { D } _ { i }$ . Then, we initialize $\Theta _ { i }$ with $\Theta _ { i - 1 }$ , and train it using $\mathcal { E } _ { 0 : i - 1 } \cup \mathcal { D } _ { i }$ . The resulting model $\Theta _ { i }$ will be evaluated with a test set containing all classes observed so far. We repeat this training and testing, and report the average accuracy across all phases.
+
+Reinforcement Learning $\mathbf { \left( R L \right) }$ aims to learn an optimal policy function $\pi$ for an agent interacting in an unknown environment [51, 54, 59]. In the CIL scenario, in each incremental phase, the agent observes the current state $s _ { i }$ from the environment, and then takes an action $a _ { i }$ (how to allocate memory) according to the policy function $\pi ( a _ { i } | s _ { i } )$ . Subsequently, the environment is updated to a new state $s _ { i + 1 }$ and the reward $r _ { i }$ is calculated to optimize the parameters of $\pi ( a _ { i } | s _ { i } )$ through cumulative reward back-propagation. Specifically, the learning objective of $\begin{array} { r } { R _ { i } ^ { ' } = \sum _ { t = i } ^ { \infty } \dot { \gamma } ^ { t - i } r _ { t } } \end{array}$ , where $\gamma \in [ 0 , 1 )$ i i is a discounting factor that determines the $\pi ( a _ { i } | s _ { i } )$ is to maximize the expected weights of future rewards. Please note that in our case, theproblem [15, 59], so we remove the discounting factor and $( N { + } 1 )$ $\textstyle R = \sum _ { t = 0 } ^ { N } r _ { t }$ task is a finite horizon, which is actually the cumulative validation accuracy of all training CIL tasks. In Section 4, we discuss the proposed RL algorithm for memory allocation and how to generate pseudo tasks for training its policy function.
+
+# 4 Reinforced Memory Management (RMM)
+
+Our RMM approach learns policy functions that propagate two levels of actions in a hierarchical way, specially designed for CIL. As illustrated in Figure 1 (b), Level-1 determines the memory split between exemplars and new data, and Level-2 allocates the memory for each individual class. We motivate and introduce the formulation of RMM, including the definitions of states, actions, rewards, and hierarchical policy functions in Section 4.1. In Section 4.2, we detail the steps of creating pseudo CIL tasks on which we learn the policy functions. In Section 4.3, we summarize the algorithm.
+
+# 4.1 Formulation
+
+In the $i$ -th incremental phase CIL, we manage the memory for two kinds of data: exemplars $\mathcal { E } _ { 0 : i - 1 }$ and new data $\mathcal { D } _ { i }$ . For the former, we have access to their images and labels so we can allocate a different memory size to a different class, e.g., based on its recognition difficulty. For the latter, we do not have such access before loading the data (otherwise, causing a violation to the CIL protocol), so we are only able to learn a total memory size, i.e., the memory size for all new classes (and then split it evenly for each individual class). Therefore, the memory management in CIL settings is inherently hierarchical: 1) coarse memory allocation between exemplars and new data; and then 2) fine-grained memory allocation among specific classes. To this end, we modify the standard reinforcement learning into a hierarchical structure.
+
+As illustrated in Figure 2 (a), in the $i$ -th incremental phase of CIL (i.e., the environment), the argent receives a state value $s _ { i }$ . Level-1 policy $\pi _ { \eta }$ takes $s _ { i }$ as the input to produce an action $a _ { i } ^ { [ 1 ] } \sim \pi _ { \eta } ( s _ { i } )$ $a _ { i } ^ { [ 1 ] }$ determines how to split memory between the exemplars and new data. After that, Level-2 policy $\pi _ { \phi }$ takes $s _ { i }$ and $a _ { i } ^ { [ 1 ] }$ as inputs to produce the second action $a _ { i } ^ { [ 2 ] } \sim \pi _ { \phi } ( s _ { i } , a _ { i } ^ { [ 1 ] } )$ that distributes the exemplar memory for each individual class.
+
+States, defined for our CIL settings, should have two properties. 1) Being transferable between CIL tasks, e.g., from a small-scale CIL task including 50 classes (in total) to a large one including 100 classes. The reason is that we need to transfer the policy functions learned from pseudo CIL tasks (defined in Section 4.2) to the target task. The states, the inputs of policy functions, should also be transferable. 2) Being distinct in each incremental phase. This is to enable the state variable to represent a specific forgetting or data imbalance degree at each different learning phase of the CIL model. To fulfill these properties, we formulate the state in the $i$ -th phase as $\begin{array} { r } { s _ { i } = \left( \frac { \mathcal { C } _ { i } } { \sum _ { t = 0 } ^ { i - 1 } \mathcal { C } _ { t } } , \frac { | \mathcal { M } _ { \mathrm { o l d } } | } { | \mathcal { M } | } \right) } \end{array}$ , where $\mathcal { C } _ { i }$ denotes the number of classes in $\mathcal { D } _ { i }$ , $\mathcal { M } _ { \mathrm { o l d } }$ denotes the memory allocated to exemplars $\mathcal { E } _ { 0 : i - 1 }$ , and $\mathcal { M }$ is the total memory.
+
+Level-1 Actions. In the 1-st incremental phase, our Level-1 policy function produces an action to allocate the memory for exemplars ${ \mathcal { E } } _ { 0 }$ and new data $\mathcal { D } _ { 1 }$ . We denote this action as $a _ { 1 } ^ { [ 1 ] }$ and assign its value with the ratio of the number of the exemplars $a _ { 1 } ^ { [ 1 ] } \in ( 0 , 1 )$ . In the $i$ -th phase $( i \geq 2 )$ ), the definition of $| \mathcal { E } _ { 0 } |$ $a _ { i } ^ { [ 1 ] }$ to the memory size is different to $a _ { 1 } ^ { [ 1 ] }$ as it is a relative , so we have change over $a _ { i - 1 } ^ { [ 1 ] }$ . Specifically, $a _ { i } ^ { [ 1 ] }$ is the ratio of increased (if its value is positive) or decreased (if negative) memory size of $\mathcal { M } _ { \mathrm { o l d } }$ compared to the (i-1)-th phase. Using this definition aims for smooth and continuous memory management. In the formulation, the memory sizes of exemplars $\mathcal { E } _ { 0 : i - 1 }$ and new data $\mathcal { D } _ { i }$ are, respectively,
+
+![](images/886c2faf44a43d3c90d5359b5aec1dfe02040e79327a3ff62ea2f7be2ca8882c.jpg)  
+Figure 2: (a) In the $i$ -th phase of the $k$ -th pseudo CIL task, Level-1 policy $\pi _ { \eta }$ takes $s _ { i }$ as the input, and produces action $a _ { i } ^ { [ 1 ] }$ . Level-2 policy $\pi _ { \phi }$ takes $s _ { i }$ and $a _ { i } ^ { [ 1 ] }$ as the inputs, then produces action $a _ { i } ^ { [ 2 ] }$ . (b) For the $k$ -th pseudo CIL task, we allocate memory for $N$ times (i.e., in $N$ phases) using the policies $\pi _ { \eta }$ and $\pi _ { \phi }$ , and compute the cumulative reward $R$ .
+
+$$
+| \mathcal { M } _ { \mathrm { o l d } } | = | \mathcal { E } _ { 0 : i - 1 } | = \sum _ { t = 1 } ^ { i } a _ { t } ^ { [ 1 ] } | \mathcal { M } | , \quad | \mathcal { M } _ { \mathrm { n e w } } | = | \mathcal { D } _ { i } | = \left( 1 - \sum _ { t = 1 } ^ { i } a _ { t } ^ { [ 1 ] } \right) | \mathcal { M } | .
+$$
+
+We set a constrain $a _ { i } ^ { [ 1 ] } \in [ - 0 . 1 , 0 . 1 ]$ for $i \geq 2$ . Otherwise, if $a _ { i } ^ { [ 1 ] }$ is too big, there are not enough exemplars to fill the memory, as most old-class data has been abandoned. If $a _ { i } ^ { [ 1 ] }$ is too small, many exemplars will be permanently deleted in this phase, making it hard or even impossible to adjust $\mathcal { M } _ { \mathrm { o l d } }$ back to a high value in the future phases. If $\textstyle \sum _ { t = 1 } ^ { i } a _ { t } ^ { [ 1 ] } > 1$ , $M _ { \mathrm { n e w } }$ will be negative. So, we force Pit=1 a[1]t $\textstyle \sum _ { t = 1 } ^ { i } a _ { t } ^ { [ 1 ] } \leq 1$ by rejection sampling [5], i.e., using $\pi _ { \eta }$ to output another action until it is feasible to execute. Note that this situation rarely happens in real training, because when $M _ { \mathrm { n e w } }$ becomes very low, $\pi _ { \eta }$ tends to produce an action to increase it.
+
+Level-2 Actions. Here, we elaborate on how to get class-specific memory allocation. In the $( i - 1 )$ -th phase, we split the classes for $\mathcal { D } _ { i - 1 }$ into two groups evenly according to training entropy values: classes with higher values (difficult classes) are in one group and the rest in the other group. Therefore, Level-2 action $a _ { i } ^ { [ 2 ] } \in ( 0 , 1 )$ determines how to split memories between harder and easier classes. During initial experiments, we observed that using two groups already yields improved results and using more groups causes a decrease.
+
+Let $\mathcal { M } _ { j } ^ { A }$ and $\mathcal { M } _ { j } ^ { B }$ denote the memory allocated for the high-entropy and low-entropy groups, respectively, in the $j$ -th phase $( j \le i )$ :
+
+$$
+| \mathcal { M } _ { j } ^ { A } | = a _ { j + 1 } ^ { [ 2 ] } | \mathcal { E } _ { j } | = \frac { a _ { j + 1 } ^ { [ 2 ] } \mathcal { C } _ { j } } { \sum _ { t = 1 } ^ { i } \mathcal { C } _ { t } } | \mathcal { M } _ { \mathrm { o l d } } | , | \mathcal { M } _ { j } ^ { B } | = ( 1 - a _ { j + 1 } ^ { [ 2 ] } ) | \mathcal { E } _ { j } | = \frac { ( 1 - a _ { j + 1 } ^ { [ 2 ] } ) \mathcal { C } _ { j } } { \sum _ { t = 1 } ^ { i } \mathcal { C } _ { t } } | \mathcal { M } _ { \mathrm { o l d } } | .
+$$
+
+Then, we allocate memory evenly to the classes within the group, e.g., if the high-entropy group has 10 classes, each class will have a memory size of $\frac { 1 } { 1 0 } | \mathcal { M } _ { j } ^ { A } |$ .
+
+Rewards. The objective of CIL is that the trained model (in any phase) should be efficient to recognize all classes seen so far. It is intuitive and convenient to use the validation accuracy as the reward in each phase. In the $i$ -th phase, the objective of RMM is to maximize the expected cumulative reward, i.e., $\textstyle R = \sum _ { i = 0 } ^ { N } r _ { i }$ , where $r _ { i }$ denotes the validation accuracy in the $i$ -th phase.
+
+# 4.2 Optimization
+
+In the CIL protocol, it is impossible to see past or future data in any incremental phase. It is thus not intuitive how to compute cumulative rewards till the last phase. We propose to solve the issue by generating pseudo CIL tasks (where all data are accessible).
+
+Pseudo CIL Tasks should meet two requirements: 1) their training and validation data are fully accessible for computing cumulative rewards, and 2) they have the same format (e.g., the same number of phases) of the target CIL task. Data Sources: For requirement 1, an intuitive solution is to use $\mathcal { D } _ { 0 }$ (available in the 0-th phase). Based on the CIL protocol [13, 18, 20, 30], $\mathcal { D } _ { 0 }$ contains half of the classes of the whole dataset, e.g., 50 classes on CIFAR-100, which supplies enough data to build downsized CIL tasks. When building the tasks, we randomly choose $1 0 \%$ training samples of each class (from $\mathcal { D } _ { 0 }$ ) to compose a pseudo validation set (note that we are not allowed to use the original validation set in training). When aiming for larger-scale data in CIL, we can leverage smaller datasets. For example, the pseudo tasks for ImageNet-Subset can be built on the data of CIFAR-100. This is also meaningful to evaluate the transferability of RMM policy functions (discussed in the Ablation Study). Task Generation Protocol is based on requirement 2. If using another dataset, we simply follow its original CIL protocol. If using the data accessed in the 0-th phase (i.e., $\mathcal { D } _ { 0 }$ ), we can reduce the number of classes (in each phase) by half. For example, for CIFAR-100, we use 50-class $\mathcal { D } _ { 0 }$ to generate a 5-phase pseudo CIL task as follows: loading 25 classes in the 0-th phase, and after that, five classes per phase. To generate another pseudo task, we simply change the order of classes.
+
+![](images/2676b7321df9fb589fa15a01c9e469e5666e2b81aca84cfb2d226b35f2b252cb.jpg)  
+Figure 3: Updating $\eta$ and $\phi$ in one epoch. To get stable gradients for $J ( \eta , \phi )$ , we create $K$ different pseudo CIL tasks, and run each task for $Z$ times.
+
+Training. We elaborate the steps of learning Level-1 policy $\pi _ { \eta }$ and Level-2 policy $\pi _ { \phi }$ in the following. The goal is to optimize the parameters $\eta$ and $\phi$ by maximizing the expected cumulative reward $J ( \eta , \phi )$ . We denote any pseudo CIL task and its cumulative reward as $\tau$ and $R$ , respectively, and have,
+
+$$
+J ( \eta , \phi ) = \mathbb { E } _ { T } \mathbb { E } _ { \pi _ { \eta } , \pi _ { \phi } } [ R ] .
+$$
+
+Policy Gradient Estimation. According to the policy gradient theorem [51], we can compute the gradients for $J ( \eta , \phi )$ as follows,
+
+$$
+\nabla _ { \eta , \phi } J ( \eta , \phi ) = \mathbb { E } _ { T } \left[ \sum _ { i = 1 } ^ { N } \mathbb { E } _ { \pi _ { \eta } , \pi _ { \phi } } \big [ \nabla _ { \eta , \phi } \log ( \pi _ { \eta } ( a _ { i } ^ { [ 1 ] } \vert s _ { i } ) \pi _ { \phi } ( a _ { i } ^ { [ 2 ] } \vert s _ { i } , a _ { i } ^ { [ 1 ] } ) ) R \big ] \right] .
+$$
+
+Following the REINFORCE algorithm [51], we replace the expectations $\mathbb { E } \tau [ \cdot ]$ and $\mathbb { E } _ { \pi _ { \eta } , \pi _ { \phi } } [ \cdot ]$ with sample averages using the Monte Carlo method [16]. Specifically, in each epoch, we create $K$ pseudo tasks and run each task for $Z$ times, as shown in Figure 3. Thus we can derive the empirical approximation of $\nabla _ { \eta , \phi } J ( \eta , \phi )$ as,
+
+$$
+\nabla _ { \eta , \phi } J ( \eta , \phi ) = \frac { 1 } { Z K } \sum _ { k = 1 } ^ { K } \sum _ { z = 1 } ^ { Z } \sum _ { i = 1 } ^ { N } \nabla _ { \eta , \phi } \log ( \pi _ { \eta } ( a _ { i } ^ { [ 1 ] } | s _ { i } ) \pi _ { \phi } ( a _ { i } ^ { [ 2 ] } | s _ { i } , a _ { i } ^ { [ 1 ] } ) ) ( R _ { z } ^ { k } - b ) ,
+$$
+
+where $R _ { z } ^ { k }$ denotes the $z$ -th reward for the $k$ -th pseudo task $\mathcal { T } _ { k }$ , and $b$ denotes the baseline function— the moving average of previous rewards. Using this baseline function is a common trick in RL to reduce the variance of estimated policy gradients [23, 42, 59].
+
+Updating Parameters. We update $\eta$ and $\phi$ in each epoch according to the gradient ascent rule [54, 59]:
+
+$$
+\eta : = \eta + \beta _ { 1 } \nabla _ { \eta } J ( \eta , \phi ) , \phi : = \phi + \beta _ { 2 } \nabla _ { \phi } J ( \eta , \phi ) ,
+$$
+
+where $\beta _ { 1 }$ and $\beta _ { 2 }$ are the learning rates. We iterate this update for $m$ epochs in total.
+
+# 4.3 Algorithm
+
+Algorithm 1 summarizes the overall training steps of the proposed RMM. There are four loops in the algorithm: 1) we train the RMM agent for $m$ epochs; 2) we create $K$ pseudo CIL tasks in each epoch; 3) we run each pseudo CIL task for $Z$ times; and 4) there are $N { + 1 }$ learning phases each time. Specifically, Line 3 initializes the parameters of policy functions. Line 6 creates the $k$ -th pseudo CIL task. Line 8 initializes the classification model. Lines 10-16 allocate the memory according to the actions produced by RMM policy. Line 17 loads new data. Lines 18-19 train the classification model and compute the accuracy. Line 20 estimates the $z$ -th cumulative reward. Lines 21-22 compute the gradients and update policy functions.
+
+# 5 Experiments
+
+We evaluate the proposed RMM method on three CIL benchmarks: CIFAR-100 [24], ImageNet-Subset [40], and ImageNet-Full [44], and use two top performing methods LUCIR $+$ AANets and POD $+$ AANets [30] as baselines. Below we introduce the datasets
+
+1: Input: Data $\mathcal { D }$ for generating pseudo CIL tasks.   
+2: Output: Policy functions $\pi _ { \eta } , \pi _ { \phi }$ .   
+3: Initialize $\eta$ and $\phi$ ;   
+4: for $m$ epochs do   
+5: for $k$ in $1 , . . . , K$ do   
+6: Create a new pseudo task $\mathcal { T } _ { k }$ using $\mathcal { D }$ ;   
+7: for z in 1, ..., Z do   
+8: Initialize classification model $\Theta _ { 0 }$ ;   
+9: for $_ i$ in 0, ..., N do   
+10: if $i \geq 1$ do   
+11: Observe $s _ { i }$ and produce $a _ { i } ^ { [ 1 ] } \sim \pi _ { \eta } ( s _ { i } )$ ;   
+12: Allocate $\mathcal { M } _ { \mathrm { o l d } }$ and $\mathcal { M } _ { \mathrm { n e w } }$ using Eq. 1;   
+13: Produce $a _ { i } ^ { [ 2 ] } \sim \pi _ { \phi } ( a _ { i } ^ { [ 1 ] } , s _ { i } )$ ;   
+14: Allocate $\{ \mathcal { M } _ { j } ^ { A } \} _ { j = 0 } ^ { i }$ and $\{ \mathcal { M } _ { j } ^ { B } \} _ { j = 0 } ^ { i }$ using Eq. 2;   
+15: Update $\mathcal { E } _ { 0 : i - 1 }$ using herding [40];   
+16: Save $\mathcal { E } _ { 0 : i - 1 }$ in $\mathcal { M } _ { \mathrm { o l d } }$ and free $\mathcal { M } _ { \mathrm { n e w } }$ ;   
+17: Observe new data and load $\mathcal { D } _ { i }$ into $\mathcal { M } _ { \mathrm { n e w } }$ randomly;   
+18: Initialize $\Theta _ { i }$ with $\Theta _ { i - 1 }$ and train it using $\mathcal { E } _ { 0 : i - 1 } \cup \mathcal { D } _ { i }$ ;   
+19: Compute validation accuracy $r _ { i }$ ;   
+20: Compute $\begin{array} { r } { R _ { z } ^ { k } = \sum _ { i = 0 } ^ { N } r _ { i } } \end{array}$ and update $b$ ;   
+21: Compute $\nabla _ { \eta , \phi } J ( \eta , \phi )$ using Eq. 5;   
+22: Update $\eta$ and $\phi$ using Eq. 6.
+
+and implementation details (Section 5.1), followed by the experimental results and analyses (Section 5.2).
+
+# 5.1 Datasets and Implementation Details
+
+Datasets. We use three benchmarks based on two datasets, CIFAR-100 [24] and ImageNet [44], following common settings [13, 18, 40, 30]. CIFAR-100 [24] contains 60, 000 samples of $3 2 \times 3 2$ color images from 100 classes. There are 500 training and 100 test samples for each class. ImageNet (ILSVRC 2012) [44] contains around 1.3 million samples of $2 2 4 \times 2 2 4$ color images from 1, 000 classes. There are about 1, 300 training and 50 test samples for each class. ImageNet has two CIL settings: ImageNet-Subset is based on a subset of 100 classes; and ImageNet-Full uses the full set of 1, 000 classes. The 100-class data for the ImageNet-Subset are sampled from ImageNet. For the experiments on PODNet [13] and POD-AANets [30], we use the same class orders and hyperparameters as [13]. For the experiments on LUCIR [18] and LUCIR-AANets [30], we use the same class orders and hyperparameters as [18].
+
+Benchmarks. We follow the benchmark protocol used in [13, 18, 30, 31]. Given a dataset, the initial (the 0-th phase) model is trained on the data of half of the classes. Then, it learns the remaining classes evenly in the subsequent $N$ phases. Assume there is an initial phase and $N$ incremental phases in the CIL system. The total number of incremental phases $N$ is set to be 5, 10 or 25 (for each the setting is called “ $N$ -phase” setting). At the end of each individual phase, the learned model in each phase is evaluated on the test set containing all seen classes. In the tables, we report average accuracy over all phases and the last-phase accuracy, where the latter indicates the degree of forgetting.
+
+Network Architectures. Following [18, 30, 40, 52], we use a 32-layer ResNet [40] for CIFAR-100 and an 18-layer ResNet [17] for ImageNet. Please note that it is standard to use a shallower ResNet for ImageNet. The 32-layer ResNet consists of an initial convolution layer and three residual blocks (in a single branch). Each block has ten convolution layers with $3 \times 3$ kernels. The number of filters starts from 16 and is doubled every next block. After these three blocks, there is an average-pooling layer to compress the output feature maps to a feature embedding. The 18-layer ResNet follows the standard settings in [17]. We deploy AANets using the same parameters as its original paper [30].
+
+Table 1: Average accuracies $( \% )$ across all phases using two state-of-the-art methods (LUCIR $+$ AANets and POD $+ .$ AANets [30]) $w /$ and $w / o$ our RMM plugged in. The upper block is for recent CIL methods. For fair comparison, we re-implement these methods using our strict memory budget (see “Memory Budget” in Section 5.1) based on the public code. The results of using another common budget setting and the detailed numbers (confidence intervals and last-phase accuracies) are provided in the supplementary materials.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">CIFAR-100</td><td colspan="3">ImageNet-Subset</td><td colspan="3">ImageNet-Full</td></tr><tr><td>N=5</td><td>10</td><td>25</td><td>5</td><td>10</td><td>25</td><td>5</td><td>10</td><td>25</td></tr><tr><td>LwF[29]</td><td>56.79</td><td>53.05</td><td>50.44</td><td>58.83</td><td>53.60</td><td>50.16</td><td>52.00</td><td>47.87</td><td>47.49</td></tr><tr><td>iCaRL [40]</td><td>60.48</td><td>56.04</td><td>52.07</td><td>67.33</td><td>62.42</td><td>57.04</td><td>50.57</td><td>48.27</td><td>49.44</td></tr><tr><td>LUCIR [18]</td><td>63.34</td><td>62.47</td><td>59.69</td><td>71.21</td><td>68.21</td><td>64.15</td><td>65.16</td><td>62.34</td><td>57.37</td></tr><tr><td>Mnemonics [31]</td><td>64.59</td><td>62.59</td><td>61.02</td><td>72.60</td><td>71.66</td><td>70.52</td><td>65.40</td><td>64.02</td><td>62.05</td></tr><tr><td>PODNet [13]</td><td>64.60</td><td>63.13</td><td>61.96</td><td>76.45</td><td>74.66</td><td>70.15</td><td>66.80</td><td>64.89</td><td>60.28</td></tr><tr><td>LUCIR-AANets [30]</td><td>66.88</td><td>65.53</td><td>63.92</td><td>72.80</td><td>69.71</td><td>68.07</td><td>65.31</td><td>62.99</td><td>61.21</td></tr><tr><td>w/ RMM (ours)</td><td>68.42</td><td>67.17</td><td>64.56</td><td>73.58</td><td>72.83</td><td>72.30</td><td>65.81</td><td>64.10</td><td>62.23</td></tr><tr><td>POD-AANets [30]</td><td>66.61</td><td>64.61</td><td>62.63</td><td>77.36</td><td>75.83</td><td>72.18</td><td>67.97</td><td>65.03</td><td>62.03</td></tr><tr><td>w/ RMM (ours)</td><td>68.86</td><td>67.61</td><td>66.21</td><td>79.52</td><td>78.47</td><td>76.54</td><td>69.21</td><td> 67.45</td><td>63.93</td></tr></table>
+
+For policy functions $\pi _ { \eta }$ and $\pi _ { \phi }$ , we use two-layer FC networks. All actions are discretized at 0.1 intervals to reduce the search space and get a tolerable training overhead.
+
+Hyperparameters and Configuration. The training of the classification model $\Theta$ exactly follows the uniform setting in [13, 18, 30, 31]. On CIFAR-100 (ImageNet-Subset/Full), we train it for 160 (90) epochs in each phase, and divide the learning rate by 10 after 80 (30) and then after 120 (60) epochs. Then, we fine-tune the model for 20 epochs using only exemplars (including the preserved exemplars of the new data to be used in future phases). We use an SGD optimizer and an ADAM optimizer for the classification model and policy functions, respectively. More details are given in the supplementary.
+
+Memory Budget. There are two popular settings about memory budget in related work. One uses a bounded memory budget with a fixed capacity for all phases [18, 31, 40]. Another one allows the memory budget to grow along with phases [18, 20, 49]. The first one is more strict and thus used as the major setting in our paper (note that the results and analyses using the second setting are given in the supplementary materials). In every benchmark, the total budget of memory depends on the phase number $N$ . For example, on CIFAR-100, the total memory budget is set as 7, 000 samples when $N { = } 5$ (7, 000 samples $= 1 0$ classes/phase $\times 5 0 0$ samples/class $+ ~ 2$ , 000 samples). Please note that 2, 000 is a bounded memory budget allocated since the 0-th phase for saving exemplars. More clarifications about memory budget are given in the supplementary. For fair comparison, we re-implement related methods and report the results in Table 1 if their original results (in the respective papers) were obtained in a different setting of memory budget.
+
+# 5.2 Results and Analyses
+
+Table 1 presents the results of two state-of-the-art methods (LUCIR $+$ AANets and POD $+$ AANets [30]) w/ and $w / o$ our RMM plugged in, and some recent CIL work [13, 18, 29, 31, 40]. Table 2 shows the ablation study in 6 settings. Figure 4 plots the changes of the average number of exemplars per old/new class for the incremental phases.
+
+Comparing to the State-of-the-Art. From Table 1, we make the following observations. 1) Our RMM consistently improves the two top baselines LUCIR $^ +$ AANets and POD $^ +$ AANets [30] in all settings. E.g., LUCIR-AANets $w /$ RMM and POD-AANets w/ RMM respectively get $2 . 7 \%$ and $3 . 1 \%$ average improvements on the ImageNet-Subset. 2) Our POD-AANets $w /$ RMM achieves the best performances. Interestingly, we find that our RMM can boost performance more when the number of phases is larger. For example, when $N { = } 2 5$ , RMM improves POD-AANets by $3 . 6 \%$ and $4 . 4 \%$ on CIFAR-100 and ImageNet-Subset, respectively. These two numbers are $2 . 3 \%$ and $2 . 1 \%$ when $N { = } 5$
+
+<table><tr><td rowspan="3">Ablation Setting</td><td colspan="4">CIFAR-100</td><td colspan="4">ImagNet-Subset</td></tr><tr><td>N=5</td><td></td><td>10</td><td>25</td><td></td><td>5</td><td>10</td><td>25</td></tr><tr><td>Avg</td><td>Last</td><td>Avg Last</td><td>Avg</td><td>Last</td><td>Avg Last</td><td>Avg Last</td><td>Avg</td><td>Last</td></tr><tr><td>1 BaseRow</td><td>66.61</td><td>57.81</td><td>64.61 55.70</td><td>62.63</td><td>52.53</td><td>77.36 70.02</td><td>75.83</td><td>68.97</td><td>72.18 63.89</td></tr><tr><td>2 One-level RL</td><td>67.92 58.61</td><td></td><td>66.94 58.31</td><td></td><td>65.95 56.44</td><td>78.50 72.00</td><td></td><td>78.15 71.00</td><td>75.47 67.47</td></tr><tr><td>3 Two-level RL (Used) 68.86 59.00</td><td></td><td></td><td>67.61 59.03</td><td></td><td>66.21 56.50</td><td>79.52 73.80</td><td></td><td>78.47 71.40</td><td>76.54 68.84</td></tr><tr><td>margin</td><td>+2.3</td><td>+1.2</td><td>+3 +3.3</td><td>+3.6</td><td>+4</td><td>+2.1</td><td>+3.8 +2.6</td><td>+2.4</td><td>+4.4 +5</td></tr><tr><td>4 Two-level RL (T.P.) margin</td><td>68.62 59.40</td><td></td><td>67.22 58.20</td><td></td><td>65.82 56.20</td><td>78.81 72.42</td><td></td><td>77.68 70.77</td><td>75.29 68.81</td></tr><tr><td>5 UpperBound RL</td><td>+2</td><td>+1.6</td><td>+2.6+2.5</td><td></td><td>+3.2 +3.7</td><td>+1.5+2.4</td><td></td><td>+1.9 +1.8</td><td>+3.1 +4.9</td></tr><tr><td>6 Cross Val Fixed</td><td>70.00 61.12</td><td></td><td>68.36 60.00</td><td></td><td>66.56 56.74 65.73 55.51</td><td>80.01 74.31 77.96 70.31</td><td></td><td>78.95 71.97</td><td>76.99 69.14</td></tr><tr><td></td><td>67.50 58.48</td><td></td><td>66.69 57.19</td><td></td><td></td><td></td><td></td><td>76.70 69.08</td><td>74.18 66.10</td></tr></table>
+
+Table 2: The evaluation results in the ablation study $( \% )$ . “T.P.” denotes our results using the Policy functions Transferred from another dataset. “Avg”, “Last”, and “Used” denote the average accuracy over all phases, the last-phase accuracy, and the results used as ours in Table 1, respectively. BaseRow is from the sota method POD-AANets [30]. Row 2 is for learning Level-1 policy. Row 3 is for learning Level-1 and Level-2 policies in a hierarchical way. Row 4 is for using Transferred Policies (from the other dataset in the table), when RL is costly or impossible on target CIL tasks. The bottom lines are two oracles: training the RL model on the target CIL task (Row 5) and using cross-validation to find the best fixed memory allocation between old and new classes (Row 6).
+
+This indicates that the superiority of our RMM is more obvious in challenging settings (where the forgetting problem is more serious due to the more frequent model re-training through phases).
+
+Ablation Settings. Table 2 shows the results of our ablation study. Row 1 is for the baseline method POD-AANets [30]. Row 2 is for learning only Level-1 policy $\pi _ { \eta }$ (where each class gets an even split of the memory). Row 3 is for learning both Level-1 policy $\pi _ { \eta }$ and Level-2 policy $\pi _ { \phi }$ in our proposed hierarchical method, and its results are used in Table 1 as “ours”. Row 4 is for using Policy functions Transferred from another dataset (T.P.), which means on the target CIL dataset there is no training of RMM. Here, for CIFAR-100, we use the policy functions learned on ImageNet-Subset, and vice versa. On the last two rows, we show two oracle settings. Row 5 is the upper bound that assumes all past and future data are accessible during training RMM on the target CIL dataset. Row 6 is for using cross-validation (i.e., all past, future, and validation data are accessible) to find the best fixed memory split between old and new class data, e.g., $\textstyle \mathrm { \frac { o l d } { n e w } } = 0 . 7$ is chosen and then used in all phases. The details of chosen split rates are given in the supplementary materials.
+
+Ablation Results. Hierarchical: In Table 2, when comparing Row 2 to Row 1, it is clear that leveraging reinforcement learning yields better results as it can derive adaptive memory allocation between old and new data. Using class-specific memory management further increases the model performance (i.e., comparing Row 3 to Row 2), even though we divide the classes into only two groups. T.P. (Transferred Policy functions): Comparing Row 4 to Row 3, we can see that using transferred policy functions (trained on another dataset) achieves comparable performance, and Row 4 does not require any reinforcement learning on the target CIL dataset. Oracle: Comparing Row 3 to Row 5, we see that learning RMM on pseudo CIL tasks is comparable to the upper bound case where all training and validate data are accessible, given the fact that the latter needs higher computational overhead and violates the standard CIL protocol. Row 6 results are consistently lower than ours in Row 3, although cross-validation has access to all past, future, and validation data.
+
+Allocated Memory. Figure 4 shows the change of the average number of samples per class in three ablative settings. Solid and dashed lines represent old and new classes, respectively. From the plots, we have two observations. 1) Learning RMM on the pseudo or target CIL tasks (green and orange lines), we can obtain similar memory management results (i.e., actions). This means the learned policy is transferrable in non-stationary continuous environments. This matches the conclusion of continuous adaptation in [2]. 2) Using our RMM method achieved more balanced memory sizes between exemplars and new data. For example, in the 1-st phase of the 5-phase setting, “UpperBound
+
+![](images/70170b079fa509f7fe9e447e26b1993b1d5aef6ac3af3e5c866ecabdd6dd20c7.jpg)  
+Figure 4: The memory allocated for “Old” and “New” across different phases on CIFAR-100. The second and fourth plots are enlarged versions of the first and third plots, respectively. Solid and phase (N=5)dashed lines denote old and new classes, respectively. The baseline is POD-AANets [30]. “Two-level RL” and “UpperBound RL” correspond to Row 3 and Row 5 in Table 2, respectively.
+
+RL” and “Two-level RL” allocate around 100 samples for both exemplars and new data. While the baseline setting has 40 and 500 samples for them, respectively. It thus addresses the data imbalance problem for CIL in a learnable way.
+
+# 6 Conclusions
+
+We propose the reinforced memory management (RMM) method specially for tackling CIL tasks. The hierarchical reinforcement learning (RL) framework (two levels) in RMM is capable of making more adaptive memory allocation actions than using standard RL (one level). Using the generated pseudo tasks in RMM solves the issue of data incompatibility between CIL and RL. Corresponding experimental results show that the policy trained on these pseudo tasks can be directly applied to target tasks without any computational overhead. Our overall method of RMM is generic, and its trained policy (with or without using an in-domain dataset) can be easily incorporated into exemplar replaying-based CIL methods to boost performance.
+
+# Limitations and Societal Impact
+
+We analyse the limitations and potential negative societal impact in the following three aspects.
+
+• Complexity. Training RMM takes an additional time cost. According to Algorithm 1, the cost is $O ( m K Z )$ times higher than the time used for the target CIL task. However, the training of RMM policy is offline and can use a different dataset (see Table 2) — RMM pre-learns a robust policy from synthesized pseudo tasks and can be directly applied for memory management in real CIL tasks. The overhead of applying this policy is very little, e.g., $0 . 6 3 \%$ and $1 . 1 2 \%$ of the total training time respectively on CIFAR-100 and ImageNet (Subset and Full), taking $\mathrm { P O D + }$ AANets as the baseline.
+
+• Technical assumptions. We build the framework of RMM based on a series of technical assumptions, which might not directly hold for all real-world continual-learning applications. When applying our method to mission-critical problems, particular care is required when modeling the system.
+
+• Privacy issues. Keeping the old class exemplars has the issue of data privacy. This calls for future research that explicitly forgets or mitigates the identifiable feature of the data.
+
+# Acknowledgments and Disclosure of Funding
+
+This research was supported by $\mathbf { A } { ^ { * } \mathbf { S } } \mathbf { T } \mathbf { A } \mathbf { R }$ under its AME YIRG Grant (Project No. A20E6c0101), Alibaba Innovative Research (AIR) programme, and Max Planck Institute for Informatics.
+
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parse/train/BkS3fnl0W/BkS3fnl0W.md

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+# SEMI-SUPERVISED OUTLIER DETECTION USING GEN-ERATIVE AND ADVERSARY FRAMEWORK
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+In a conventional binary/multi-class classification task, the decision boundary is supported by data from two or more classes. However, in one-class classification task, only data from one class are available. To build a robust outlier detector using only data from the positive class, we propose a corrupted GAN (CorGAN), a deep convolutional Generative Adversary Network requiring no convergence during the training process. In the adversarial process of training the CorGAN, the Generator is supposed to generate outlier samples for the negative class, and the Discriminator is trained to distinguish training datasets (i.e., positive samples) from generated data from the Generator (i.e., negative samples). We also propose a lot of techniques to improve the performance of the built classifier (i.e., the Discriminator). The proposed model outperforms the traditional method $\mathrm { P C A } +$ PSVM (Scholkopf et al., 2000) and the solution based on Autoencoder (Thompson ¨ et al., 2002).
+
+# 1 INTRODUCTION
+
+(Hodge & Austin, 2004) addresses three fundamental approaches detecting outliers. The first approach is unsupervised clustering that identifies outliers without using any prior knowledge of the data. The second approach, supervised classification, requires labeled data from both positive class and negative class. The third addressed approach detects outliers using only data from the positive class via semi-supervised learning. Semi-supervised learning has gained increasing attention in recent years. One-class classification(OCC), as a typical semi-supervised learning technique, is applied to detect outliers using only positive examples from one class. The semi-supervised learning in this paper focuses on the OCC technique.
+
+To motivate the importance of OCC, we first make an introduction to a classic application scenario. In industry, machine monitoring system is used everywhere to detect machine faults. A classifier should be constructed to detect when the machine behaves abnormally. Obviously, the training data for the positive class is easy to obtain by measuring the normal operations of the machine. However, only limited training data is available, even totally unavailable. In such case, a classifier should be built only on positive training data. This kind of task is known as OCC task. The name ”oneclass classification” originates from the paper Moya et al. (1993). Other researchers also present similar tasks with other terms such as Outlier Detection (Ritter & Gallegos, 1997), Novelty Detection (Bishop, 1994) or Concept Learning (Japkowicz, 1999). They are used interchangeably in this paper, even though they have specific meanings in other works. One-class classification can be used not only in machine monitoring task but also in many other domains, e.g. Text mining (Basu et al., 2004), Sentiment Analysis (Agarwal et al., 2015) and IT security (Lakhina et al., 2005).
+
+Many solutions have been proposed to solve the one-class classification problem. However, almost none of them shows acceptable performance in high-dimensional space. Neural Network with deep architecture is well known for the ability to manipulate high-dimensional data. It achieves state-ofart results in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics (LeCun et al., 2015). This paper applies a neural network with deep architecture in outlier detection task. Generative adversary framework(GAN) is composed of a Generator $G$ that can be used to generate outliers and a Discriminator that can be trained as a binary classifier. The framework is a potential solution to detect outliers through generating counterexamples. Usually, the Nash equilibrium of the training process of GANs cannot be guaranteed in practice. Our proposed model requires no convergence of the training process since the $G$ is used to generate only outliers instead of high-quality images that are from the distribution the training dataset. The proposed deep architecture solution is implemented, analyzed and compared to other methods.
+
+The first section introduces the one-class classification problem and a potential solution with deeparchitecture neral network. The second section presents the work related to one-class classification problems (i.e., semi-supervised outlier detection). Then, the two primary steps of our solution for one-class classification problem are described in the third section, namely, the training step to optimize model and the detecting step to make an inference. Next, the fourth section proposes a technique to break Nash equilibrium so that the $G$ of GAN can keep generating outliers. Besides, this section also proposes other techniques to improve. The fifth section shows experiments, analyzes the results and compares the performance with that of other methods. Finally, the last section concludes our work and describes future work that remains to be further researched.
+
+# 2 RELATED WORK
+
+Five approaches to solve OCC problem are summarized in (Pimentel et al., 2014). Probabilistic approach estimates the generative probability density function (pdf) of the data from the positive class. The boundaries of normality in the data space are defined by the resultant distribution together with a specified threshold, and an unseen sample is tested whether it comes from the same distribution or not. Thereinto, Gaussian Mixture Models (GMMs) (Lindsay et al., 1989; Bishop, 2006) and Kernel Density Estimators (Parzen, 1962; Vincent & Bengio, 2003; Bengio et al., 2006) have proven to be popular. This approach requires complete density estimation in the feature space. If the data in feature space are high dimensional, huge amounts of data are required to fit the model because of the curse of dimensionality. Only when the data from the target class are large enough can this kind of method perform well. Another well-known approach, Reconstruction-based approach, first train a model minimising the reconstruction error of training data with positive labels. Then, the trained model assigns an outlier score, the distance between the input representation vector and the output of the model, for each test example. (Markou & Singh, 2003) reviews lots of the neural network-based methods. Additionally, PCA can also detect outliers by comparing the example before and after transformation. The reconstruction error approach abandons some information with low variance during reconstruction. However, the abandoned low-variance information has proven to be most informative (Tax & Muller, 2003). ¨
+
+Additionally, Distance-based approach, e.g. Nearest neighbour-based methods (Bay & Schwabacher, 2003; Breunig et al., 2000) and Clustering-based methods (Barbara et al., 2002; He ´ et al., 2003), avoids estimating pdf explicitly, but it requires a well-defined distance/similarity measure, which is especially difficult in high-dimensional space. Another approach is domain-based, which creates the boundary based on the structure of normal data without considering the density of the positive class. One-class SVM (Scholkopf et al., 2000) and Support vector data description ¨ (SVDD) (Tax & Duin, 1999) are two basic ones. However, the choice of an appropriate kernel function is not easy, which determines the computational cost. Moreover, the hyperparameters that control the tightness of the boundary are also difficult to select. Lastly, Information-theoretic approach tries to distinguish normal data and outliers by computing information content of dataset using information measure. Similarly, the selection of appropriate information-theoretic measure is challenging.
+
+The approaches described above learn from available positive samples only. Approaches that learn from both target samples and artificial outliers are also researched. (Hempstalk et al., 2008; Fan et al., 2004) generate outlier with a predefined distribution. The strong assumptions about the outlier data distribution in these approaches may be violated in real datasets (Abe et al., 2006). (Tax & Duin, 2001) proposes a method for generating artificial outliers, uniformly distributed in a hypersphere. However, in high-dimensional data space, their proposed technique is not feasible anymore because it is tough to get a confident estimate of the target volume due to the large difference in volume of the target and outlier class. (Banhalmi et al., 2007) extends dataset by generating outlier ´ examples distributed around the positive class. The approach first finds boundary points explicitly using SVM, which is computationally expensive. Then it generates negative examples only around positive class using a distance measure, which causes infeasibility in high-dimensional space. Our proposed CorGAN generates negative examples including both ones around the positive class and ones far from the positive class. Moreover, the model requires no explicit distance measure and does not need to find boundary points explicitly.
+
+Neural networks with deep architecture have already been used in OCC task, but mostly in Reconstruction error approaches (Markou & Singh, 2003). To our knowledge, our proposed CorGAN is the first work to generate outliers for OCC via deep architecture (i.e., Generative Adversary Network). A variant of the GAN framework (CatGAN) is applied to solve multi-class classification task in unsupervised or semi-supervised fashion (Springenberg, 2015). (Odena, 2016) does a further research about semi-supervised learning using GANs. (Schlegl et al., 2017) proposes AnoGAN to apply GAN in Anomaly Detection, which requires the Nash-equilibrium at the end of the training process. Nevertheless, all variants of GAN and the original one are known for its unstable training process.
+
+# 3 OUTLIER DETECTION USING CORGAN
+
+The proposed model and the improved techniques can be generalized to various kinds of data. To show the performance in high-dimensional space, we illustrate our model on image data. The proposed parametric method is composed of two steps:
+
+1. Training Step: Training the CorGAN with the improved techniques;   
+2. Inference Step: Detecting outliers using the resulting $D$ of the trained CorGAN
+
+# 3.1 GENERATIVE ADVERSARY NETWORK
+
+Generative Adversary Network(GAN) is a framework for training generative models via an adversarial process (Goodfellow et al., 2014). The framework consists of two components, a generative model (Generator $G$ ) and a discriminative model (Discriminator $D$ ). The $G$ aims to capture the data distribution. The $D$ estimates the probability that a sample came from the training data rather than the Generator. This framework corresponds to a minimax two-player game. In the training procedure, the $D$ is trained to distinguish samples in training datasets from generated samples by assigning a high probability to the former and a low probability to the latter. Contrarily, the objective of $G$ is to maximize the probability of $D$ making a mistake. After the Nash-equilibrium of the training process, the output probability of the $D$ is always 0.5. In case of the convergence, the $G$ is capable of generating realistic images that have same/similar distribution as in training dataset, and the $D$ cannot make right discrimination anymore. The biggest advantage of this framework is that no Markov chains or unrolled approximate inference networks are required in the training and sampling process.
+
+# 3.2 STEP1: TRAINING THE CORGAN
+
+Architectures of the Generator and the Discriminator are neural networks, such as Multilayer Perceptron, Deep Convolutional Neural Network (LeCun et al., 1989), Convolutional Neural Network Cascade (Springenberg, 2015) and Recurrent Neural Network (Rumelhart et al., 1988). The BackPropagation algorithm can be used to train both the generative model and the discriminative model. The architecture applied in the proposed CorGAN is shown in Figure 1.
+
+The $G$ generally starts from prior distribution $p _ { z } ( z )$ (input noise variable $_ z$ ). In the case of convergent GANs, the $G$ maps the prior distribution to the training data distribution $p _ { i n l i e r } ( { \pmb x } )$ . The $G$ of CorGAN is used to generate outlier examples. Hence, it is supposed to map the prior distribution to outlier data distribution $G ( z ; \theta _ { g } )$ instead of the training data distribution. As usual, the $D$ maps the input (i.e. the training data or the generated samples) to a single scalar, which represents the probability that the input came from training datasets instead of the $G$ . The target value of the $D$ is $a _ { t } = 1$ for the input data from training dataset and $a _ { o } = 0$ for the input data generated by the $G$ . The $D$ as a binary classifier is trained to minimize the cost V(D):
+
+$$
+\displaystyle { \operatorname* { m i n } _ { D } V ( D ) = \mathbb { E } _ { z \sim p _ { z } ( z ) } \log ( D ( G ( z ) ) - a _ { o } ) + \mathbb { E } _ { { \mathbf { x } } \sim p _ { i n l i e r } ( { \mathbf { x } } ) } \log ( a _ { t } - D ( { \mathbf { x } } ) ) }
+$$
+
+The objective of the $G$ of the CorGAN is to fool the D, but not necessarily maximise the probability D making a mistake. The new target value is $a _ { n e w } \in [ 0 , 1 ]$ (see section 4.2). The $G$ of the CorGAN
+
+![](images/b0691fb608dbcbacd24c0cc26dcae649d23a97aefb6b0fa4cc6e96ced0eede19.jpg)  
+Figure 1: The basic architecture of the CorGAN
+
+is trained to minimise the cost U(G):
+
+$$
+\operatorname* { m i n } _ { G } U ( G ) = \mathbb { E } _ { z \sim p _ { z } ( z ) } \log ( | a _ { n e w } - D ( G ( z ) ) | )
+$$
+
+The CorGAN model is updated via back-propagation algorithm. If the $D$ is overly optimised without updating the $G$ , it will result in overfitting problem. The $D$ and the $G$ will be updated simultaneously or alternately to avoid the problem, e.g. k steps of optimizing the $D$ and one step of optimizing the $G$ . The traditional GANs reach Nash equilibrium after several training epochs. The new objective of the $G$ of CorGAN breaks Nash equilibrium of the training process, which causes that the $G$ can keep generating outlier samples.
+
+The inlier data is taken as training data in the CorGAN. In the adversarial process of training CorGAN, the $G$ is supposed to generate outlier samples for the negative class. The $D$ is trained to assign a high probability value to data from training datasets (i.e., the positive class) and a small probability value to generated data from the G (i.e., the negative class). The generated outliers not only distribute around the positive class but also cover feature space far away from the positive class. In order that the $G$ can map a prior distribution to a huge data space except for the positive class, we proposed a lot of improved techniques (section 4).
+
+# 3.3 STEP2: DETECTING OUTLIERS USING DISCRIMINATOR
+
+In the inference step, the resulting $D$ outputs a relatively high probability for data subjective to the distribution $p _ { i n l i e r }$ and a relatively low probability for data not from the distribution $p _ { i n l i e r }$ . That is to say that, if the output is a low probability in the outlier-detecting process, the input is predicted as an outlier. What is a low probability? So, we need a probability threshold to decide whether an output probability is high or low. The output of the sigmoid activation function of the last layer is a scalar value in the interval $( 0 , 1 )$ , we can intuitively set $t$ as the threshold. In that case, the input is an outlier, if the output from the $D$ is small than $t$ , otherwise an inlier.
+
+The one-class classification task is an extreme case of the imbalanced training. The optimal value of the threshold $t$ is not 0.5. It mainly depends on how the model is trained and the concrete application scenario. If the model is trained by specifying a new objective for the $G$ (like in CorGAN), the $D$ model learns distribution from training datasets for a long time. However, the $D$ is trained with data from a more extensive outlier distribution using the same time. The resulting $D$ will present a relatively higher probability for data that follow the same distribution as the training data (i.e., for inliers). So, the threshold $t$ with a value higher than 0.5 shows a better performance. We do not evaluate the $D$ on a single user-specified threshold.
+
+One-class classification, also called Outlier Detection, can be evaluated with F1-score, which is harmonic mean of precision and recall. The accepted fraction of the positive class $f _ { T + }$ and the rejected fraction of the negative class $f _ { O - }$ are both together also as a popular measure for OCC. However, the score of those measures strongly depends on the specified threshold. To justify our model objectively, the performance of the $D$ in this paper will be evaluated with Receiver operating characteristic curve (ROC) and Area under the ROC curve (AUC). The robustness of the built $D$ will be tested on various datasets.
+
+# 4 IMPROVED TECHNIQUES FOR GAN IN OCC
+
+If the training process reaches Nash equilibrium, the $G$ is able to generate examples following the distribution $p _ { i n l i e r }$ (see figure 2), and the output probability of the $D$ is always 0.5 for inliers and an unexpected value for outliers. It is difficult to distinguish outliers from inliers via a threshold. Our proposed corrupted generative adversary network (CorGAN) is a GAN without convergence. To avoid the Nash equilibrium that the training process can reach, we propose several techniques to break the convergence and build a robust outlier identifier. Thereinto, specifying a new objective for the $G$ is a basic one to keep it generating outlier samples, and other optional techniques further improve the performance of the model.
+
+![](images/b282e3949b137bb05b809ba6630e74990cf02e792104df3e154b5d11dd8c22d5.jpg)  
+Figure 2: Comparison between the generated data and the training data: The images of handwritten digit nine are training data. After several training epochs, the generated images and the training data are visualised in the figure.
+
+# 4.1 EARLY STOPPING
+
+In early training epochs (i.e., before convergence), the $G$ has no ability to generate data that follows the distribution $p _ { i n l i e r }$ . Meanwhile, the $D$ is trained with the training data with positive labels and the generated data with negative labels. Distributions from $G$ are different from the distribution of training datasets before convergence. The $D$ recognizes the distribution of training datasets by presenting a high probability. Early Stopping before convergence can obtain a well-behaved Discriminator.
+
+In term of implementation of this technique, we do not explicitly stop the training at a particular epoch, but always save the best model. Similar to the model selection, we take the best Discriminator as the final classifier, which appears definitely before the convergence of the training process. The performance of the $D$ is tested regularly during the training process. The score Area Under the Curve of $f _ { T + }$ (inlier accepted fraction), called positively biased AUC (see figure 3) is used to evaluate the performance of the $D$ . The $D$ saved with best biased AUC score shows not optimal but near-optimal performance on the test datasets. The objective of Early Stopping is defined as follows:
+
+$$
+\operatorname* { m a x } _ { D } A U C _ { b i a s e d } = \int _ { 0 } ^ { 1 } f _ { T + } ( t ) d t
+$$
+
+where $t$ is the threshold and $f _ { T + } ( t )$ is inlier accepted fraction of the Discriminator given the specific threshold $t$ .
+
+![](images/a9528f61872dc2205ff7dd657ee76cbca461c73439f091c6ab5769fdab4e713f.jpg)  
+Figure 3: Area Under the Curve of inlier accepted fraction: The figure describes the relationship between the inlier accepted fraction and the specified threshould. Given the specified threshold $0 . 7$ , the point $P$ in the curve corresponds to the accepted fraction of inliers 0.68. Since no outlier is available, the area under this curve (positively biased AUC) is a good measure to select the near optimal model.
+
+Table 1: The behavior of the $G$ and the performance of the $D$ are presented in case of different new target values.   
+
+<table><tr><td rowspan=1 colspan=1>new target value anew</td></tr><tr><td rowspan=1 colspan=1>anew = 1: The objective of G is the exact same as that of the convergent GAN(Goodfellow et al., 2014). The training will converge.</td></tr><tr><td rowspan=1 colspan=1>anew E (~ O.9,1): The such adjustment of the objective of the G is proposed in(Salimans et al.,2O16) to improve the training process of GANs. The training processwill converge as well.</td></tr><tr><td rowspan=1 colspan=1>anew ∈ (~ O.5,~ 0.9): The G will generate data far from the distribution pinlierat the beginning of the training phase because of the random initialization.After several training epochs,it will generate data that distribute around the positive class.The tighter the boundary is,the larger space the generated data cover. The value 0.9results in most tight boundary.</td></tr><tr><td rowspan=1 colspan=1>anew ∈ [0,~ O.5): The G has similar objective to that of the D. It will tend togenerate data,from which the D can easily distinguish the training data. That is to say that allthe generated data distribute far from the distribution Pinlier·</td></tr></table>
+
+# 4.2 SPECIFYING A NEW OBJECTIVE FOR THE GENERATOR
+
+Even though Early Stopping avoids the problem the convergence causes, GAN can only be trained with a limited number of epochs. Hence, Early Stopping can only guarantee a high inlier accepted fraction $f _ { T + }$ , but not necessarily high outlier rejected fraction $f _ { O - }$ because the $\mathbf { D }$ is only trained with a certain number of generated samples (i.e., outliers). To build a robust outlier identifier against as many kinds of outlier distributions as possible, we should train the $D$ with as many generated samples as possible, which have different distribution from the distribution $p _ { i n l i e r }$ .
+
+We can explicitly break Nash equilibrium by specifying a new objective for $G$ . Without modification, the objective of $G$ is to maximise the probability of the $D$ making a mistake. We propose a new objective for $G$ :
+
+$$
+\operatorname* { m i n } _ { G } U ( G ) = \mathbb { E } _ { z \sim p _ { z } ( z ) } \log ( | 0 . 9 - D ( G ( z ) ) | )
+$$
+
+Instead of maximising the probability that $D$ makes a mistake, the new objective is that the $D$ makes a mistake with a certain probability. The new target value used to calculate the cost for updating the $\mathbf { G }$ is $a _ { n e w } = 0 . 9$ . The choice of the value $a _ { n e w }$ is justified in the table 1. In case of $a _ { n e w } = 0 . 9$ , the $G$ explores the largest space, and the built $D$ will show robust performance.
+
+# 4.3 ATTACHING MORE IMPORTANCE TO GENERATED DATA
+
+The cost of the $D$ consists of two parts. These two parts are caused respectively by the training data and the generated data. Generally, the two parts are simply added together as the total cost for updating the parameters of the $D$ . That is to say that the training data and the generated data are treated with the same importance. They can be treated differently by assigning a weight to one of them to broaden the search space of parameters. The objective of the $D$ is defined as follows:
+
+$$
+\operatorname* { m i n } _ { D } V ( D ) = \mathbb { E } _ { z \sim p _ { z } ( z ) } \log ( D ( G ( z ) ) - a _ { o } ) + w * \mathbb { E } _ { { \pi } \sim p _ { i n l i e r } ( { \bf x } ) } \log ( a _ { t } - D ( { \bf x } ) )
+$$
+
+, where $w \in ( 0 , 1 )$ is a hyperparameter. The value of $w$ can be selected by validation process with positively biased AUC score. While the outlier distributions are various and difficult to recover all of them, the inlier distribution is rather simple and easy to learn. During the training process, the cost that generated data caused should be reduced as far as possible by updating parameters of the $D$ . In other words, the generated data should be attached more importance by specifying the value of weight. Compared to the general case that the two parts of cost are not treated differently, this method shows a better performance on the test datasets whose distributions are far from the training dataset.
+
+# 4.4 COMBINING PREVIOUSLY GENERATED DATA
+
+Compared to the method of Early Stopping, the method of specifying a new objective for G presents a better performance, because the new objective trains $D$ with arbitrarily more generated data that are not from the distribution $p _ { i n l i e r }$ . With the new specified objective, the training procedure does not converge, and the $G$ is able to keep generating outliers. The $D$ can be trained with arbitrarily many generated distributions. However, the space of distribution learned by $D$ is limited to a great extent. On the one hand, the generated distribution always stays near the positive class after several training epochs. On the other hand, the $D$ can forget the previously learned distributions because of the limited capacity.
+
+In this subsection, we proposed a technique to broaden the learned distributions. The performance of the $D$ can be improved by being regularly trained with previously generated data. We can train the CorGAN with mini batches (batch size $s$ ) that combine the data generated recently and previously. The combined training data can avoid that the $D$ forgets the learned distribution to some degree.
+
+There exist a large amount of generated data in the training procedure. Which ones should be chosen to train $D$ and prevent it forgetting the previously generated distributions? Because the generated data can be arbitrarily many, it is inadvisable and impossible to save all of them. In this case, the generated data can be treated as stream data $\left( X _ { 1 } , X _ { 2 } , \ldots , X _ { t } \right)$ . We apply a Reservoir Sampling Algorithm (Vitter, 1985) to sample previously generated images. This algorithm samples examples from the stream data with the same probability (see equation 6) and specifies a reservoir $R$ to save the sampled examples.
+
+$$
+P ( X _ { i } \in R ) = \frac { 1 } { t - ( s / 2 ) }
+$$
+
+, where $i \in [ 1 , t - ( s / 2 ) ]$ . The mini batches that are composed of newly generated examples and the sampled examples saved in a reservoir is used to train $D$ . The mini batch $B$ at the timestamp $t$ is defined as follows:
+
+$$
+B = \left\{ R , X _ { t - ( s / 2 ) + 1 } , X _ { t - ( s / 2 ) + 2 } , \ldots , X _ { t } \right\}
+$$
+
+, where $R$ is the reservoir. The objective of the $D$ remains unchanged in the equation 1. The resultant $D$ can identify not only recently generated outliers but also previous ones.
+
+# 5 EXPERIMENTS AND ANALYSIS
+
+In this section, we justify our proposed model and improved techniques with experiments. To demonstrate the robust performance of the built classifier, we evaluate the $D$ on various outlier datasets. We describe the experiment settings of our models and the models to be compared. The experiment results, followed by a strong discussion, are presented in this section.
+
+Table 2: Training -, validation - and test datasets of experiments setting.   
+
+<table><tr><td>Datasets:</td><td>Source of images:</td><td>The Number of images:</td></tr><tr><td>Training dataset</td><td>digit of 9 in MNIST</td><td>4967</td></tr><tr><td>Validation dataset</td><td>digit of 9 in MNIST</td><td>900</td></tr><tr><td rowspan="4">Test dataset</td><td>Inliers: digit of 9 in MNIST</td><td>900</td></tr><tr><td>1.Outliers: digits of O-8 in MNIST</td><td>900</td></tr><tr><td>2.Outliers: CIFAR10</td><td>900</td></tr><tr><td>3.Outliers: Images composed of noise</td><td>900</td></tr></table>
+
+# 5.1 DATASETS AND EVALUATION:
+
+Three datasets are used in the experiments, namely, MNIST (LeCun et al., 1998), CIFAR10 (Krizhevsky, 2009) and an artificial noise image dataset. The image size in MINIST is (28, 28). The size of CIFAR10 images is cropped into (28, 28) by removing pixels along the sides. Especially, we specify a dataset composed of three group of noise images with the same size (28, 28). The values of their pixels are respectively subject to uniform distribution, Gaussian distribution and random values. The table 2 lists training dataset, validation dataset and test datasets. The performance of various approaches will be evaluated and compared with Receiver Operating Characteristic (ROC) and the Area Under the ROC Curve (AUC).
+
+# 5.2 EXPERIMENTS SETTING:
+
+PCA+PSVM: PCA is used to reduce the dimensionality of the high-dimensional data (i.e., images). The number of components K is set such that $9 5 \%$ of the variance is retained $\scriptstyle ( \mathrm { K = 1 } 1 1 $ ). Oneclass SVM proposed in (Scholkopf et al., 2000) is plane-based, called PSVM. To identify outliers ¨ in the feature space, PSVM tries to find a hyperplane that best separates the data from the origin. RBF kernel is used in this experiment. Other settings are defaults in sklearn.svm.OneClassSVM (Pedregosa et al., 2011).
+
+Autoencoder: Autoencoder detects outliers by computing reconstruction error and compares it with a specified threshold. The threshold is based on the difference between the inputs and outputs for the training data. If the reconstruction error for a test sample is larger than the threshold, then the sample is identified as an outlier, otherwise as inlier. To justify our proposal, we compare our model to convolutional autoencoder. The encoder has the same architecture as the Discriminator in CorGAN except for output layer. The decoder also has a same architecture as the Generator in CorGAN. The model is regularised with weight decay $\lambda = 0 . 0 1$ . The parameters are updated with SGD optimisation algorithm, minibatc $\scriptstyle \imath = 1 2 8$ and learning rate $l r { = } 0 . 1$ . The cost function is the cross-entropy function. The model is trained for 30 epochs without pretraining.
+
+CorGAN: The basic architecture of CorGAN, as well as the number of its layers and units, is shown in figure 1. We propose a lot of improved techniques. Since its combinations are numerous, we justify only three main models. The first model is a basic one, $\mathrm { C o r G A N } = \mathrm { G A N }$ with early stopping technique and a new objective for the $G$ (see section 4.2). The new target value $a _ { n e w }$ is set manually to 0.9 for the $G$ . The $G$ is regularised with weight decay $\lambda = 0 . 1$ . The optimisation algorithm is Adam, minibatch $= 1 2 8$ and learning rate $l r = 0 . 0 0 0 2$ . No pretraining is performed. The second model to be justified is based on the first one, $\mathrm { C o r G A N ^ { 2 } = C o r G A N + }$ Attaching more importance to generated images (see section 4.3). The weight is set to 0.5 manually. The third illustrated model is also based on the first one, $\mathrm { C o r G A N ^ { 3 } \bar { \ s } = C o r G A N \ s + \Delta }$ Combining previously generated images (see section 4.4). The minibatch size is composed of 64 images sampled from previous training epoch and 64 newly generated images.
+
+# 5.3 RESULTS AND ANALYSIS:
+
+The results of the experiments are shown in the figure 4 and the table 3. The outlier distribution of the handwritten digits images of the numbers (0-8) is relatively close to the inlier distribution of the number 9. Hence, all the approaches show the worse AUC scores on the first test dataset. The $\mathrm { P C A + P S V M }$ approach shows the better score on the second test dataset than on the noise test dataset. The traditional approach is not robust enough for noise outliers. The solutions based on neural networks often show a better performance against noise data because of the random initialization of its parameters. Especially, our proposed solution based on GAN framework, in which Generator generates many noise examples. The convolutional autoencoder can reconstruct natural images well by detects edges, corners and objects. Therefore, the convolutional autoencoder shows the poor score on natural images. Our proposed solution classifies test examples without reconstruction process, which shows robust performance against outlier natural images as well as noise images.
+
+![](images/596ea6ac1282ab797e6dc3c1a138bfb8fc3bae75d6216625d1ecd5e9bda53ae6.jpg)  
+Figure 4: The figures show the ROC curves of all models on three differenct test datasets. The area under the ROC curve represents the overall performance of a one-class classifier. The model $\mathrm { C o r G A N ^ { 3 } }$ shows robust performance on all the three datasets.
+
+Table 3: The AUC socres of various models are shown in the table. All the models are tested in three datasets: MNIST(9) $^ +$ MNIST(0-8), MNIST(9) $^ +$ CIFAR10, MNIST(9) $^ +$ Noise. Within MNIST(9) images are inliers, and other images are outliers. CorGAN, $\mathrm { C o r G A N ^ { 2 } }$ and $\mathrm { C o r G A N ^ { 3 } }$ are described in section 5.2.   
+
+<table><tr><td rowspan=3 colspan=1></td><td rowspan=1 colspan=3>AUC score:</td></tr><tr><td rowspan=1 colspan=3>MNIST(9)</td></tr><tr><td rowspan=1 colspan=1>MNIST(0-8)</td><td rowspan=1 colspan=1>CIFAR10</td><td rowspan=1 colspan=1>Noise</td></tr><tr><td rowspan=1 colspan=1>PCA+PSVM</td><td rowspan=1 colspan=1>0.8623</td><td rowspan=1 colspan=1>0.9720</td><td rowspan=1 colspan=1>0.9302</td></tr><tr><td rowspan=1 colspan=1>Autoencoder</td><td rowspan=1 colspan=1>0.8943</td><td rowspan=1 colspan=1>0.6785</td><td rowspan=1 colspan=1>0.9704</td></tr><tr><td rowspan=1 colspan=1>CorGAN</td><td rowspan=1 colspan=1>0.8974</td><td rowspan=1 colspan=1>0.9739</td><td rowspan=1 colspan=1>0.9995</td></tr><tr><td rowspan=1 colspan=1>CorGAN2</td><td rowspan=1 colspan=1>0.8343</td><td rowspan=1 colspan=1>0.9937</td><td rowspan=1 colspan=1>0.9999</td></tr><tr><td rowspan=1 colspan=1>CorGAN3</td><td rowspan=1 colspan=1>0.9253</td><td rowspan=1 colspan=1>0.9943</td><td rowspan=1 colspan=1>0.9999</td></tr></table>
+
+Compared to CorGAN, $\mathrm { C o r G A N ^ { 2 } }$ attaches more importance to generated images, which makes classifier more robust again the outliers whose distribution is far from inlier distribution. In consequence, $\mathrm { C o r G A N ^ { 2 } }$ shows the low score on the first dataset, in which the distributions of inliers and outliers are relatively close. In the model $\mathrm { C o r G A N ^ { 3 } }$ , the outlier examples generated previously are combined with newly generated examples to train the Discriminator. In this way, the Discriminator learned a large space of outlier distribution. The model $\mathrm { C o r G A N ^ { 3 } }$ shows the best scores on various test datasets. The robust $\mathrm { C o r G A N ^ { 3 } }$ learns a tight boundary in high-dimensional space. The farther the outlier distribution is from the inlier distribution $p _ { i n l i e r }$ , the better score it shows (see figure 4d).
+
+# 6 CONCLUSION AND FUTURE WORK
+
+In this paper, we present a solution to solve one-class classification problem based on GAN framework and successfully apply the Discriminator of the framework to detect outliers. We illuminate a few techniques to improve the performance and verify the proposed techniques with experiments. First, we choose the near optimal model to detect outliers by saving a better model during the training procedure. Then we specify a new objective for the $G$ so that it can keep generating outliers. Attaching more importance to generated images can further improve the performance of the $D$ . To prevent the $D$ forgetting the previously generated outliers, we combine previously generated outliers from the Generator to train the outlier identifier. These techniques show comparable AUC scores.
+
+In future work, We can further vary the generated outliers to train $D$ . We can specify multiple Generators in the generative adversary framework. The mini batch can combine the data generated by different Generators, which have different objectives, e.g. the different probabilities of D making a mistake. To further explore more generated distribution used to train the $D$ , we can even combine CorGAN with other generative models. Similarly, we must also change the objective of them to fit our goal, since the other generative models are also supposed to generate outliers.
+
+All the proposals in this paper do not leverage distance information(KLD) between distributions within a batch both in the training process and detecting process. Another topic worth studying is the clustering-based method to detect outlier using $D$ of GAN. One potential method of leveraging distance information is to model the closeness between examples in a mini-batch. The modeling process is described in Minibatch Discrimination (Salimans et al., 2016), an improved technique for training GANs.
+
+Regarding the task of detecting of outlier images, we will try to identify more fine attributes of images. For instance, the built outlier identifier should be able to distinguish images taken under different illumination as well as different viewpoints, which describe the same object. Furthermore, we can take images of a group of objects as inliers. We will build a one-class classifier to make a decision whether the object described by the given image comes from the group.
+
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+    {
+        "type": "text",
+        "text": "SEMI-SUPERVISED OUTLIER DETECTION USING GEN-ERATIVE AND ADVERSARY FRAMEWORK",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+            234,
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+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In a conventional binary/multi-class classification task, the decision boundary is supported by data from two or more classes. However, in one-class classification task, only data from one class are available. To build a robust outlier detector using only data from the positive class, we propose a corrupted GAN (CorGAN), a deep convolutional Generative Adversary Network requiring no convergence during the training process. In the adversarial process of training the CorGAN, the Generator is supposed to generate outlier samples for the negative class, and the Discriminator is trained to distinguish training datasets (i.e., positive samples) from generated data from the Generator (i.e., negative samples). We also propose a lot of techniques to improve the performance of the built classifier (i.e., the Discriminator). The proposed model outperforms the traditional method $\\mathrm { P C A } +$ PSVM (Scholkopf et al., 2000) and the solution based on Autoencoder (Thompson ¨ et al., 2002). ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            474,
+            336,
+            491
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(Hodge & Austin, 2004) addresses three fundamental approaches detecting outliers. The first approach is unsupervised clustering that identifies outliers without using any prior knowledge of the data. The second approach, supervised classification, requires labeled data from both positive class and negative class. The third addressed approach detects outliers using only data from the positive class via semi-supervised learning. Semi-supervised learning has gained increasing attention in recent years. One-class classification(OCC), as a typical semi-supervised learning technique, is applied to detect outliers using only positive examples from one class. The semi-supervised learning in this paper focuses on the OCC technique. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To motivate the importance of OCC, we first make an introduction to a classic application scenario. In industry, machine monitoring system is used everywhere to detect machine faults. A classifier should be constructed to detect when the machine behaves abnormally. Obviously, the training data for the positive class is easy to obtain by measuring the normal operations of the machine. However, only limited training data is available, even totally unavailable. In such case, a classifier should be built only on positive training data. This kind of task is known as OCC task. The name ”oneclass classification” originates from the paper Moya et al. (1993). Other researchers also present similar tasks with other terms such as Outlier Detection (Ritter & Gallegos, 1997), Novelty Detection (Bishop, 1994) or Concept Learning (Japkowicz, 1999). They are used interchangeably in this paper, even though they have specific meanings in other works. One-class classification can be used not only in machine monitoring task but also in many other domains, e.g. Text mining (Basu et al., 2004), Sentiment Analysis (Agarwal et al., 2015) and IT security (Lakhina et al., 2005). ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Many solutions have been proposed to solve the one-class classification problem. However, almost none of them shows acceptable performance in high-dimensional space. Neural Network with deep architecture is well known for the ability to manipulate high-dimensional data. It achieves state-ofart results in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics (LeCun et al., 2015). This paper applies a neural network with deep architecture in outlier detection task. Generative adversary framework(GAN) is composed of a Generator $G$ that can be used to generate outliers and a Discriminator that can be trained as a binary classifier. The framework is a potential solution to detect outliers through generating counterexamples. Usually, the Nash equilibrium of the training process of GANs cannot be guaranteed in practice. Our proposed model requires no convergence of the training process since the $G$ is used to generate only outliers instead of high-quality images that are from the distribution the training dataset. The proposed deep architecture solution is implemented, analyzed and compared to other methods. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The first section introduces the one-class classification problem and a potential solution with deeparchitecture neral network. The second section presents the work related to one-class classification problems (i.e., semi-supervised outlier detection). Then, the two primary steps of our solution for one-class classification problem are described in the third section, namely, the training step to optimize model and the detecting step to make an inference. Next, the fourth section proposes a technique to break Nash equilibrium so that the $G$ of GAN can keep generating outliers. Besides, this section also proposes other techniques to improve. The fifth section shows experiments, analyzes the results and compares the performance with that of other methods. Finally, the last section concludes our work and describes future work that remains to be further researched. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            318,
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+            334
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Five approaches to solve OCC problem are summarized in (Pimentel et al., 2014). Probabilistic approach estimates the generative probability density function (pdf) of the data from the positive class. The boundaries of normality in the data space are defined by the resultant distribution together with a specified threshold, and an unseen sample is tested whether it comes from the same distribution or not. Thereinto, Gaussian Mixture Models (GMMs) (Lindsay et al., 1989; Bishop, 2006) and Kernel Density Estimators (Parzen, 1962; Vincent & Bengio, 2003; Bengio et al., 2006) have proven to be popular. This approach requires complete density estimation in the feature space. If the data in feature space are high dimensional, huge amounts of data are required to fit the model because of the curse of dimensionality. Only when the data from the target class are large enough can this kind of method perform well. Another well-known approach, Reconstruction-based approach, first train a model minimising the reconstruction error of training data with positive labels. Then, the trained model assigns an outlier score, the distance between the input representation vector and the output of the model, for each test example. (Markou & Singh, 2003) reviews lots of the neural network-based methods. Additionally, PCA can also detect outliers by comparing the example before and after transformation. The reconstruction error approach abandons some information with low variance during reconstruction. However, the abandoned low-variance information has proven to be most informative (Tax & Muller, 2003). ¨ ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Additionally, Distance-based approach, e.g. Nearest neighbour-based methods (Bay & Schwabacher, 2003; Breunig et al., 2000) and Clustering-based methods (Barbara et al., 2002; He ´ et al., 2003), avoids estimating pdf explicitly, but it requires a well-defined distance/similarity measure, which is especially difficult in high-dimensional space. Another approach is domain-based, which creates the boundary based on the structure of normal data without considering the density of the positive class. One-class SVM (Scholkopf et al., 2000) and Support vector data description ¨ (SVDD) (Tax & Duin, 1999) are two basic ones. However, the choice of an appropriate kernel function is not easy, which determines the computational cost. Moreover, the hyperparameters that control the tightness of the boundary are also difficult to select. Lastly, Information-theoretic approach tries to distinguish normal data and outliers by computing information content of dataset using information measure. Similarly, the selection of appropriate information-theoretic measure is challenging. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The approaches described above learn from available positive samples only. Approaches that learn from both target samples and artificial outliers are also researched. (Hempstalk et al., 2008; Fan et al., 2004) generate outlier with a predefined distribution. The strong assumptions about the outlier data distribution in these approaches may be violated in real datasets (Abe et al., 2006). (Tax & Duin, 2001) proposes a method for generating artificial outliers, uniformly distributed in a hypersphere. However, in high-dimensional data space, their proposed technique is not feasible anymore because it is tough to get a confident estimate of the target volume due to the large difference in volume of the target and outlier class. (Banhalmi et al., 2007) extends dataset by generating outlier ´ examples distributed around the positive class. The approach first finds boundary points explicitly using SVM, which is computationally expensive. Then it generates negative examples only around positive class using a distance measure, which causes infeasibility in high-dimensional space. Our proposed CorGAN generates negative examples including both ones around the positive class and ones far from the positive class. Moreover, the model requires no explicit distance measure and does not need to find boundary points explicitly. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Neural networks with deep architecture have already been used in OCC task, but mostly in Reconstruction error approaches (Markou & Singh, 2003). To our knowledge, our proposed CorGAN is the first work to generate outliers for OCC via deep architecture (i.e., Generative Adversary Network). A variant of the GAN framework (CatGAN) is applied to solve multi-class classification task in unsupervised or semi-supervised fashion (Springenberg, 2015). (Odena, 2016) does a further research about semi-supervised learning using GANs. (Schlegl et al., 2017) proposes AnoGAN to apply GAN in Anomaly Detection, which requires the Nash-equilibrium at the end of the training process. Nevertheless, all variants of GAN and the original one are known for its unstable training process. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 OUTLIER DETECTION USING CORGAN",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The proposed model and the improved techniques can be generalized to various kinds of data. To show the performance in high-dimensional space, we illustrate our model on image data. The proposed parametric method is composed of two steps: ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Training Step: Training the CorGAN with the improved techniques;   \n2. Inference Step: Detecting outliers using the resulting $D$ of the trained CorGAN ",
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+    {
+        "type": "text",
+        "text": "3.1 GENERATIVE ADVERSARY NETWORK ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Generative Adversary Network(GAN) is a framework for training generative models via an adversarial process (Goodfellow et al., 2014). The framework consists of two components, a generative model (Generator $G$ ) and a discriminative model (Discriminator $D$ ). The $G$ aims to capture the data distribution. The $D$ estimates the probability that a sample came from the training data rather than the Generator. This framework corresponds to a minimax two-player game. In the training procedure, the $D$ is trained to distinguish samples in training datasets from generated samples by assigning a high probability to the former and a low probability to the latter. Contrarily, the objective of $G$ is to maximize the probability of $D$ making a mistake. After the Nash-equilibrium of the training process, the output probability of the $D$ is always 0.5. In case of the convergence, the $G$ is capable of generating realistic images that have same/similar distribution as in training dataset, and the $D$ cannot make right discrimination anymore. The biggest advantage of this framework is that no Markov chains or unrolled approximate inference networks are required in the training and sampling process. ",
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+    {
+        "type": "text",
+        "text": "3.2 STEP1: TRAINING THE CORGAN ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Architectures of the Generator and the Discriminator are neural networks, such as Multilayer Perceptron, Deep Convolutional Neural Network (LeCun et al., 1989), Convolutional Neural Network Cascade (Springenberg, 2015) and Recurrent Neural Network (Rumelhart et al., 1988). The BackPropagation algorithm can be used to train both the generative model and the discriminative model. The architecture applied in the proposed CorGAN is shown in Figure 1. ",
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+    },
+    {
+        "type": "text",
+        "text": "The $G$ generally starts from prior distribution $p _ { z } ( z )$ (input noise variable $_ z$ ). In the case of convergent GANs, the $G$ maps the prior distribution to the training data distribution $p _ { i n l i e r } ( { \\pmb x } )$ . The $G$ of CorGAN is used to generate outlier examples. Hence, it is supposed to map the prior distribution to outlier data distribution $G ( z ; \\theta _ { g } )$ instead of the training data distribution. As usual, the $D$ maps the input (i.e. the training data or the generated samples) to a single scalar, which represents the probability that the input came from training datasets instead of the $G$ . The target value of the $D$ is $a _ { t } = 1$ for the input data from training dataset and $a _ { o } = 0$ for the input data generated by the $G$ . The $D$ as a binary classifier is trained to minimize the cost V(D): ",
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+        "type": "equation",
+        "img_path": "images/2ba40a5211490384d6cd088f819c33de0d7965a3e2d9f9bf365f17707ed539e4.jpg",
+        "text": "$$\n\\displaystyle { \\operatorname* { m i n } _ { D } V ( D ) = \\mathbb { E } _ { z \\sim p _ { z } ( z ) } \\log ( D ( G ( z ) ) - a _ { o } ) + \\mathbb { E } _ { { \\mathbf { x } } \\sim p _ { i n l i e r } ( { \\mathbf { x } } ) } \\log ( a _ { t } - D ( { \\mathbf { x } } ) ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The objective of the $G$ of the CorGAN is to fool the D, but not necessarily maximise the probability D making a mistake. The new target value is $a _ { n e w } \\in [ 0 , 1 ]$ (see section 4.2). The $G$ of the CorGAN ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b0691fb608dbcbacd24c0cc26dcae649d23a97aefb6b0fa4cc6e96ced0eede19.jpg",
+        "image_caption": [
+            "Figure 1: The basic architecture of the CorGAN "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "is trained to minimise the cost U(G): ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9db534096373cf67eab43341f58affb795fb56fb5cf015f8e93a2754c8282e37.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { G } U ( G ) = \\mathbb { E } _ { z \\sim p _ { z } ( z ) } \\log ( | a _ { n e w } - D ( G ( z ) ) | )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The CorGAN model is updated via back-propagation algorithm. If the $D$ is overly optimised without updating the $G$ , it will result in overfitting problem. The $D$ and the $G$ will be updated simultaneously or alternately to avoid the problem, e.g. k steps of optimizing the $D$ and one step of optimizing the $G$ . The traditional GANs reach Nash equilibrium after several training epochs. The new objective of the $G$ of CorGAN breaks Nash equilibrium of the training process, which causes that the $G$ can keep generating outlier samples. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The inlier data is taken as training data in the CorGAN. In the adversarial process of training CorGAN, the $G$ is supposed to generate outlier samples for the negative class. The $D$ is trained to assign a high probability value to data from training datasets (i.e., the positive class) and a small probability value to generated data from the G (i.e., the negative class). The generated outliers not only distribute around the positive class but also cover feature space far away from the positive class. In order that the $G$ can map a prior distribution to a huge data space except for the positive class, we proposed a lot of improved techniques (section 4). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 STEP2: DETECTING OUTLIERS USING DISCRIMINATOR ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the inference step, the resulting $D$ outputs a relatively high probability for data subjective to the distribution $p _ { i n l i e r }$ and a relatively low probability for data not from the distribution $p _ { i n l i e r }$ . That is to say that, if the output is a low probability in the outlier-detecting process, the input is predicted as an outlier. What is a low probability? So, we need a probability threshold to decide whether an output probability is high or low. The output of the sigmoid activation function of the last layer is a scalar value in the interval $( 0 , 1 )$ , we can intuitively set $t$ as the threshold. In that case, the input is an outlier, if the output from the $D$ is small than $t$ , otherwise an inlier. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The one-class classification task is an extreme case of the imbalanced training. The optimal value of the threshold $t$ is not 0.5. It mainly depends on how the model is trained and the concrete application scenario. If the model is trained by specifying a new objective for the $G$ (like in CorGAN), the $D$ model learns distribution from training datasets for a long time. However, the $D$ is trained with data from a more extensive outlier distribution using the same time. The resulting $D$ will present a relatively higher probability for data that follow the same distribution as the training data (i.e., for inliers). So, the threshold $t$ with a value higher than 0.5 shows a better performance. We do not evaluate the $D$ on a single user-specified threshold. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "One-class classification, also called Outlier Detection, can be evaluated with F1-score, which is harmonic mean of precision and recall. The accepted fraction of the positive class $f _ { T + }$ and the rejected fraction of the negative class $f _ { O - }$ are both together also as a popular measure for OCC. However, the score of those measures strongly depends on the specified threshold. To justify our model objectively, the performance of the $D$ in this paper will be evaluated with Receiver operating characteristic curve (ROC) and Area under the ROC curve (AUC). The robustness of the built $D$ will be tested on various datasets. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 IMPROVED TECHNIQUES FOR GAN IN OCC ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "If the training process reaches Nash equilibrium, the $G$ is able to generate examples following the distribution $p _ { i n l i e r }$ (see figure 2), and the output probability of the $D$ is always 0.5 for inliers and an unexpected value for outliers. It is difficult to distinguish outliers from inliers via a threshold. Our proposed corrupted generative adversary network (CorGAN) is a GAN without convergence. To avoid the Nash equilibrium that the training process can reach, we propose several techniques to break the convergence and build a robust outlier identifier. Thereinto, specifying a new objective for the $G$ is a basic one to keep it generating outlier samples, and other optional techniques further improve the performance of the model. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b282e3949b137bb05b809ba6630e74990cf02e792104df3e154b5d11dd8c22d5.jpg",
+        "image_caption": [
+            "Figure 2: Comparison between the generated data and the training data: The images of handwritten digit nine are training data. After several training epochs, the generated images and the training data are visualised in the figure. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1 EARLY STOPPING ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In early training epochs (i.e., before convergence), the $G$ has no ability to generate data that follows the distribution $p _ { i n l i e r }$ . Meanwhile, the $D$ is trained with the training data with positive labels and the generated data with negative labels. Distributions from $G$ are different from the distribution of training datasets before convergence. The $D$ recognizes the distribution of training datasets by presenting a high probability. Early Stopping before convergence can obtain a well-behaved Discriminator. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In term of implementation of this technique, we do not explicitly stop the training at a particular epoch, but always save the best model. Similar to the model selection, we take the best Discriminator as the final classifier, which appears definitely before the convergence of the training process. The performance of the $D$ is tested regularly during the training process. The score Area Under the Curve of $f _ { T + }$ (inlier accepted fraction), called positively biased AUC (see figure 3) is used to evaluate the performance of the $D$ . The $D$ saved with best biased AUC score shows not optimal but near-optimal performance on the test datasets. The objective of Early Stopping is defined as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/956ae9dbf2088ab021e221e2adca932f2f3627f45f36e29a53d2c4de9f428d24.jpg",
+        "text": "$$\n\\operatorname* { m a x } _ { D } A U C _ { b i a s e d } = \\int _ { 0 } ^ { 1 } f _ { T + } ( t ) d t\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $t$ is the threshold and $f _ { T + } ( t )$ is inlier accepted fraction of the Discriminator given the specific threshold $t$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/a9528f61872dc2205ff7dd657ee76cbca461c73439f091c6ab5769fdab4e713f.jpg",
+        "image_caption": [
+            "Figure 3: Area Under the Curve of inlier accepted fraction: The figure describes the relationship between the inlier accepted fraction and the specified threshould. Given the specified threshold $0 . 7$ , the point $P$ in the curve corresponds to the accepted fraction of inliers 0.68. Since no outlier is available, the area under this curve (positively biased AUC) is a good measure to select the near optimal model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            379,
+            111,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d65f3ab14172365a1f95937e2b58e23bebb3af99d321793a806d33ab89f7087e.jpg",
+        "table_caption": [
+            "Table 1: The behavior of the $G$ and the performance of the $D$ are presented in case of different new target values. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>new target value anew</td></tr><tr><td rowspan=1 colspan=1>anew = 1: The objective of G is the exact same as that of the convergent GAN(Goodfellow et al., 2014). The training will converge.</td></tr><tr><td rowspan=1 colspan=1>anew E (~ O.9,1): The such adjustment of the objective of the G is proposed in(Salimans et al.,2O16) to improve the training process of GANs. The training processwill converge as well.</td></tr><tr><td rowspan=1 colspan=1>anew ∈ (~ O.5,~ 0.9): The G will generate data far from the distribution pinlierat the beginning of the training phase because of the random initialization.After several training epochs,it will generate data that distribute around the positive class.The tighter the boundary is,the larger space the generated data cover. The value 0.9results in most tight boundary.</td></tr><tr><td rowspan=1 colspan=1>anew ∈ [0,~ O.5): The G has similar objective to that of the D. It will tend togenerate data,from which the D can easily distinguish the training data. That is to say that allthe generated data distribute far from the distribution Pinlier·</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 SPECIFYING A NEW OBJECTIVE FOR THE GENERATOR",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Even though Early Stopping avoids the problem the convergence causes, GAN can only be trained with a limited number of epochs. Hence, Early Stopping can only guarantee a high inlier accepted fraction $f _ { T + }$ , but not necessarily high outlier rejected fraction $f _ { O - }$ because the $\\mathbf { D }$ is only trained with a certain number of generated samples (i.e., outliers). To build a robust outlier identifier against as many kinds of outlier distributions as possible, we should train the $D$ with as many generated samples as possible, which have different distribution from the distribution $p _ { i n l i e r }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We can explicitly break Nash equilibrium by specifying a new objective for $G$ . Without modification, the objective of $G$ is to maximise the probability of the $D$ making a mistake. We propose a new objective for $G$ : ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e73c3af311feaf94c6d8804420933403a1caa6f84267a2a97363823ab99c0d4f.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { G } U ( G ) = \\mathbb { E } _ { z \\sim p _ { z } ( z ) } \\log ( | 0 . 9 - D ( G ( z ) ) | )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            346,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Instead of maximising the probability that $D$ makes a mistake, the new objective is that the $D$ makes a mistake with a certain probability. The new target value used to calculate the cost for updating the $\\mathbf { G }$ is $a _ { n e w } = 0 . 9$ . The choice of the value $a _ { n e w }$ is justified in the table 1. In case of $a _ { n e w } = 0 . 9$ , the $G$ explores the largest space, and the built $D$ will show robust performance. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 ATTACHING MORE IMPORTANCE TO GENERATED DATA ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The cost of the $D$ consists of two parts. These two parts are caused respectively by the training data and the generated data. Generally, the two parts are simply added together as the total cost for updating the parameters of the $D$ . That is to say that the training data and the generated data are treated with the same importance. They can be treated differently by assigning a weight to one of them to broaden the search space of parameters. The objective of the $D$ is defined as follows: ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e52f2e14e112551c5bbad47b3fec6021665d46b33c43929e98461599515e1963.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { D } V ( D ) = \\mathbb { E } _ { z \\sim p _ { z } ( z ) } \\log ( D ( G ( z ) ) - a _ { o } ) + w * \\mathbb { E } _ { { \\pi } \\sim p _ { i n l i e r } ( { \\bf x } ) } \\log ( a _ { t } - D ( { \\bf x } ) )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": ", where $w \\in ( 0 , 1 )$ is a hyperparameter. The value of $w$ can be selected by validation process with positively biased AUC score. While the outlier distributions are various and difficult to recover all of them, the inlier distribution is rather simple and easy to learn. During the training process, the cost that generated data caused should be reduced as far as possible by updating parameters of the $D$ . In other words, the generated data should be attached more importance by specifying the value of weight. Compared to the general case that the two parts of cost are not treated differently, this method shows a better performance on the test datasets whose distributions are far from the training dataset. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 COMBINING PREVIOUSLY GENERATED DATA ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Compared to the method of Early Stopping, the method of specifying a new objective for G presents a better performance, because the new objective trains $D$ with arbitrarily more generated data that are not from the distribution $p _ { i n l i e r }$ . With the new specified objective, the training procedure does not converge, and the $G$ is able to keep generating outliers. The $D$ can be trained with arbitrarily many generated distributions. However, the space of distribution learned by $D$ is limited to a great extent. On the one hand, the generated distribution always stays near the positive class after several training epochs. On the other hand, the $D$ can forget the previously learned distributions because of the limited capacity. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this subsection, we proposed a technique to broaden the learned distributions. The performance of the $D$ can be improved by being regularly trained with previously generated data. We can train the CorGAN with mini batches (batch size $s$ ) that combine the data generated recently and previously. The combined training data can avoid that the $D$ forgets the learned distribution to some degree. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "There exist a large amount of generated data in the training procedure. Which ones should be chosen to train $D$ and prevent it forgetting the previously generated distributions? Because the generated data can be arbitrarily many, it is inadvisable and impossible to save all of them. In this case, the generated data can be treated as stream data $\\left( X _ { 1 } , X _ { 2 } , \\ldots , X _ { t } \\right)$ . We apply a Reservoir Sampling Algorithm (Vitter, 1985) to sample previously generated images. This algorithm samples examples from the stream data with the same probability (see equation 6) and specifies a reservoir $R$ to save the sampled examples. ",
+        "bbox": [
+            173,
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/af6c2e05f2e6b57bacaef83a7c11947231e50eb73cef01c8d07146f39a17f8a0.jpg",
+        "text": "$$\nP ( X _ { i } \\in R ) = \\frac { 1 } { t - ( s / 2 ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            415,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": ", where $i \\in [ 1 , t - ( s / 2 ) ]$ . The mini batches that are composed of newly generated examples and the sampled examples saved in a reservoir is used to train $D$ . The mini batch $B$ at the timestamp $t$ is defined as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/17cee7fde3b4fab32f0431327a62edd7329fb8055263387357336a6f562e6402.jpg",
+        "text": "$$\nB = \\left\\{ R , X _ { t - ( s / 2 ) + 1 } , X _ { t - ( s / 2 ) + 2 } , \\ldots , X _ { t } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": ", where $R$ is the reservoir. The objective of the $D$ remains unchanged in the equation 1. The resultant $D$ can identify not only recently generated outliers but also previous ones. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS AND ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            834,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section, we justify our proposed model and improved techniques with experiments. To demonstrate the robust performance of the built classifier, we evaluate the $D$ on various outlier datasets. We describe the experiment settings of our models and the models to be compared. The experiment results, followed by a strong discussion, are presented in this section. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/d843ae0fa5e1e2005ef7cc02937a24edd2737f7ae2cbe28b4ae5a64bad0798bf.jpg",
+        "table_caption": [
+            "Table 2: Training -, validation - and test datasets of experiments setting. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets:</td><td>Source of images:</td><td>The Number of images:</td></tr><tr><td>Training dataset</td><td>digit of 9 in MNIST</td><td>4967</td></tr><tr><td>Validation dataset</td><td>digit of 9 in MNIST</td><td>900</td></tr><tr><td rowspan=\"4\">Test dataset</td><td>Inliers: digit of 9 in MNIST</td><td>900</td></tr><tr><td>1.Outliers: digits of O-8 in MNIST</td><td>900</td></tr><tr><td>2.Outliers: CIFAR10</td><td>900</td></tr><tr><td>3.Outliers: Images composed of noise</td><td>900</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1 DATASETS AND EVALUATION: ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Three datasets are used in the experiments, namely, MNIST (LeCun et al., 1998), CIFAR10 (Krizhevsky, 2009) and an artificial noise image dataset. The image size in MINIST is (28, 28). The size of CIFAR10 images is cropped into (28, 28) by removing pixels along the sides. Especially, we specify a dataset composed of three group of noise images with the same size (28, 28). The values of their pixels are respectively subject to uniform distribution, Gaussian distribution and random values. The table 2 lists training dataset, validation dataset and test datasets. The performance of various approaches will be evaluated and compared with Receiver Operating Characteristic (ROC) and the Area Under the ROC Curve (AUC). ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 EXPERIMENTS SETTING: ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "PCA+PSVM: PCA is used to reduce the dimensionality of the high-dimensional data (i.e., images). The number of components K is set such that $9 5 \\%$ of the variance is retained $\\scriptstyle ( \\mathrm { K = 1 } 1 1 $ ). Oneclass SVM proposed in (Scholkopf et al., 2000) is plane-based, called PSVM. To identify outliers ¨ in the feature space, PSVM tries to find a hyperplane that best separates the data from the origin. RBF kernel is used in this experiment. Other settings are defaults in sklearn.svm.OneClassSVM (Pedregosa et al., 2011). ",
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+    },
+    {
+        "type": "text",
+        "text": "Autoencoder: Autoencoder detects outliers by computing reconstruction error and compares it with a specified threshold. The threshold is based on the difference between the inputs and outputs for the training data. If the reconstruction error for a test sample is larger than the threshold, then the sample is identified as an outlier, otherwise as inlier. To justify our proposal, we compare our model to convolutional autoencoder. The encoder has the same architecture as the Discriminator in CorGAN except for output layer. The decoder also has a same architecture as the Generator in CorGAN. The model is regularised with weight decay $\\lambda = 0 . 0 1$ . The parameters are updated with SGD optimisation algorithm, minibatc $\\scriptstyle \\imath = 1 2 8$ and learning rate $l r { = } 0 . 1$ . The cost function is the cross-entropy function. The model is trained for 30 epochs without pretraining. ",
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+    {
+        "type": "text",
+        "text": "CorGAN: The basic architecture of CorGAN, as well as the number of its layers and units, is shown in figure 1. We propose a lot of improved techniques. Since its combinations are numerous, we justify only three main models. The first model is a basic one, $\\mathrm { C o r G A N } = \\mathrm { G A N }$ with early stopping technique and a new objective for the $G$ (see section 4.2). The new target value $a _ { n e w }$ is set manually to 0.9 for the $G$ . The $G$ is regularised with weight decay $\\lambda = 0 . 1$ . The optimisation algorithm is Adam, minibatch $= 1 2 8$ and learning rate $l r = 0 . 0 0 0 2$ . No pretraining is performed. The second model to be justified is based on the first one, $\\mathrm { C o r G A N ^ { 2 } = C o r G A N + }$ Attaching more importance to generated images (see section 4.3). The weight is set to 0.5 manually. The third illustrated model is also based on the first one, $\\mathrm { C o r G A N ^ { 3 } \\bar { \\ s } = C o r G A N \\ s + \\Delta }$ Combining previously generated images (see section 4.4). The minibatch size is composed of 64 images sampled from previous training epoch and 64 newly generated images. ",
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+    {
+        "type": "text",
+        "text": "5.3 RESULTS AND ANALYSIS: ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The results of the experiments are shown in the figure 4 and the table 3. The outlier distribution of the handwritten digits images of the numbers (0-8) is relatively close to the inlier distribution of the number 9. Hence, all the approaches show the worse AUC scores on the first test dataset. The $\\mathrm { P C A + P S V M }$ approach shows the better score on the second test dataset than on the noise test dataset. The traditional approach is not robust enough for noise outliers. The solutions based on neural networks often show a better performance against noise data because of the random initialization of its parameters. Especially, our proposed solution based on GAN framework, in which Generator generates many noise examples. The convolutional autoencoder can reconstruct natural images well by detects edges, corners and objects. Therefore, the convolutional autoencoder shows the poor score on natural images. Our proposed solution classifies test examples without reconstruction process, which shows robust performance against outlier natural images as well as noise images. ",
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+        "type": "image",
+        "img_path": "images/596ea6ac1282ab797e6dc3c1a138bfb8fc3bae75d6216625d1ecd5e9bda53ae6.jpg",
+        "image_caption": [
+            "Figure 4: The figures show the ROC curves of all models on three differenct test datasets. The area under the ROC curve represents the overall performance of a one-class classifier. The model $\\mathrm { C o r G A N ^ { 3 } }$ shows robust performance on all the three datasets. "
+        ],
+        "image_footnote": [],
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+        "type": "table",
+        "img_path": "images/126168cca09ea092645f851371d6cb947895b4bc5a69327d110418efc11afa2a.jpg",
+        "table_caption": [
+            "Table 3: The AUC socres of various models are shown in the table. All the models are tested in three datasets: MNIST(9) $^ +$ MNIST(0-8), MNIST(9) $^ +$ CIFAR10, MNIST(9) $^ +$ Noise. Within MNIST(9) images are inliers, and other images are outliers. CorGAN, $\\mathrm { C o r G A N ^ { 2 } }$ and $\\mathrm { C o r G A N ^ { 3 } }$ are described in section 5.2. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=3 colspan=1></td><td rowspan=1 colspan=3>AUC score:</td></tr><tr><td rowspan=1 colspan=3>MNIST(9)</td></tr><tr><td rowspan=1 colspan=1>MNIST(0-8)</td><td rowspan=1 colspan=1>CIFAR10</td><td rowspan=1 colspan=1>Noise</td></tr><tr><td rowspan=1 colspan=1>PCA+PSVM</td><td rowspan=1 colspan=1>0.8623</td><td rowspan=1 colspan=1>0.9720</td><td rowspan=1 colspan=1>0.9302</td></tr><tr><td rowspan=1 colspan=1>Autoencoder</td><td rowspan=1 colspan=1>0.8943</td><td rowspan=1 colspan=1>0.6785</td><td rowspan=1 colspan=1>0.9704</td></tr><tr><td rowspan=1 colspan=1>CorGAN</td><td rowspan=1 colspan=1>0.8974</td><td rowspan=1 colspan=1>0.9739</td><td rowspan=1 colspan=1>0.9995</td></tr><tr><td rowspan=1 colspan=1>CorGAN2</td><td rowspan=1 colspan=1>0.8343</td><td rowspan=1 colspan=1>0.9937</td><td rowspan=1 colspan=1>0.9999</td></tr><tr><td rowspan=1 colspan=1>CorGAN3</td><td rowspan=1 colspan=1>0.9253</td><td rowspan=1 colspan=1>0.9943</td><td rowspan=1 colspan=1>0.9999</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "Compared to CorGAN, $\\mathrm { C o r G A N ^ { 2 } }$ attaches more importance to generated images, which makes classifier more robust again the outliers whose distribution is far from inlier distribution. In consequence, $\\mathrm { C o r G A N ^ { 2 } }$ shows the low score on the first dataset, in which the distributions of inliers and outliers are relatively close. In the model $\\mathrm { C o r G A N ^ { 3 } }$ , the outlier examples generated previously are combined with newly generated examples to train the Discriminator. In this way, the Discriminator learned a large space of outlier distribution. The model $\\mathrm { C o r G A N ^ { 3 } }$ shows the best scores on various test datasets. The robust $\\mathrm { C o r G A N ^ { 3 } }$ learns a tight boundary in high-dimensional space. The farther the outlier distribution is from the inlier distribution $p _ { i n l i e r }$ , the better score it shows (see figure 4d). ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION AND FUTURE WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we present a solution to solve one-class classification problem based on GAN framework and successfully apply the Discriminator of the framework to detect outliers. We illuminate a few techniques to improve the performance and verify the proposed techniques with experiments. First, we choose the near optimal model to detect outliers by saving a better model during the training procedure. Then we specify a new objective for the $G$ so that it can keep generating outliers. Attaching more importance to generated images can further improve the performance of the $D$ . To prevent the $D$ forgetting the previously generated outliers, we combine previously generated outliers from the Generator to train the outlier identifier. These techniques show comparable AUC scores. ",
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+    {
+        "type": "text",
+        "text": "In future work, We can further vary the generated outliers to train $D$ . We can specify multiple Generators in the generative adversary framework. The mini batch can combine the data generated by different Generators, which have different objectives, e.g. the different probabilities of D making a mistake. To further explore more generated distribution used to train the $D$ , we can even combine CorGAN with other generative models. Similarly, we must also change the objective of them to fit our goal, since the other generative models are also supposed to generate outliers. ",
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+    {
+        "type": "text",
+        "text": "All the proposals in this paper do not leverage distance information(KLD) between distributions within a batch both in the training process and detecting process. Another topic worth studying is the clustering-based method to detect outlier using $D$ of GAN. One potential method of leveraging distance information is to model the closeness between examples in a mini-batch. The modeling process is described in Minibatch Discrimination (Salimans et al., 2016), an improved technique for training GANs. ",
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+    {
+        "type": "text",
+        "text": "Regarding the task of detecting of outlier images, we will try to identify more fine attributes of images. For instance, the built outlier identifier should be able to distinguish images taken under different illumination as well as different viewpoints, which describe the same object. Furthermore, we can take images of a group of objects as inliers. We will build a one-class classifier to make a decision whether the object described by the given image comes from the group. ",
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+    {
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parse/train/BygdyxHFDS/BygdyxHFDS.md

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+# META-LEARNING CURIOSITY ALGORITHMS
+
+Ferran Alet∗, Martin F. Schneider∗, Tomas Lozano-P ´ erez & Leslie Pack Kaelbling ´
+
+Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology Cambridge, MA 02139, USA {alet,martinfs,tlp,lpk}@mit.edu
+
+# ABSTRACT
+
+We hypothesize that curiosity is a mechanism found by evolution that encourages meaningful exploration early in an agent’s life in order to expose it to experiences that enable it to obtain high rewards over the course of its lifetime. We formulate the problem of generating curious behavior as one of meta-learning: an outer loop will search over a space of curiosity mechanisms that dynamically adapt the agent’s reward signal, and an inner loop will perform standard reinforcement learning using the adapted reward signal. However, current meta-RL methods based on transferring neural network weights have only generalized between very similar tasks. To broaden the generalization, we instead propose to meta-learn algorithms: pieces of code similar to those designed by humans in ML papers. Our rich language of programs combines neural networks with other building blocks such as buffers, nearest-neighbor modules and custom loss functions. We demonstrate the effectiveness of the approach empirically, finding two novel curiosity algorithms that perform on par or better than human-designed published curiosity algorithms in domains as disparate as grid navigation with image inputs, acrobot, lunar lander, ant and hopper.
+
+# 1 INTRODUCTION
+
+When a reinforcement-learning agent is learning to behave, it is critical that it both explores its domain and exploits its rewards effectively. One way to think of this problem is in terms of curiosity or intrisic motivation: constructing reward signals that augment or even replace the extrinsic reward from the domain, which induce the RL agent to explore their domain in a way that results in effective longer-term learning and behavior (Pathak et al., 2017; Burda et al., 2018; Oudeyer, 2018). The primary difficulty with this approach is that researchers are hand-designing these strategies: it is difficult for humans to systematically consider the space of strategies or to tailor strategies for the distribution of environments an agent might be expected to face.
+
+We take inspiration from the curious behavior observed in young humans and other animals
+
+![](images/cef77ccc92b7d5d7ce1872f70326e7f1af5e39bc3832f0fe30c74bab4580472b.jpg)  
+Figure 1: Our RL agent is augmented with a curiosity module, obtained by meta-learning over a complex space of programs, which computes a pseudo-reward $\widehat { r }$ at every time step.
+
+and hypothesize that curiosity is a mechanism found by evolution that encourages meaningful exploration early in an agent’s life. This exploration exposes it to experiences that enable it to learn to obtain high rewards over the course of its lifetime. We propose to formulate the problem of generating curious behavior as one of meta-learning: an outer loop, operating at “evolutionary” scale will search over a space of algorithms for generating curious behavior by dynamically adapting the agent’s reward signal, and an inner loop will perform standard reinforcement learning using the adapted reward signal. This process is illustrated in figure 1; note that the aggregate agent, outlined in gray, has the standard interface of an RL agent. The inner RL algorithm is continually adapting to its input stream of states and rewards, attempting to learn a policy that optimizes the discounted sum of proxy rewards $\textstyle \sum _ { k \geq 0 } \gamma ^ { k } \widehat { r } _ { t + k }$ . The outer “evolutionary” search is attempting to find a program for the curiosity module, so as to optimize the agent’s lifetime return $\textstyle \sum _ { t = 0 } ^ { T } r _ { t }$ , or another global objective like the mean performance on the last few trials.
+
+In this meta-learning setting, our objective is to find a curiosity module that works well given a distribution of environments from which we can sample at meta-learning time. Meta-RL has been widely explored recently, in some cases with a focus on reducing the amount of experience needed by initializing the RL algorithm well (Finn et al., 2017; Clavera et al., 2019) and, in others, for efficient exploration (Duan et al., 2016; Wang et al., 2017). The environment distributions in these cases have still been relatively low-diversity, mostly limited to variations of the same task, such as exploring different mazes or navigating terrains of different slopes. We would like to discover curiosity mechanisms that can generalize across a much broader distribution of environments, even those with different state and action spaces: from image-based games, to joint-based robotic control tasks. To do that, we perform meta-learning in a rich, combinatorial, open-ended space of programs.
+
+This paper makes three novel contributions.
+
+We focus on a regime of meta-reinforcement-learning in which the possible environments the agent might face are dramatically disparate and in which the agent’s lifetime is very long. This is a substantially different setting than has been addressed in previous work on meta-RL and it requires substantially different techniques for representation and search.
+
+We propose to do meta-learning in a rich, combinatorial space of programs rather than transferring neural network weights. The programs are represented in a domain-specific language (DSL) which includes sophisticated building blocks including neural networks complete with gradient-descent mechanisms, learned objective functions, ensembles, buffers, and other regressors. This language is rich enough to represent many previously reported hand-designed exploration algorithms. We believe that by performing meta-RL in such a rich space of mechanisms, we will be able to discover highly general, fundamental curiosity-based exploration methods. This generality means that a relatively computationally expensive meta-learning process can be amortized over the lifetimes of many agents in a wide variety of environments.
+
+We make the search over programs feasible with relatively modest amounts of computation. It is a daunting search problem to find a good solution in a combinatorial space of programs, where evaluating a single potential solution requires running an RL algorithm for up to millions of time steps. We address this problem in multiple ways. By including environments of substantially different difficulty and character, we can evaluate candidate programs first on relatively simple and short-horizon domains: if they don’t perform well in those domains, they are pruned early, which saves a significant amount of computation time. In addition, we predict the performance of an algorithm from its structure and operations, thus trying the most promising algorithms early in our search. Finally, we also monitor the learning curve of agents and stop unpromising programs before they reach all $T$ environment steps.
+
+We demonstrate the effectiveness of the approach empirically, finding curiosity strategies that perform on par or better than those in published literature. Interestingly, the top 2 algorithms, to the best of our knowledge, had not been proposed before, despite making sense in hindsight. We conjecture the first one (shown in figure 3) is deceptively simple and that the complexity of the other one (figure 10 in the appendix) makes it relatively implausible for humans to discover.
+
+# 2 PROBLEM FORMULATION
+
+# 2.1 META-LEARNING PROBLEM
+
+Let us assume we have an agent equipped with an RL algorithm (such as DQN or PPO, with all hyperparameters specified), $\mathcal { A }$ , which receives states and rewards from and outputs actions to an environment $\mathcal { E }$ , generating a stream of experienced transitions $e ( \boldsymbol { \mathcal { A } } ; \boldsymbol { \mathcal { E } } ) _ { t } = ( s _ { t } , a _ { t } , \bar { r } _ { t } , s _ { t + 1 } )$ . The agent continually learns a policy $\pi ( t ) : s _ { t } \to a _ { t }$ , which will change in time as described by algorithm $\mathcal { A }$ ;
+
+so $\pi ( t ) = \boldsymbol { \mathcal { A } } ( e _ { 1 : t - 1 } )$ and thus $a _ { t } \sim \mathcal { A } ( e _ { 1 : t - 1 } ) ( s _ { t } )$ . Although this need not be the case, we can think of $\mathcal { A }$ as an algorithm that tries to maximize the discounted reward $\textstyle \sum _ { i } \gamma ^ { i } r _ { t + i } , \gamma < 1$ and that, at any time-step $t$ , always takes the greedy action that maximizes its estimated expected discounted reward.
+
+To add exploration to this policy, we include a curiosity module $\mathcal { C }$ that has access to the stream of state transitions $e _ { t }$ experienced by the agent and that, at every time-step $t$ , outputs a proxy reward $\widehat { r } _ { t }$ . We connect this module so that the original RL agent receives these modified rewards, thus bobserving $e ( \boldsymbol { A } , \mathcal { C } ; \mathcal { E } ) _ { t } = ( s _ { t } , a _ { t } , \widehat { r } _ { t } = \mathcal { C } ( \bar { e _ { 1 : t - 1 } } ) , s _ { t + 1 } ) $ , without having access to the original $r _ { t }$ . bNow, even though the inner RL algorithm acts in a purely exploitative manner with respect to $\widehat { r }$ , it may efficiently explore in the outer environment.
+
+Our overall goal is to design a c osity module $\mathcal { C }$ that induces the agent to maximize $\textstyle \sum _ { t = 0 } ^ { T } r _ { t }$ , for $T$   
+episodic problem, $T$ will span many episodes. More formally, given a single environment $\mathcal { E }$ , RL algorithm $\mathcal { A }$ , and curiosity module $\mathcal { C }$ , we can see the triplet (environment, curiosity module, agent) as a dynamical system that induces state transitions for the environment, and learning updates for the curiosity module and the agent. Our objective is to find $\mathcal { C }$ that maximizes the expected original reward obtained by the composite system in the environment. Note that the expectation is over two different distributions at different time scales: there is an “outer” expectation over environments $\mathcal { E }$ , and in “inner” expectation over the rewards received by the composite system in that environment, so our final objective is:
+
+$$
+\operatorname* { m a x } _ { \mathcal { C } } \left[ \mathbb { E } _ { \mathcal { E } } \left[ \mathbb { E } _ { r _ { t } \sim e ( A , \mathcal { C } ; \mathcal { E } ) } \left[ \sum _ { t = 0 } ^ { T } r _ { t } \right] \right] \right] \ .
+$$
+
+# 2.2 PROGRAMS FOR CURIOSITY
+
+In science and computing, mathematical language has been very successful in describing varied phenomena and powerful algorithms with short descriptions. As Valiant points out: “the power [of mathematics and algorithms] comes from the implied generality, that knowledge of one equation alone will allow one to make accurate predictions about a host of situations not even conceived when the equation was first written down” (Valiant, 2013). Therefore, in order to obtain curiosity modules that can generalize over a very broad range of tasks and that are sophisticated enough to provide exploration guidance over very long horizons, we describe them in terms of general programs in a domain-specific language. Algorithms in this language will map a history of $( s _ { t } , s _ { t + 1 } , a _ { t } , r _ { t } )$ tuples into a proxy reward $\widehat { r } _ { t }$ .
+
+Inspired by human-designed systems that compute and use intrinsic rewards, and to simplify the search, we decompose the curiosity module into two components: the first, $I$ , outputs an intrinsic reward value $i _ { t }$ based on the current experienced transition $\left( { { s _ { t } } , { a _ { t } } , { s _ { t + 1 } } } \right)$ (and past transitions $\left( s _ { 1 : t - 1 } , a _ { 1 : t - 1 } \right)$ indirectly through its memory); the second, $\chi$ , takes the current time-step $t$ , the actual reward $r _ { t }$ , and the intrinsic reward $i _ { t }$ (and, if it chooses to store them, their histories) and combines them to yield the proxy reward $\widehat { r _ { t } }$ . To ease generalization across different timescales, in practice, before feeding $t$ into $\chi$ bwe normalize it by the total length of the agent’s lifetime, $T$ .
+
+Both programs consist of a directed acyclic graph (DAG) of modules with polymorphically typed inputs and outputs. As shown in figure 2, there are four classes of modules:
+
+• Input modules (shown in blue), drawn from the set $\left\{ { { s } _ { t } } , { { a } _ { t } } , { { s } _ { t + 1 } } \right\}$ for the $I$ component and from the set $\{ i _ { t } , r _ { t } \}$ for the $\chi$ component. They have no inputs, and their outputs have the type corresponding to the types of states and actions in whatever domain they are applied to, or the reals numbers for rewards. Buffer and parameter modules (shown in gray) of two kinds: FIFO queues that provide as output a finite list of the $k$ most recent inputs, and neural network weights initialized at random at the start of the program and which may (pink border) or may not (black border) get updated via back-propagation depending on the computation graph.   
+• Functional modules (shown in white), which compute output values given the inputs from their parent modules.
+
+![](images/0a0c4e6a4bd6852b56d0df731e28f96775adc6b10506ef1c8a6dbe02b4eb42aa.jpg)  
+Figure 2: Example diagrams of published algorithms covered by our language (larger figures in the appendix). The green box represents the output of the intrinsic curiosity function, the pink box is the loss to be minimized. Pink arcs represent paths and networks along which gradients flow back from the minimizer to update parameters.
+
+• Update modules (shown in pink), which are functional modules (such as $\mathbf { k }$ -NearestNeighbor) that either add variables to buffers or modules which add real-valued outputs to a global loss that will provide error signals for gradient descent.
+
+A single node in the DAG is designated as the output node (shown in green): the output of this node is considered to be the output of the entire program, but it need not be a leaf node of the DAG.
+
+On each call to a program (corresponding to one time-step of the system) the current input values and parameter values are propagated through the functional modules, and the output node’s output is given to the RL algorithm. Before the call terminates, the FIFO buffers are updated and the adjustable parameters are updated via gradient descent using the Adam optimizer (Kingma & Ba, 2014). Most operations are differentiable and thus able to propagate gradients backwards. Some operations are not differentiable, including buffers (to avoid backpropagating through time) and ”Detach” whose purpose is stopping the gradient from flowing back. In practice, we have multiple copies of the same agent running at the same time, with both a shared policy and shared curiosity module. Thus, we execute multiple reward predictions on a batch and then update on a batch.
+
+Programs representing several published designs for curiosity modules that perform internal gradient descent, including inverse features (Pathak et al., 2017), random network distillation (RND) (Burda et al., 2018), and ensemble predictive variance (Pathak et al., 2019), are shown in figure 2 (bigger versions can be found in appendix A.3). We can also represent algorithms similar to novelty search (Lehman & Stanley, 2008) and $E X ^ { 2 }$ (Fu et al., 2017), which include buffers and nearest neighbor regression modules. Details on the data types and module library are given in appendix A.
+
+A crucial, and possibly somewhat counter-intuitive, aspect of these programs is their use of neural network weight updates via gradient descent as a form of memory. In the parameter update step, all adjustable parameters are decremented by the gradient of the sum of the outputs of the loss modules, with respect to the parameters. This type of update allows the program to, for example, learn to make some types of predictions, online, and use the quality of those predictions in a state to modulate the proxy reward for visiting that state (as is done, for example, in RND).
+
+Key to our program search are polymorphic data types: the inputs and outputs to each module are typed, but the instantiation of some types, and thus of some operations, depends on the environment. We have four types: reals $\mathbb { R }$ , state space of the given environment $\mathbb { S }$ , action space of the given environment A and feature space $\mathbb { F }$ , used for intermediate computations and always set to $\mathbb { R } ^ { 3 2 }$ in our current implementation. For example, a neural network module going from $\mathbb { S }$ to $\mathbb { F }$ will be instantiated as a convolutional neural network if $\mathbb { S }$ is an image and as a fully connected neural network of the appropriate dimension if $\mathbb { S }$ is a vector. Similarly, if we are measuring an error in action space A we use mean-squared error for continuous action spaces and negative log-likelihood for discrete action spaces. This facility means that the same curiosity program can be applied, independent of whether states are represented as images or vectors, or whether the actions are discrete or continuous, or the dimensionality of either.
+
+This type of abstraction enables our meta-learning approach to discover curiosity modules that generalize radically, applying not just to new tasks, but to tasks with substantially different input and output spaces than the tasks they were trained on.
+
+To clarify the semantics of these programs, we walk through the operation of the RND program in figure 2. Its only input is $s _ { t + 1 }$ , which might be an image or an input vector, which is processed by two NNs with parameters $\Theta _ { 1 }$ and $\Theta _ { 2 }$ , respectively. The structure of the NNs (and, hence, the dimensions of the $\Theta _ { i }$ ) depends on the type of $s _ { t + 1 }$ : if $s _ { t + 1 }$ is an image, then they are CNNs, otherwise a fully connected networks. Each NN outputs a 32-dimensional vector; the $L _ { 2 }$ distance between these vectors is the output of the program on this iteration, and is also the input to a loss module. So, given an input $s _ { t + 1 }$ , the output intrinsic reward is large if the two NNs generate different outputs and small otherwise. After each forward pass, the weights in $\Theta _ { 2 }$ are updated to minimize the loss while $\Theta _ { 1 }$ remains constant, which causes the trainable NN to mimic the output of the randomly initialized NN. As the program’s ability to predict the output of the randomized NN on an input improves, the intrinsic reward for visiting that state decreases, driving the agent to visit new states.
+
+To limit the search space and prioritize short, meaningful programs we limit the total number of modules of the computation graph to 7. Our language is expressive enough to describe many (but far from all) curiosity mechanisms in the existing literature, as well as many other potential alternatives, but the expressiveness leads to a very large search space. Additionally, removing or adding a single operation can drastically change the behavior of a program, making the objective function nonsmooth and, therefore, the space hard to search. In the next section we explore strategies for speeding up the search over tens of thousands of programs.
+
+# 3 IMPROVING THE EFFICIENCY OF OUR SEARCH
+
+We wish to find curiosity programs that work effectively in a wide range of environments, from simple to complex. However, evaluating tens of thousands of programs in the most expensive environments would consume decades of GPU computation. Therefore, we designed multiple strategies for quickly discarding less promising programs and focusing computation on a few promising programs. In doing so, we take inspiration from efforts in the AutoML community (Hutter et al., 2018).
+
+We divide these pruning efforts into three categories: simple tests that are independent of running the program in any environment, “filtering” by ruling out some programs based on poor performance in simple environments, and “meta-meta-RL”: learning to predict which curiosity programs will produce good RL agents based on syntactic features.
+
+# 3.1 PRUNING INVALID ALGORITHMS WITHOUT RUNNING THEM
+
+Many programs are obviously bad curiosity programs. We have developed two heuristics to immediately prune these programs without an expensive evaluation.
+
+• Checking that programs are not duplicates. Since our language is highly expressive, there are many non-obvious ways of getting equivalent programs. To find duplicates, we designed a randomized test where we identically seed two programs, feed them both identical fake environment data for tens of steps and check whether their outputs are identical. Checking that the loss functions cannot be minimized independently of the input data. Many programs optimize some loss depending on neural network regressors. If we treat inputs as uncontrollable variables and networks as having the ability to become any possible function, then for every variable, we can determine whether neural networks can be optimized to minimize it, independently of the input data. For example, if our loss function is $| N N _ { \theta } ( s ) | ^ { 2 }$ the neural network can learn to make it 0 by disregarding $s$ and optimizing the weights $\theta$ to 0. We discard any program that has this property.
+
+# 3.2 PRUNING ALGORITHMS IN CHEAP ENVIRONMENTS
+
+Our ultimate goal is to find algorithms that perform well on many different environments, both simple and complex. We make two key observations. First, there may be only tens of reasonable programs that perform well on all environments but hundreds of thousands of programs that perform poorly. Second, there are some environments that are solvable in a few hundred steps while others require tens of millions. Therefore, a key idea in our search is to try many programs in cheap environments and only a few promising candidates in the most expensive environments. This was inspired by the effective use of sequential halving (Karnin et al., 2013) in hyper-parameter optimization (Jamieson & Talwalkar, 2016).
+
+By pruning programs aggressively, we may be losing multiple programs that perform well on complex environments. However, by definition, these programs will tend to be less general and robust than those that succeed in all environments. Moreover, we seek generalization not only for its own sake, but also to ease the search since, even if we only cared about the most expensive environment, performing the complete search only in this environment would be impractical.
+
+# 3.3 PREDICTING ALGORITHM PERFORMANCE
+
+Perhaps surprisingly, we find that we can predict program performance directly from program structure. Our search process bootstraps an initial training set of (program structure, program performance) pairs, then uses this training set to select the most promising next programs to evaluate. We encode each program’s structure with features representing how many times each operation is used, thus having as many features as number of operations in our vocabulary. We use a $k$ -nearestneighbor regressor, with $k = 1 0$ . We then try the most promising programs and update the regressor with their results. Finally, we add an $\epsilon$ -greedy exploration policy to make sure we explore all the search space. Even though the correlation between predictions and actual values is only moderately high (0.54 on a holdout test), this is enough to discover most of the top programs searching only half of the program space, which is our ultimate goal. Results are shown in appendix C.
+
+We can also prune algorithms during the training process of the RL agent. In particular, at any point during the meta-search, we use the top $K$ current best programs as benchmarks for all $T$ timesteps. Then, during the training of a new candidate program we compare its current performance at time $t$ with the performance at time $t$ of the top $K$ programs and stop the run if its performance is significantly lower. If the program is not pruned and reaches the final time-step $T$ with one of the top $K$ performances, it becomes part of the benchmark for the future programs.
+
+# 4 EXPERIMENTS
+
+Our RL agent uses PPO (Schulman et al., 2017) based on the implementation by Kostrikov (2018) in PyTorch (Paszke et al., 2017). Our code (https://github.com/mfranzs/ meta-learning-curiosity-algorithms) can take in any OpenAI gym environment (Brockman et al., 2016) with a specification of the desired exploration horizon $T$ .
+
+We evaluate each curiosity algorithm for multiple trials, using a seed dependent on the trial but independent of the algorithm, which leads to the PPO weights and curiosity data-structures being initialized identically on the same trials for all algorithms. As is common in PPO, we run multiple rollouts (5, except for MuJoCo which only has 1), with independent experiences but shared policy and curiosity modules. Curiosity predictions and updates are batched across these rollouts, but not across time. PPO policy updates are batched both across rollouts and multiple timesteps.
+
+# 4.1 FIRST SEARCH PHASE IN SIMPLE ENVIRONMENT
+
+We start by searching for a good intrinsic curiosity program $I$ in a purely exploratory environment, designed by Chevalier-Boisvert et al. (2018), which is an image-based grid world where agents navigate in an image of a 2D room either by moving forward in the grid or rotating left or right. We optimize the total number of distinct cells visited across the agent’s lifetime. This allows us to evaluate intrinsic reward programs in a fast and simple environment, without worrying about combining it with external reward.
+
+To bias towards simple, interpretable algorithms and keep the search space manageable, we search for programs with at most 7 operations. We first discard duplicate and invalid programs, as described in section 3.1, resulting in about 52,000 programs. We then randomly split the programs across 4 machines, each with 8 Nvidia Tesla K80 GPUs for 10 hours; thus a total of 13 GPU days.
+
+Each machine finds the highest-scoring 625 programs in its section of the search space and prunes programs whose partial learning curve is statistically significantly lower than the current top 625 programs. To do so, after every episode of every trial, we check whether $m e a n _ { p r o g r a m } ( s t e p ) \leq$ $m e a n _ { t o p 6 2 5 } ( s t e p ) - 2 s t d _ { t o p 6 2 5 } - s t d _ { p r o g r a m }$ .Thus, we account for both inter-program variability among the top 625 programs and intra-program variability among multiple trials of the same program.
+
+We use a 10-nearest-neighbor regressor to predict program performance and choose the next program to evaluate with an $\epsilon$ -greedy strategy, choosing the best predicted program ${ \dot { 9 } } 0 \%$ of the time and a random program $1 \bar { 0 } \%$ of the time. By doing this, we try the most promising programs early in our search. This is important for two reasons: first, we only try 26,000 programs, half of the whole search space, which we estimated from earlier results (shown in figure 8 in the appendix) would be enough to get $8 8 \%$ of the top $1 \%$ of programs. Second, the earlier we run our best programs, the higher the bar for later programs, thus allowing us to prune them earlier, further saving computation time. Searching through this space took a total of 13 GPU days. As shown in figure 9 in the appendix, we find that most programs perform relatively poorly, with a long tail of programs that are statistically significantly better, comprising roughly $0 . 5 \%$ of the whole program space.
+
+![](images/b553da7ff7105014e117ad7a78c9f8a55c2196b065b5491fecdfc7d901275e12.jpg)  
+Figure 3: Fast Action-Space Transition(FAST): top-performing intrinsic curiosity algorithm discovered in our phase 1 search.
+
+The highest scoring program (a few other programs have lower average performance but are statistically equivalent) is surprisingly simple and meaningful, comprised of only 5 operations, even though the limit was 7. This program, which we call FAST (Fast Action-Space Transition), is shown in figure 3; it trains a single neural network (a CNN or MLP depending on the type of state) to predict the action from $s _ { t + 1 }$ and then compares its predictions based on $s _ { t + 1 }$ with its predictions based on $s _ { t }$ , generating high intrinsic reward when the difference is large. The action prediction loss module either computes a softmax followed by NLL loss or appends zeros to the action to match dimensions and applies MSE loss, depending on the type of the action space. Note that this is not the same as rewarding taking a different action in the previous time-step. The network predicting the action is learning to imitate the policy learned by the internal RL agent, because the curiosity module does not have direct access to the RL agent’s internal state.
+
+Of the top 16 programs, 13 are variants of FAST, including versions that predict the action from $s _ { t }$ instead of $s _ { t + 1 }$ . The other 3 are variants of a more complex program that is hard to understand at first glance, but we finally determined to be using ideas similar to cycle-consistency in the GAN literature Zhu et al. (2017) (we thus name it Cycle-consistency intrinsic motivation); the diagram and explanation are in figure 10 in the appendix. Interestingly, to the best of our knowledge neither algorithm had been proposed before: we conjecture the former was too simple for humans to believe it would be effective and the latter too hard for humans to design, as it was already very hard to understand in hindsight.
+
+# 4.2 TRANSFERRING TO NEW ENVIRONMENTS
+
+Our reward combiner was developed in lunar lander (the simplest environment with meaningful extrinsic reward) based on the best program among a preliminary set of 16,000 programs (which resembled Random Network Distillation; its computation graph is shown in appendix E). Among a set of 2,500 candidates (with 5 or fewer operations) the best reward combiner discovered by our search was $\begin{array} { r } { \widehat { r _ { t } } = \frac { ( 1 + i _ { t } - t / T ) \cdot i _ { t } + t / T \cdot r _ { t } } { 1 + i _ { t } } } \end{array}$ . Notice that for $0 < i _ { t } \ll 1$ (usually the case) this is approximately $\widehat { r _ { t } } \approx i _ { t } ^ { 2 } + ( 1 - t / T ) i _ { t } + ( t / T ) r _ { t }$ , which is a down-scaled version of intrinsic reward plus a linear binterpolation that ranges from all intrinsic reward at $t = 0$ to all extrinsic reward at $t = T$ . In future work, we hope to co-adapt the search for intrinsic reward programs and combiners as well as find multiple reward combiners.
+
+![](images/552033e508c214ab3ef95cd0920da9ca6592eef4b36621777c13c1f263d582fc.jpg)  
+Figure 4: Correlation between program performance in gridworld and in harder environments (lunar lander on the left, acrobot on the right), using the top 2,000 programs in gridworld. Performance is evaluated using mean reward across all learning episodes, averaged over trials (two trials for acrobot / lunar lander and five for gridworld). The high number of algorithms performing around -300 in the middle of the right plot is an artifact of averaging the performance of two seeds and the mean performance in Acrobot having two peaks. Almost all intrinsic curiosity programs that had statistically significant performance for grid world also do well on the other two environments. In green, the performance of three published works; in increasing gridworld performance: disagreement (Pathak et al., 2019), inverse features (Pathak et al., 2017) and random distillation (Burda et al., 2018).
+
+Given the fixed reward combiner and the list of 2,000 selected programs found in the image-based grid world, we evaluate the programs on both lunar lander and acrobot, in their discrete action space versions. Notice that both environments have much longer horizons than the image-based grid world (37,500 and 50,000 vs 2,500) and they have vector-based, rather than image-based, inputs. The results in figure 4 show good correlation between performance on grid world and on each of the new environments. Especially interesting is that, for both environments, when intrinsic reward in grid world is above 400 (the lowest score that is statistically significantly good), performance on the other two environments is also good in more than $9 0 \%$ of cases.
+
+Finally, we evaluate on two MuJoCo environments (Todorov et al., 2012): hopper and ant. These environments have more than an order of magnitude longer exploration horizon than acrobot and lunar lander, exploring for 500K time-steps, as well as continuous action-spaces instead of discrete. We then compare the best 16 programs on grid world (most of which also did well on lunar lander and acrobot) to four weak baselines (constant 0,-1,1 intrinsic reward and Gaussian noise reward) and three published algorithms expressible in our language (shown in figure 2). We run two trials for each algorithm and pool all results in each category to get a confidence interval for the mean of that category. All trials used the reward combiner found on lunar lander. For both environments we find that the performance of our top programs is statistically equivalent to published work and significantly better than the weak baselines, confirming that we meta-learned good curiosity programs.
+
+Note that we meta-trained our intrinsic curiosity programs only on one environment (GridWorld) and showed they generalized well to other very different environments: they perform better than published works in this meta-train task and one meta-test task (Acrobot) and on par in the other 3 tasks meta-test tasks. Adding more meta-training tasks would be as simple as standardising the perfor
+
+<table><tr><td>Class</td><td>Ant</td><td>Hopper</td></tr><tr><td>Baseline algorithms</td><td>[-95.3, -39.9]</td><td>[318.5, 525.0]</td></tr><tr><td>Meta-learned algorithms</td><td>[+67.5, +80.0]</td><td>[589.2, 650.6]</td></tr><tr><td>Published algorithms</td><td>[+67.4, +98.8]</td><td>[627.7, 692.6]</td></tr></table>
+
+Table 1: Meta-learned algorithms perform significantly better than constant rewards and statistically equivalently to published algorithms found by human researchers (see 2). The table shows the confidence interval (one standard deviation) for the mean performance (across trials, across algorithms) for each algorithm category. Performance is defined as mean episode reward for all episodes.
+
+mance within each task (to make results comparable) and then selecting the programs with best mean performance. We chose to only meta-train on a single, simple, task because it (surprisingly!) already gave great results, highlighting the broad generalization of meta-learning program representations.
+
+# 5 RELATED WORK
+
+In some regards our work is similar to neural architecture search (NAS) (Stanley & Miikkulainen, 2002; Zoph & Le, 2016; Elsken et al., 2018; Pham et al., 2018) or hyperparameter optimization for deep networks (Mendoza et al., 2016), which aim at finding the best neural network architecture and hyper-parameters for a particular task. However, in contrast to most (but not all, see Zoph et al. (2018)) NAS work, we want to generalize to many environments instead of just one. Moreover, we search over programs, which include non-neural operations and data structures, rather than just neural-network architectures, and decide what loss functions to use for training. Our work also resembles work in the AutoML community (Hutter et al., 2018) that searches in a space of programs, for example in the case of SAT solving (KhudaBukhsh et al., 2009) or auto-sklearn (Feurer et al., 2015) and concurrent work on learning loss functions to replace cross-entropy for training a fixed architecture on MNIST and CIFAR (Gonzalez & Miikkulainen, 2019; 2020). Although we took inspiration from ideas in that community (Jamieson & Talwalkar, 2016; Li et al., 2016), our algorithms specify both how to compute their outputs and their own optimization objectives in order to work well in synchrony with an expensive deep RL algorithm.
+
+There has been work on meta-learning with genetic programming (Schmidhuber, 1987), searching over mathematical operations within neural networks (Ramachandran et al., 2017; Gaier & Ha, 2019), searching over programs to solve games (Wilson et al., 2018; Kelly & Heywood, 2017; Silver et al., 2019) and to optimize neural networks (Bengio et al., 1995; Bello et al., 2017), and neural networks that learn programs (Reed & De Freitas, 2015; Pierrot et al., 2019). Our work uses neural networks as basic operations within larger algorithms. Finally, modular meta-learning (Alet et al., 2018; 2019) trains the weights of small neural modules and transfers to new tasks by searching for a good composition of modules; as such, it can be seen as a (restricted) dual of our approach.
+
+There has been much interesting work in designing intrinsic curiosity algorithms. We take inspiration from many of them to design our domain-specific language. In particular, we rely on the idea of using neural network training as an implicit memory, which scales well to millions of time-steps, as well as buffers and nearest-neighbour regressors. As we showed in figure 2 we can represent several prominent curiosity algorithms. We can also generate meaningful algorithms similar to novelty search (Lehman & Stanley, 2008) and $E X ^ { 2 }$ $\mathrm { F u }$ et al., 2017); which include buffers and nearest neighbours. However, there are many exploration algorithm classes that we do not cover, such as those focusing on generating goals (Srivastava et al., 2013; Kulkarni et al., 2016; Florensa et al., 2018), learning progress (Oudeyer et al., 2007; Schmidhuber, 2008; Azar et al., 2019), generating diverse skills (Eysenbach et al., 2018), stochastic neural networks (Florensa et al., 2017; Fortunato et al., 2017), count-based exploration (Tang et al., 2017) or object-based curiosity measures (Forestier & Oudeyer, 2016). Finally, part of our motivation stems from Ta¨ıga et al. (2019) showing that some bonus-based curiosity algorithms have trouble generalising to new environments.
+
+There have been research efforts on meta-learning exploration policies: Duan et al. (2016); Wang et al. (2017) learn an LSTM that explores an environment for one episode, retains its hidden state and is spawned in a second episode in the same environment; by training the network to maximize the reward in the second episode alone it learns to explore efficiently in the first episode. Stadie et al. (2018) improves their exploration and that of Finn et al. (2017) by considering the importance of sampling in RL policies. Gupta et al. (2018) combine gradient-based meta-learning with a learned latent exploration space in which they add structured noise for meaningful exploration. Closer to our formulation, Zheng et al. (2018) parametrize an intrinsic reward function which influences policygradient updates in a differentiable manner, allowing them to backpropagate through a single step of the policy-gradient update to optimize the intrinsic reward function for a single task. In contrast to all three of these methods, we search over algorithms, which will allows us to generalize more broadly and to consider the effect of exploration on up to $1 0 ^ { 5 } - 1 0 ^ { 6 }$ time-steps instead of the $1 0 ^ { 2 } - 1 0 ^ { 3 }$ of previous work. Finally, Chiang et al. (2019); Faust et al. (2019) have a setting similar to ours where they modify reward functions over the entire agent’s lifetime, but instead of searching over intrinsic curiosity algorithms they tune the parameters of a hand-designed reward function.
+
+Related work on meta-learning (Schmidhuber, 1987; Thrun & Pratt, 1998; Clune, 2019) and efforts to increase its generalization can be found in appendix B. Closest to our work, evolved policy gradients (EPG, Houthooft et al. (2018)) use evolutionary strategies to meta-learn a neural network that acts as a loss function and is used to train a policy network. EPG generalizes by meta-training with target locations east of the start location and meta-testing with target locations to the west. In contrast, we showed that by meta-learning programs, we can generalize between radically different environments, not just goal variations of a single environment. Concurrent to our work, Kirsch et al. (2019) also show generalization capabilities between environments similar to ours (lunar lander, hopper and half-cheetah). Their approach transfers a parametric representation, for which it is unclear how to adapt the learned neural losses to an unseen environment with a different observation space. Their approach thus does not encode states into the loss function, which is critical for efficient exploration. In contrast, our algorithms can leverage polymorphic data types that adapt the neural networks to the environment they are running in, adapting both the size and the type of network (CNN vs MLP) running in each environment.
+
+# 6 CONCLUSIONS
+
+In this work, we proposed to meta-learn algorithms and show that by transferring programs we can generalize between tasks much more varied than previously possible in meta-RL, even between those with different input or output spaces. In many settings, however, the input and output space remain the same as we change tasks. This opens the possibility of getting the best of both worlds by meta-learning weights along with structure, thus simultaneously transferring domain-specific knowledge in the weights and higher-level algorithmic knowledge in the architecture. In addition, we note that the approach of meta-learning programs instead of network weights may have further applications beyond finding curiosity algorithms, such as meta-learning optimization algorithms or even meta-learning meta-learning algorithms. Our relatively modest compute (2 GPU-weeks) and a simple search method restricted us to a medium-sized search space, but we expect that future work could search over significantly bigger spaces. It thus may be possible to automatically search for new machine learning algorithms from more fundamental building blocks for a wide variety of problems.
+
+# ACKNOWLEDGMENTS
+
+We thank Kelsey Allen, Peter Karkus, Kevin Smith, Josh Tenenbaum and the rest of the HondaCMM MIT team for their insightful feedback. We thank Chris Lu for his idea on what the algorithm in figure 10 is computing. We also want to thank Bernadette Bucher, Chelsea Finn, Abhishek Gupta, Deepak Pathak, Lerrel Pinto, Oleh Rybkin, Karl Schmeckpeper and Joaquin Vanschoren for valuable conversations. Finally, we also want to thank Maria Bauza and Tej Chajed for their feedback on early drafts and Clement Gehring for his help setting up the experiments.
+
+We gratefully acknowledge support from NSF grants 1523767 and 1723381, AFOSR grant FA9550- 17-1-0165, ONR grant N00014-18-1-2847, the Honda Research Institute, SUTD Temasek Laboratories and the MIT Quest for Intelligence. Any opinions, findings, and conclusions or recommendations expressed in this material do not necessarily reflect the views of our sponsors.
+
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+# A DETAILS OF OUR DOMAIN-SPECIFIC LANGUAGE FOR CURIOSITYALGORITHMS
+
+We have the following types. Note that $\mathbb { S }$ and $\mathbb { A }$ get defined differently for every environment.
+
+• $\mathbb { R }$ : real numbers such as $r _ { t }$ or the dot-product between two vectors.   
+• $\mathbb { R } ^ { + }$ : numbers guaranteed to be positive, such as the distance between two vectors. The only difference to our program search between $\mathbb { R }$ and $\mathbb { R } ^ { + }$ is in pruning programs that can optimize objectives without looking at the data. For $\mathbb { R } ^ { + }$ we check whether they can optimize down to 0, for $\mathbb { R }$ we check whether they can optimize to arbitrarily negative values.   
+• state space $\mathbb { S }$ : the environment state, such as a matrix of pixels or a vector with robot joint values. The particular form of this type is adapted to each environment.   
+• action space A: either a 1-hot description of the action or the action itself. The particular form of this type is adapted to each environment.   
+• feature-space $\mathbb { F } = \mathbb { R } ^ { 3 2 }$ : a space mostly useful to work with neural network embeddings. For simplicity, we only have a single feature space.   
+• List[X]: for each type we may also have a list of elements of that type. All operations that take a particular type as input can also be applied to lists of elements of that type by mapping the function to every element in the list. Lists also support extra operations such as average or variance.
+
+A.1 CURIOSITY OPERATIONS  
+
+<table><tr><td rowspan=1 colspan=1>Operation</td><td rowspan=1 colspan=3>Input type(s)</td><td rowspan=1 colspan=2>State</td><td rowspan=1 colspan=2>Output type</td></tr><tr><td rowspan=1 colspan=1>Add</td><td rowspan=1 colspan=3>R,R</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>RunningNorm</td><td rowspan=1 colspan=3>R</td><td rowspan=1 colspan=2>R</td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>VariableAsBuffer</td><td rowspan=1 colspan=3>X</td><td rowspan=1 colspan=1>List[X]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>List[X]</td></tr><tr><td rowspan=1 colspan=1>NearestNeighborRegressor</td><td rowspan=1 colspan=3>F,F</td><td rowspan=1 colspan=1>List[F]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>F</td></tr><tr><td rowspan=1 colspan=1>SubtractOneTenth</td><td rowspan=1 colspan=3>R</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>NormalDistribution</td><td rowspan=1 colspan=3></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>Subtract</td><td rowspan=1 colspan=3>R,R</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>Sqrt(Abs(x))</td><td rowspan=1 colspan=3>R</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R+</td></tr><tr><td rowspan=1 colspan=1>NN F,F → F</td><td rowspan=1 colspan=3>F,F</td><td rowspan=1 colspan=2>OF,F→F</td><td rowspan=1 colspan=2>F</td></tr><tr><td rowspan=1 colspan=1>NNF,F→A</td><td rowspan=1 colspan=3>F,F</td><td rowspan=1 colspan=2>OF,F→A</td><td rowspan=1 colspan=2>A</td></tr><tr><td rowspan=1 colspan=1>NNF→A</td><td rowspan=1 colspan=3>F</td><td rowspan=1 colspan=2>OF→A</td><td rowspan=1 colspan=2>A</td></tr><tr><td rowspan=1 colspan=1>NN A→F</td><td rowspan=1 colspan=3>A</td><td rowspan=1 colspan=2>OA→F</td><td rowspan=1 colspan=2>F</td></tr><tr><td rowspan=1 colspan=1>(C)NN</td><td rowspan=1 colspan=3>S</td><td rowspan=1 colspan=2>Os→F</td><td rowspan=1 colspan=2>F</td></tr><tr><td rowspan=1 colspan=1>(C)NN, Detach</td><td rowspan=1 colspan=3>S</td><td rowspan=1 colspan=2>Os→F</td><td rowspan=1 colspan=2>F</td></tr><tr><td rowspan=1 colspan=1>(C)NNEnsemble</td><td rowspan=1 colspan=3>S</td><td rowspan=1 colspan=2>5xOs-→F</td><td rowspan=1 colspan=1>List[F]</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>NN Ensemble F→F</td><td rowspan=1 colspan=3>F</td><td rowspan=1 colspan=2>5xOF→F</td><td rowspan=1 colspan=1>List[F]</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>NN Ensemble F,F → F</td><td rowspan=1 colspan=3>F,F</td><td rowspan=1 colspan=2>5xOF,F→F</td><td rowspan=1 colspan=1>List[F]</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>NN Ensemble F,A →F</td><td rowspan=1 colspan=3>F,A</td><td rowspan=1 colspan=2>5xOA,F→F</td><td rowspan=1 colspan=1>List[F]</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>MinimizeValue</td><td rowspan=1 colspan=3>R</td><td rowspan=1 colspan=2>Adam</td><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>L2Norm</td><td rowspan=1 colspan=3>X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R+</td></tr><tr><td rowspan=1 colspan=1>L2Distance</td><td rowspan=1 colspan=3>X, X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>ActionSpaceLoss</td><td rowspan=1 colspan=3>X,A</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R+</td></tr><tr><td rowspan=1 colspan=1>DotProduct</td><td rowspan=1 colspan=3>X, X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>Add</td><td rowspan=1 colspan=3>X, X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>X</td></tr><tr><td rowspan=1 colspan=1>Detach</td><td rowspan=1 colspan=3>X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>X</td></tr><tr><td rowspan=1 colspan=1>Mean</td><td rowspan=1 colspan=2>List[R]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R</td></tr><tr><td rowspan=1 colspan=1>Variance</td><td rowspan=1 colspan=2>List[X]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>R+</td></tr><tr><td rowspan=1 colspan=1>Mean</td><td rowspan=1 colspan=1>List[X]</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=2>X</td></tr><tr><td rowspan=1 colspan=1>Mapped L2 Norm</td><td rowspan=1 colspan=1>List[X]</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>List[R]</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Average Distance</td><td rowspan=1 colspan=1>List</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>，X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>R</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Minus</td><td rowspan=1 colspan=1>List</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>，X</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>List[X]</td><td rowspan=1 colspan=1></td></tr></table>
+
+Note that $\mathbb { X }$ stands for the option of being $\mathbb { F }$ or A. NearestNeighborRegressor takes a query and a target, automatically creates a buffer of the target (thus keeps a list as a state) and answers based on the buffer. RunningNorm keeps track of the variance of the input and normalizes by that variance.
+
+A.2 REWARD COMBINER OPERATIONS  
+
+<table><tr><td rowspan=1 colspan=1>Operation</td><td rowspan=1 colspan=2>Input type(s)</td><td rowspan=1 colspan=1>State</td><td rowspan=1 colspan=1>Output type</td></tr><tr><td rowspan=1 colspan=1>Constant {0.01,0.1,0.5,1]</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>NormalDistribution</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>Add</td><td rowspan=1 colspan=2>R,R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>Max</td><td rowspan=1 colspan=2>R,R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>Min</td><td rowspan=1 colspan=2>R,R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>WeightedNormalizedSum</td><td rowspan=1 colspan=2>R, R, R, R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>RunningNorm</td><td rowspan=1 colspan=2>R</td><td rowspan=1 colspan=1>R</td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>VariableAsBuffer</td><td rowspan=1 colspan=2>R</td><td rowspan=1 colspan=1>List[R]</td><td rowspan=1 colspan=1>List[R]</td></tr><tr><td rowspan=1 colspan=1>Subtract</td><td rowspan=1 colspan=2>R,R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>Multiply</td><td rowspan=1 colspan=2>R,R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr><tr><td rowspan=1 colspan=1>Sqrt(Abs(x))</td><td rowspan=1 colspan=2>R</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R+</td></tr><tr><td rowspan=1 colspan=1>Mean</td><td rowspan=1 colspan=1>List[R]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>R</td></tr></table>
+
+Note that W eightedNormaliz $\begin{array} { r } { { \mathrm { { ? } } d } S u m ( a , b , c , d ) = \frac { a b + c d } { | a | + | c | } } \end{array}$ RunningNorm keeps track of the variance of the input and normalizes by that variance.
+
+# A.3 TWO OTHER PUBLISHED ALGORITHMS COVERED BY OUR DSL
+
+![](images/b4cc34407c965592a423660e66969c6e87cad82e11880ebcfb4d6d75a22388fc.jpg)  
+Figure 5: Curiosity by predictive error on inverse features by Pathak et al. (2017). In pink, paths and networks where gradients flow back from the minimizer.
+
+![](images/f85208832013cc57f31c9b9fa0280d7d355f5ed53f429fdfa9865b1864521ed9.jpg)  
+Figure 6: Curiosity by ensemble predictive variance Pathak et al. (2019). In pink, paths and networks where gradients flow back from the minimizer.
+
+# B RELATED WORK ON META-RL AND GENERALIZATION
+
+Most work on meta-RL has focused on learning transferable feature representations or parameter values for quickly adapting to new tasks (Finn et al., 2017; Finn, 2018; Clavera et al., 2019) or improving performance on a single task (Xu et al., 2018; Veeriah et al., 2019). However, the range of variability between tasks is typically limited to variations of the same goal (such as moving at different speeds or to different locations) or generalizing to different environment variations (such as different mazes or different terrain slopes). There have been some attempts to broaden the spectrum of generalization, showing transfer between Atari games thanks to modularity (Fernando et al., 2017; Rusu et al., 2016) or proper pretraining (Parisotto et al., 2015). However, as noted by Nichol et al. (2018), Atari games are too different to get big gains with current feature-transfer methods; they instead suggest using different levels of the game Sonic to benchmark generalization. Moreover, Yu et al. (2019) recently proposed a benchmark of many tasks. Wang et al. (2019) automatically generate different terrains for a bipedal walker and transfer policies between terrains, showing that this is more effective than learning a policy on hard terrains from scratch; similar to our suggestion in section 3.2. In contrast to these methods, we aim at generalization between completely different environments, even between environments that do not share the same state and action spaces.
+
+# C PREDICTING ALGORITHM PERFORMANCE
+
+![](images/9fbd5530cd73dffdf09f1a91c62ababc4d138fed0b39aab5576c1922197146bc.jpg)  
+Figure 7: Predicting algorithm performance from the structure of the program alone. Comparison between predicted and actual performance on a test set; showing a correlation of 0.54. In black, the identity line.
+
+![](images/153b3a788ffb7f48d93db180f61630a8be94107849ad3322edd2a6a72d37e025.jpg)  
+Figure 8: Predicting algorithm performance allows us to find the best programs faster. We investigate the number of the top $1 \%$ of programs found vs. the number of programs evaluated, and observe that the optimized search (in blue) finds $8 8 \%$ of the best programs after only evaluating $50 \%$ of the programs (highlighted in green). The naive search order would have only found $50 \%$ of the best programs at that point.
+
+![](images/d24148dd967ff4158d9e4bab9070cfef40799a69bf62f4671f0e8561668ef5d6.jpg)  
+Figure 9: In black, mean performance across 5 trials for all 26,000 programs evaluated (out of their finished trials). In green mean plus one standard deviation for the mean estimate and in red one minus one standard deviation for the mean estimate. On the right, you can see program means form roughly a gaussian distribution of very big noise (thus probably not significant) with a very small (between ${ \bar { 0 . 5 \% } }$ and $1 \%$ of programs) long tail of programs with statistically significantly good performance (their red dots are much higher than almost all green dots), composed of algorithms leading to good exploration.
+
+![](images/2cbb2b0db2b07eb57741a7d3006980c4c6a3c7a2faa959745bb458fb9c064012.jpg)  
+Figure 10: Cycle-Consistency Intrinsic Motivation algorithm, found by our search (3 of the top 16 programs on grid world are variants of this program). The purple Predict Target From Query boxes feed the query to a neural network, return the prediction as output and add the prediction loss to the optimization, back-propagating to the network and the query, but not the target. Notice that $\theta _ { 1 }$ is not getting trained because no loss back-propagates there; thus producing a random feature embedding $s _ { f } ( t )$ from $s ( t )$ . The algorithm combines several concepts seen in the literature, such as an untrained network like RND Burda et al. (2018) and predicting another state in feature space like Pathak et al. (2017; 2019), but also includes weight sharing between both predictions, which makes the algorithm hard to interpret at first sight, see below for an in-depth explanation.
+
+One can give meaning to the role of all 3 neural networks by considering how they contribute to minimizing the loss. To do so, let us name the networks: $\theta \{ 1 \}$ (as labeled in the figure) as $r _ { \theta _ { 1 } }$ (for random embedding), $\theta \{ 2 \}$ as $b _ { \theta _ { 2 } }$ (for backwards) and $\theta \{ 3 \}$ as $f r _ { \theta _ { 3 } }$ (for forward and random embedding) and look at the algorithm in equation form:
+
+$$
+i _ { t } = \left. b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t } ) \right) - b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } \left( s _ { t + 1 } \right) \right) \right.
+$$
+
+$$
+\begin{array} { c } { { \displaystyle \theta _ { 2 } : = \theta _ { 2 } - \eta \displaystyle \frac { \partial } { \partial \theta _ { 2 } } \Big ( \| b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t } ) \right) - r _ { \theta _ { 1 } } ( s _ { t } ) \| + } } \\ { { \displaystyle \| b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t + 1 } ) \right) - f r _ { \theta _ { 3 } } ( s _ { t } ) \| \Big ) } } \\ { { \displaystyle \theta _ { 3 } : = \theta _ { 3 } - \eta \displaystyle \frac { \partial } { \partial \theta _ { 3 } } \Big ( \| b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t } ) \right) - r _ { \theta _ { 1 } } ( s _ { t } ) \| \Big ) } } \end{array}
+$$
+
+We can see that $r _ { \theta _ { 1 } }$ will indeed be a random embedding because the network is randomly initialized and is not trained. Then, we observe that the second term in the loss for $\theta _ { 2 }$ , which does not involve $\theta _ { 3 }$ and thus $\theta _ { 2 }$ has to minimize alone, is $\| b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t + 1 } ) \right) - f r _ { \theta _ { 3 } } ( s _ { t } ) \|$ . In this term, $b _ { \theta _ { 2 } }$ receives a transformation of $s _ { t + 1 }$ and has to make it very similar to the same transformation applied to $s _ { t }$ ; therefore, this term is similar to cycle-consistency found in some other parts of machine learning Zhu et al. (2017) and $b _ { \theta _ { 2 } }$ must act like a backward model. Finally, looking at the minimization of $\theta _ { 3 }$ receives the original $s _ { t }$ and has to output a vector such that the backward model will bring it close to the random embedding of $s _ { t }$ . Therefore $\theta _ { 3 }$ must learn a forward model composed with the random embedding of $\theta _ { 1 }$ . Finally, we see that the algorithm outputs $\left. b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } ( s _ { t } ) \right) - b _ { \theta _ { 2 } } \left( f r _ { \theta _ { 3 } } \left( s _ { t + 1 } \right) \right) \right.$ , going forward and backward for both $s _ { t + 1 }$ and $s _ { t }$ and comparing the difference. In summary, this distance combines errors in the cycle-consistency of predictions (which will be higher in unvisited parts of the state) with distance in the random embedding space between $s ( t )$ and $s ( t + 1 )$ , i.e. moving to a very different state.
+
+![](images/4c51720083f85eb941721494621924294fc86ad54d62196f5ac81f66b3351227.jpg)  
+Figure 11: Top variant in preliminary search on grid world; variant on random network distillation using an ensemble of trained networks instead of a single one.

parse/train/HJlA0C4tPS/HJlA0C4tPS.md

@@ -0,0 +1,284 @@
+# A PROBABILISTIC FORMULATION OF UNSUPERVISED TEXT STYLE TRANSFER
+
+Junxian $\mathbf { H e } ^ { * }$ , Xinyi Wang∗, Graham Neubig Carnegie Mellon University {junxianh,xinyiw1,gneubig}@cs.cmu.edu
+
+Taylor Berg-Kirkpatrick University of California San Diego tberg@eng.ucsd.edu
+
+# ABSTRACT
+
+We present a deep generative model for unsupervised text style transfer that unifies previously proposed non-generative techniques. Our probabilistic approach models non-parallel data from two domains as a partially observed parallel corpus. By hypothesizing a parallel latent sequence that generates each observed sequence, our model learns to transform sequences from one domain to another in a completely unsupervised fashion. In contrast with traditional generative sequence models (e.g. the HMM), our model makes few assumptions about the data it generates: it uses a recurrent language model as a prior and an encoder-decoder as a transduction distribution. While computation of marginal data likelihood is intractable in this model class, we show that amortized variational inference admits a practical surrogate. Further, by drawing connections between our variational objective and other recent unsupervised style transfer and machine translation techniques, we show how our probabilistic view can unify some known non-generative objectives such as backtranslation and adversarial loss. Finally, we demonstrate the effectiveness of our method on a wide range of unsupervised style transfer tasks, including sentiment transfer, formality transfer, word decipherment, author imitation, and related language translation. Across all style transfer tasks, our approach yields substantial gains over state-of-the-art non-generative baselines, including the state-of-the-art unsupervised machine translation techniques that our approach generalizes. Further, we conduct experiments on a standard unsupervised machine translation task and find that our unified approach matches the current state-of-the-art.1
+
+# 1 INTRODUCTION
+
+Text sequence transduction systems convert a given text sequence from one domain to another. These techniques can be applied to a wide range of natural language processing applications such as machine translation (Bahdanau et al., 2015), summarization (Rush et al., 2015), and dialogue response generation (Zhao et al., 2017). In many cases, however, parallel corpora for the task at hand are scarce. Therefore, unsupervised sequence transduction methods that require only non-parallel data are appealing and have been receiving growing attention (Bannard & Callison-Burch, 2005; Ravi & Knight, 2011; Mizukami et al., 2015; Shen et al., 2017; Lample et al., 2018; 2019). This trend is most pronounced in the space of text style transfer tasks where parallel data is particularly challenging to obtain (Hu et al., 2017; Shen et al., 2017; Yang et al., 2018). Style transfer has historically referred to sequence transduction problems that modify superficial properties of text – i.e. style rather than content.2 We focus on a standard suite of style transfer tasks, including formality transfer (Rao & Tetreault, 2018), author imitation (Xu et al., 2012), word decipherment (Shen et al., 2017), sentiment transfer (Shen et al., 2017), and related language translation (Pourdamghani & Knight, 2017). General unsupervised translation has not typically been considered style transfer, but for the purpose of comparison we also conduct evaluation on this task (Lample et al., 2017).
+
+Recent work on unsupervised text style transfer mostly employs non-generative or non-probabilistic modeling approaches. For example, Shen et al. (2017) and Yang et al. (2018) design adversarial discriminators to shape their unsupervised objective – an approach that can be effective, but often introduces training instability. Other work focuses on directly designing unsupervised training objectives by incorporating intuitive loss terms (e.g. backtranslation loss), and demonstrates state-ofthe-art performance on unsupervised machine translation (Lample et al., 2018; Artetxe et al., 2019) and style transfer (Lample et al., 2019). However, the space of possible unsupervised objectives is extremely large and the underlying modeling assumptions defined by each objective can only be reasoned about indirectly. As a result, the process of designing such systems is often heuristic.
+
+In contrast, probabilistic models (e.g. the noisy channel model (Shannon, 1948)) define assumptions about data more explicitly and allow us to reason about these assumptions during system design. Further, the corresponding objectives are determined naturally by principles of probabilistic inference, reducing the need for empirical search directly in the space of possible objectives. That said, classical probabilistic models for unsupervised sequence transduction (e.g. the HMM or semi-HMM) typically enforce overly strong independence assumptions about data to make exact inference tractable (Knight et al., 2006; Ravi & Knight, 2011; Pourdamghani & Knight, 2017). This has restricted their development and caused their performance to lag behind unsupervised neural objectives on complex tasks. Luckily, in recent years, powerful variational approximation techniques have made it more practical to train probabilistic models without strong independence assumptions (Miao & Blunsom, 2016; Yin et al., 2018). Inspired by this, we take a new approach to unsupervised style transfer.
+
+We directly define a generative probabilistic model that treats a non-parallel corpus in two domains as a partially observed parallel corpus. Our model makes few independence assumptions and its true posterior is intractable. However, we show that by using amortized variational inference (Kingma & Welling, 2013), a principled probabilistic technique, a natural unsupervised objective falls out of our modeling approach that has many connections with past work, yet is different from all past work in specific ways. In experiments across a suite of unsupervised text style transfer tasks, we find that the natural objective of our model actually outperforms all manually defined unsupervised objectives from past work, supporting the notion that probabilistic principles can be a useful guide even in deep neural systems. Further, in the case of unsupervised machine translation, our model matches the current state-of-the-art non-generative approach.
+
+# 2 UNSUPERVISED TEXT STYLE TRANSFER
+
+We first overview text style transfer, which aims to transfer a text (typically a single sentence or a short paragraph – for simplicity we refer to simply “sentences” below) from one domain to another while preserving underlying content. For example, formality transfer (Rao & Tetreault, 2018) is the task of transforming the tone of text from informal to formal without changing its content. Other examples include sentiment transfer (Shen et al., 2017), word decipherment (Knight et al., 2006), and author imitation (Xu et al., 2012). If parallel examples were available from each domain (i.e. the training data is a bitext consisting of pairs of sentences from each domain), supervised techniques could be used to perform style transfer (e.g. attentional Seq2Seq (Bahdanau et al., 2015) and Transformer (Vaswani et al., 2017)). However, for most style transfer problems, only non-parallel corpora (one corpus from each domain) can be easily collected. Thus, work on style transfer typically focuses on the more difficult unsupervised setting where systems must learn from non-parallel data alone.
+
+The model we propose treats an observed non-parallel text corpus as a partially observed parallel corpus. Thus, we introduce notation for both observed text inputs and those that we will treat as latent variables. Specifically, we let $X = \{ x ^ { ( 1 ) } , x ^ { ( 2 ) } , \cdot \cdot \cdot , x ^ { ( \bar { m } ) } \}$ represent observed data from domain $\mathcal { D } _ { 1 }$ , while we let $Y = \{ y ^ { ( m + 1 ) } , y ^ { ( m + \overset { \cdot } { 2 } ) } , \cdot \cdot \cdot , y ^ { ( n ) } \}$ represent observed data from domain $\mathcal { D } _ { 2 }$ . Corresponding indices represent parallel sentences. Thus, none of the observed sentences share indices. In our model, we introduce latent sentences to complete the parallel corpus. Specifically, $\bar { X } = \{ \bar { x } ^ { ( m + 1 ) } , \bar { x } ^ { ( m + 2 ) } , \cdot \cdot \cdot , \bar { x } ^ { ( n ) } \}$ represents the set of latent parallel sentences in $\mathcal { D } _ { 1 }$ , while $\bar { Y } = \{ \bar { y } ^ { ( 1 ) } , \bar { y } ^ { ( 2 ) } , \cdot \cdot \cdot , \bar { y } ^ { ( m ) } \}$ represents the set of latent parallel sentences in $\mathcal { D } _ { 2 }$ . Then the goal of unsupervised text transduction is to infer these latent variables conditioned the observed non-parallel corpora; that is, to learn $p ( { \bar { y } } | x )$ and $p ( { \bar { x } } | y )$ .
+
+![](images/41384ec1945473ca58fdedb371d1e2b9339b296d94ddeac4f8b18385ad392414.jpg)  
+Figure 1: Proposed graphical model for style transfer via bitext completion. Shaded circles denote the observed variables and unshaded circles denote the latents. The generator is parameterized as an encoder-decoder architecture and the prior on the latent variable is a pretrained language model.
+
+# 3 THE DEEP LATENT SEQUENCE MODEL
+
+First we present our generative model of bitext, which we refer to as a deep latent sequence model.   
+We then describe unsupervised learning and inference techniques for this model class.
+
+# 3.1 MODEL STRUCTURE
+
+Directly modeling $p ( { \bar { y } } | x )$ and $p ( { \bar { x } } | y )$ in the unsupervised setting is difficult because we never directly observe parallel data. Instead, we propose a generative model of the complete data that defines a joint likelihood, $p ( X , { \bar { X } } , Y , { \bar { Y } } )$ . In order to perform text transduction, the unobserved halves can be treated as latent variables: they will be marginalized out during learning and inferred via posterior inference at test time.
+
+Our model assumes that each observed sentence is generated from an unobserved parallel sentence in the opposite domain, as depicted in Figure 1. Specifically, each sentence $\boldsymbol { x } ^ { ( i ) }$ in domain $\mathcal { D } _ { 1 }$ is generated as follows: First, a latent sentence $\bar { y } ^ { ( i ) }$ in domain $\mathcal { D } _ { 2 }$ is sampled from a prior, $p _ { { D _ { 2 } } } ( \bar { y } ^ { ( i ) } )$ . Then, $x ^ { ( i ) }$ is sampled conditioned on $\bar { y } ^ { ( i ) }$ from a transduction model, $p ( \boldsymbol { x } ^ { ( i ) } | \bar { y } ^ { ( i ) } )$ . Similarly, each observed sentence $y ^ { ( j ) }$ in domain $\mathcal { D } _ { 2 }$ is generated conditioned on a latent sentence, $\bar { x } ^ { ( j ) }$ , in domain $\mathcal { D } _ { 1 }$ via the opposite transduction model, $p ( \boldsymbol { y } ^ { ( j ) } | \bar { x } ^ { ( j ) } )$ , and prior, $p _ { \mathcal { D } _ { 1 } } ( \bar { x } ^ { ( j ) } )$ . We let $\theta _ { x | \bar { y } }$ and $\theta _ { y | \bar { x } }$ represent the parameters of the two transduction distributions respectively. We assume the prior distributions are pretrained on the observed data in their respective domains and therefore omit their parameters for simplicity of notation. Together, this gives the following joint likelihood:
+
+$$
+p ( X , \bar { X } , Y , \bar { Y } ; \theta _ { x | \bar { y } } , \theta _ { y | \bar { x } } ) = \left( \prod _ { i = 1 } ^ { m } p \big ( x ^ { ( i ) } | \bar { y } ^ { ( i ) } ; \theta _ { x | \bar { y } } \big ) p _ { \mathcal { D } _ { 2 } } \big ( \bar { y } ^ { ( i ) } \big ) \right) \left( \prod _ { j = m + 1 } ^ { n } p \big ( y ^ { ( j ) } | \bar { x } ^ { ( j ) } ; \theta _ { y | \bar { x } } \big ) p _ { \mathcal { D } _ { 1 } } \big ( \bar { x } ^ { ( j ) } \big ) \right)
+$$
+
+The log marginal likelihood of the data, which we will approximate during training, is:
+
+$$
+\log p ( X , Y ; \theta _ { x | \bar { y } } , \theta _ { y | \bar { x } } ) = \log \sum _ { \bar { X } } \sum _ { \bar { Y } } p ( X , \bar { X } , Y , \bar { Y } ; \theta _ { x | \bar { y } } , \theta _ { y | \bar { x } } )
+$$
+
+Note that if the two transduction models share no parameters, the training problems for each observed domain are independent. Critically, we introduce parameter sharing through our variational inference procedure, which we describe in more detail in Section 3.2.
+
+Architecture: Since we would like to be able to model a variety of transfer tasks, we choose a parameterization for our transduction distributions that makes no independence assumptions. Specifically, we employ an encoder-decoder architecture based on the standard attentional Seq2Seq model which has been shown to be successful across various tasks (Bahdanau et al., 2015; Rush et al., 2015). Similarly, our prior distributions for each domain are parameterized as recurrent language models which, again, make no independence assumptions. In contrast, traditional unsupervised generative sequence models typically make strong independence assumptions to enable exact inference (e.g. the HMM makes a Markov assumption on the latent sequence and emissions are one-to-one). Our model is more flexible, but exact inference via dynamic programming will be intractable. We address this problem in the next section.
+
+![](images/465557888fae2116dee1e4e4dd348b9e4d1230bed6a6f3b67479bcd78b680d54.jpg)  
+Figure 2: Depiction of amortized variational approximation. Distributions $q ( { \bar { y } } | x )$ and $q ( { \bar { x } } | y )$ represent inference networks that approximate the model’s true posterior. Critically, parameters are shared between the generative model and inference networks to tie the learning problems for both domains.
+
+# 3.2 LEARNING
+
+Ideally, learning should directly optimize the log data likelihood, which is the marginal of our model shown in Eq. 2. However, due to our model’s neural parameterization which does not factorize, computing the data likelihood cannot be accomplished using dynamic programming as can be done with simpler models like the HMM. To overcome the intractability of computing the true data likelihood, we adopt amortized variational inference (Kingma & Welling, 2013) in order to derive a surrogate objective for learning, the evidence lower bound (ELBO) on log marginal likelihood3 :
+
+$$
+\begin{array} { r l } & { \log p ( X , Y ; \theta _ { x | \bar { y } } , \theta _ { y | \bar { x } } ) } \\ & { \ge \mathcal { L } _ { \mathrm { E L B O } } ( X , Y ; \theta _ { x | \bar { y } } , \theta _ { y | \bar { x } } , \phi _ { \bar { x } | y } , \phi _ { \bar { y } | x } ) } \\ & { = \sum _ { i } \Big [ \mathbb { E } _ { q ( \bar { y } | x ^ { ( i ) } ; \phi _ { \bar { y } | x } ) } [ \log p ( x ^ { ( i ) } | \bar { y } ; \theta _ { x | \bar { y } } ) ] - D _ { \mathrm { K L } } \big ( q ( \bar { y } | x ^ { ( i ) } ; \phi _ { \bar { y } | x } ) | | p _ { \mathcal { D } _ { 2 } } ( \bar { y } ) \big ) \Big ] } \\ & { + \sum _ { j } \underbrace { \Big [ \mathbb { E } _ { q ( \bar { x } | y ^ { ( j ) } ; \phi _ { \bar { x } | y } ) } [ \log p ( y ^ { ( j ) } | \bar { x } ; \theta _ { y | \bar { x } } ) ] } _ { \mathrm { R e c o n s t u c i o n ~ l i k e l i h o o d } } - \underbrace { D _ { \mathrm { K L } } \big ( q ( \bar { x } | y ^ { ( j ) } ; \phi _ { \bar { x } | y } ) \big ) | p _ { \bar { D } _ { 1 } } ( \bar { x } ) \big ) } _ { \mathrm { K L ~ r e g u l a r i z e r } } \Big ] } \end{array}
+$$
+
+The surrogate objective introduces $q ( \bar { y } | x ^ { ( i ) } ; \phi _ { \bar { y } | x } )$ and $q ( \bar { x } | y ^ { ( j ) } ; \phi _ { \bar { x } | y } )$ , which represent two separate inference network distributions that approximate the model’s true posteriors, $p ( \bar { y } | x ^ { ( i ) } ; \theta _ { x | \bar { y } } )$ and $p ( \bar { x } | y ^ { ( j ) } ; \theta _ { y | \bar { x } } )$ , respectively. Learning operates by jointly optimizing the lower bound over both variational and model parameters. Once trained, the variational posterior distributions can be used directly for style transfer. The KL terms in Eq. 3, that appear naturally in the ELBO objective, can be intuitively viewed as regularizers that use the language model priors to bias the induced sentences towards the desired domains. Amortized variational techniques have been most commonly applied to continuous latent variables, as in the case of the variational autoencoder (VAE) (Kingma & Welling, 2013). Here, we use this approach for inference over discrete sequences, which has been shown to be effective in related work on a semi-supervised task (Miao & Blunsom, 2016).
+
+Inference Network and Parameter Sharing: Note that the approximate posterior on one domain aims to learn the reverse style transfer distribution, which is exactly the goal of the generative distribution in the opposite domain. For example, the inference network $\bar { q } ( \bar { y } | x ^ { ( i ) } ; \phi _ { \bar { y } | x } )$ and the generative distribution $p ( y | \bar { x } ^ { ( i ) } ; \theta _ { y | \bar { x } } )$ both aim to transform $\mathcal { D } _ { 1 }$ to $\mathcal { D } _ { 2 }$ . Therefore, we use the same architecture for each inference network as used in the transduction models, and tie their parameters: $\phi _ { \bar { x } | y } = \theta _ { x | \bar { y } } , \phi _ { \bar { y } | x } = \theta _ { y | \bar { x } }$ . This means we learn only two encoder-decoders overall – which are parameterized by $\theta _ { x | \bar { y } }$ and $\theta _ { y | \bar { x } }$ respectively – to represent two directions of transfer. In addition to reducing the number of learnable parameters, this parameter tying couples the learning problems for both domains and allows us to jointly learn from the full data. Moreover, inspired by recent work that builds a universal Seq2Seq model to translate between different language pairs (Johnson et al., 2017), we introduce further parameter tying between the two directions of transduction: the same encoder is employed for both $x$ and $y$ , and a domain embedding $c$ is provided to the same decoder to specify the transfer direction, as shown in Figure 2. Ablation analysis in Section 5.3 suggests that parameter sharing is important to achieve good performance.
+
+Approximating Gradients of ELBO: The reconstruction and KL terms in Eq. 3 still involve intractable expectations due to the marginalization over the latent sequence, thus we need to approximate their gradients. Gumbel-softmax (Jang et al., 2017) and REINFORCE (Sutton et al., 2000) are often used as stochastic gradient estimators in the discrete case. Since the latent text variables have an extremely large domain, we find that REINFORCE-based gradient estimates result in high variance. Thus, we use the Gumbel-softmax straight-through estimator to backpropagate gradients from the KL terms.4 However, we find that approximating gradients of the reconstruction loss is much more challenging – both the Gumbel-softmax estimator and REINFORCE are unable to outperform a simple stop-gradient method that does not back-propagate the gradient of the latent sequence to the inference network. This confirms a similar observation in previous work on unsupervised machine translation (Lample et al., 2018). Therefore, we use greedy decoding without recording gradients to approximate the reconstruction term.5 Note that the inference networks still receive gradients from the prior through the KL term, and their parameters are shared with the decoders which do receive gradients from reconstruction. We consider this to be the best empirical compromise at the moment.
+
+Initialization. Good initialization is often necessary for successful optimization of unsupervised learning objectives. In preliminary experiments, we find that the encoder-decoder structure has difficulty generating realistic sentences during the initial stages of training, which usually results in a disastrous local optimum. This is mainly because the encoder-decoder is initialized randomly and there is no direct training signal to specify the desired latent sequence in the unsupervised setting. Therefore, we apply a self-reconstruction loss $\mathcal { L } _ { \mathrm { r e c } }$ at the initial epochs of training. We denote the output the encoder as $e ( \cdot )$ and the decoder distribution as $p _ { \mathrm { d e c } }$ , then
+
+$$
+\mathcal { L } _ { \mathrm { { r e c } } } = - \alpha \cdot \sum _ { i } [ p _ { \mathrm { d e c } } ( e ( x ^ { ( i } ) , c _ { x } ) ] - \alpha \cdot \sum _ { j } [ p _ { \mathrm { d e c } } ( e ( y ^ { ( j } ) , c _ { y } ) ] ,
+$$
+
+$\alpha$ decays from 1.0 to 0.0 linearly in the first $k$ epochs. $k$ is a tunable parameter and usually less than 3 in all our experiments.
+
+# 4 CONNECTION TO RELATED WORK
+
+Our probabilistic formulation can be connected with recent advances in unsupervised text transduction methods. For example, back translation loss (Sennrich et al., 2016) plays an important role in recent unsupervised machine translation (Artetxe et al., 2018; Lample et al., 2018; Artetxe et al., 2019) and unsupervised style transfer systems (Lample et al., 2019). In order to incorporate back translation loss the source language $x$ is translated to the target language $y$ to form a pseudo-parallel corpus, then a translation model from $y$ to $x$ can be learned on this pseudo bitext just as in supervised setting. While back translation was often explained as a data augmentation technique, in our probabilistic formulation it appears naturally with the ELBO objective as the reconstruction loss term.
+
+Some previous work has incorporated a pretrained language models into neural semi-supervised or unsupervised objectives. He et al. (2016) uses the log likelihood of a pretrained language model as the reward to update a supervised machine translation system with policy gradient. Artetxe et al. (2019) utilize a similar idea for unsupervised machine translation. Yang et al. (2018) employed a similar approach, but interpret the LM as an adversary, training the generator to fool the LM. We show how our ELBO objective is connected with these more heuristic LM regularizers by expanding the KL loss term (assume $x$ is observed):
+
+$$
+D _ { \mathrm { K L } } ( q ( \bar { y } | x ) | | p _ { \mathcal { D } _ { 2 } } ( \bar { y } ) ) = - H _ { q } - \mathbb { E } _ { q } [ \log p _ { \mathcal { D } _ { 2 } } ( \bar { y } ) ] ,
+$$
+
+Note that the loss used in previous work does not include the negative entropy term, $- H _ { q }$ . Our objective results in this additional “regularizer”, the negative entropy of the transduction distribution, $- H _ { q }$ . Intuitively, $- H _ { q }$ helps avoid a peaked transduction distribution, preventing the transduction from constantly generating similar sentences to satisfy the language model. In experiments we will show that this additional regularization is important and helps bypass bad local optima and improve performance. These important differences with past work suggest that a probabilistic view of the unsupervised sequence transduction may provide helpful guidance in determining effective training objectives.
+
+# 5 EXPERIMENTS
+
+We test our model on five style transfer tasks: sentiment transfer, word substitution decipherment, formality transfer, author imitation, and related language translation. For completeness, we also evaluate on the task of general unsupervised machine translation using standard benchmarks.
+
+We compare with the unsupervised machine translation model (UNMT) which recently demonstrated state-of-the-art performance on transfer tasks such as sentiment and gender transfer (Lample et al., 2019).6 To validate the effect of the negative entropy term in the KL loss term Eq. 5, we remove it and train the model with a back-translation loss plus a language model negative log likelihood loss (which we denote as $_ { \mathrm { B T + N L L } }$ ) as an ablation baseline. For each task, we also include strong baseline numbers from related work if available. For our method we select the model with the best validation ELBO, and for UNMT or $_ { \mathrm { B T + N L L } }$ we select the model with the best back-translation loss. Complete model configurations and hyperparameters can be found in Appendix A.1.
+
+# 5.1 DATASETS AND EXPERIMENT SETUP
+
+Word Substitution Decipherment. Word decipherment aims to uncover the plain text behind a corpus that was enciphered via word substitution where word in the vocabulary is mapped to a unique type in a cipher dictionary (Dou & Knight, 2012; Shen et al., 2017; Yang et al., 2018). In our formulation, the model is presented with a non-parallel corpus of English plaintext and the ciphertext. We use the data in (Yang et al., 2018) which provides 200K sentences from each domain. While previous work (Shen et al., 2017; Yang et al., 2018) controls the difficulty of this task by varying the percentage of words that are ciphered, we directly evaluate on the most difficult version of this task $- 1 0 0 \%$ of the words are enciphered (i.e. no vocabulary sharing in the two domains). We select the model with the best unsupervised reconstruction loss, and evaluate with BLEU score on the test set which contains 100K parallel sentences. Results are shown in Table 2.
+
+Sentiment Transfer. Sentiment transfer is a task of paraphrasing a sentence with a different sentiment while preserving the original content. Evaluation of sentiment transfer is difficult and is still an open research problem (Mir et al., 2019). Evaluation focuses on three aspects: attribute control, content preservation, and fluency. A successful system needs to perform well with respect to all three aspects. We follow prior work by using three automatic metrics (Yang et al., 2018; Lample et al., 2019): classification accuracy, self-BLEU (BLEU of the output with the original sentence as the reference), and the perplexity (PPL) of each system’s output under an external language model. We pretrain a convolutional classifier (Kim, 2014) to assess classification accuracy, and use an LSTM language model pretrained on each domain to compute the PPL of system outputs.
+
+We use the Yelp reviews dataset collected by Shen et al. (2017) which contains 250K negative sentences and 380K positive sentences. We also use a small test set that has 1000 human-annotated parallel sentences introduced in Li et al. (2018). We denote the positive sentiment as domain $\mathcal { D } _ { 1 }$ and the negative sentiment as domain $\mathcal { D } _ { 2 }$ . We use Self-BLEU and BLEU to represent the BLEU score of the output against the original sentence and the reference respectively. Results are shown in Table 1.
+
+Formality Transfer. Next, we consider a harder task of modifying the formality of a sequence. We use the GYAFC dataset (Rao & Tetreault, 2018), which contains formal and informal sentences from two different domains. In this paper, we use the Entertainment and Music domain, which has about 52K training sentences, 5K development sentences, and 2.5K test sentences. This dataset actually contains parallel data between formal and informal sentences, which we use only for evaluation. We follow the evaluation of sentiment transfer task and test models on three axes. Since the test set is a parallel corpus, we only compute reference BLEU and ignore self-BLEU. We use $\mathcal { D } _ { 1 }$ to denote formal text, and $\mathcal { D } _ { 2 }$ to denote informal text. Results are shown in Table 1.
+
+Table 1: Results on the sentiment transfer, author imitation, and formality transfer. We list the PPL of pretrained LMs on the test sets of both domains. We only report Self-BLEU on the sentiment task to compare with existing work.   
+
+<table><tr><td>Task</td><td>Model</td><td>Acc.</td><td>BLEU</td><td>Self-BLEU</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td rowspan="7">Sentiment</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>31.97</td><td>21.87</td></tr><tr><td>Shen et al. (2017)</td><td>79.50</td><td>6.80</td><td>12.40</td><td>50.40</td><td>52.70</td></tr><tr><td>Hu et al. (2017)</td><td>87.70</td><td>-</td><td>65.60</td><td>115.60</td><td>239.80</td></tr><tr><td>Yang et al. (2018)</td><td>83.30</td><td>13.40</td><td>38.60</td><td>30.30</td><td>42.10</td></tr><tr><td>UNMT</td><td>87.17</td><td>16.99</td><td>44.88</td><td>26.53</td><td>35.72</td></tr><tr><td>BT+NLL</td><td>88.36</td><td>12.36</td><td>31.48</td><td>8.75</td><td>12.82</td></tr><tr><td>Ours</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr><tr><td rowspan="4">AuthorImitation</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>132.95</td><td>85.25</td></tr><tr><td>UNMT</td><td>80.23</td><td>7.13</td><td>=</td><td>40.11</td><td>39.38</td></tr><tr><td>BT+NLL</td><td>76.98</td><td>10.80</td><td>=</td><td>61.70</td><td>65.51</td></tr><tr><td>Ours</td><td>81.43</td><td>10.81</td><td>=</td><td>49.62</td><td>44.86</td></tr><tr><td rowspan="4">Formality</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>71.30</td><td>135.50</td></tr><tr><td>UNMT</td><td>78.06</td><td>16.11</td><td>-</td><td>26.70</td><td>10.38</td></tr><tr><td>BT+NLL</td><td>82.43</td><td>8.57</td><td></td><td>6.57</td><td>8.21</td></tr><tr><td>Ours</td><td>80.46</td><td>18.54</td><td>-</td><td>22.65</td><td>17.23</td></tr></table>
+
+Author Imitation. Author imitation is the task of paraphrasing a sentence to match another author’s style. The dataset we use is a collection of Shakespeare’s plays translated line by line into modern English. It was collected by $\mathrm { X u }$ et al. $( 2 0 1 2 ) ^ { 7 }$ and used in prior work on supervised style transfer (Jhamtani et al., 2017). This is a parallel corpus and thus we follow the setting in the formality transfer task. We use $\mathcal { D } _ { 1 }$ to denote modern English, and $\mathcal { D } _ { 2 }$ to denote Shakespeare-style English. Results are shown in Table 1.
+
+Related Language Translation. Next, we test our method on a challenging related language translation task (Pourdamghani & Knight, 2017; Yang et al., 2018). This task is a natural test bed for unsupervised sequence transduction since the goal is to preserve the meaning of the source sentence while rewriting it into the target language. For our experiments, we choose Bosnian (bs) and Serbian (sr) as the related language pairs. We follow Yang et al. (2018) to report BLEU-1 score on this task since BLEU-4 score is close to zero. Results are shown in Table 2.
+
+Unsupervised MT. In order to draw connections with a related work on general unsupervised machine translation, we also evaluate on the WMT’16 German English translation task. This task is substantially more difficult than the style transfer tasks considered so far. We compare with the state-of-the-art UNMT system using the existing implementation from the XLM codebase,8 and implement our approach in the same framework with XLM initialization for fair comparison. We train both systems on 5M non-parallel sentences from each language. Results are shown in Table 2.
+
+In Tables 1 we also list the PPL of the test set under the external LM for both the source and target domain. PPL of system outputs should be compared to PPL of the test set itself because extremely low PPL often indicates that the generated sentences are short or trivial.
+
+Table 2: BLEU for decipherment, related language translation (Sr-Bs), and general unsupervised translation (En-De).   
+
+<table><tr><td>Model</td><td>Decipher</td><td>Sr-Bs</td><td>Bs-Sr</td><td>En-De</td><td>De-En</td></tr><tr><td>Shen et al. (2017)</td><td>50.8</td><td>1</td><td>-</td><td></td><td>1</td></tr><tr><td>Yang et al. (2018)</td><td>49.3</td><td>31.0</td><td>33.4</td><td>1</td><td>-</td></tr><tr><td>UNMT</td><td>76.4</td><td>31.4</td><td>33.4</td><td>26.5</td><td>32.2</td></tr><tr><td>BT+NLL</td><td>78.0</td><td>29.6</td><td>31.4</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>78.4</td><td>36.2</td><td>38.3</td><td>26.9</td><td>32.0</td></tr></table>
+
+# 5.2 RESULTS
+
+Tables 1 and 2 demonstrate some general trends. First, UNMT is able to outperform
+
+other prior methods in unsupervised text style transfer, such as (Yang et al., 2018; Hu et al., 2017; Shen et al., 2017). The performance improvements of UNMT indicate that flexible and powerful architectures are crucial (prior methods generally do not have an attention mechanism). Second, our model achieves comparable classification accuracy to UNMT but outperforms it in all style transfer tasks in terms of the reference-BLEU, which is the most important metric since it directly measures the quality of the final generations against gold parallel data. This indicates that our method is both effective and consistent across many different tasks. Finally, the $_ { \mathrm { B T + N L L } }$ baseline is sometimes quite competitive, which indicates that the addition of a language model alone can be beneficial. However, our method consistently outperforms the simple $_ { \mathrm { B T + N L L } }$ method, which indicates the effectiveness of the additional entropy regularizer in Eq. 5 that is the byproduct of our probabilistic formulation.
+
+Next, we examine the PPL of the system outputs under pretrained domain LMs, which should be evaluated in comparison with the PPL of the test set itself. For both the sentiment transfer and the formality transfer tasks in Table 1, $_ { \mathrm { B T + N L L } }$ achieves extremely low PPL, lower than the PPL of the test corpus in the target domain. After a close examination of the output, we find that it contains many repeated and overly simple outputs. For example, the system generates many examples of “I love this place” when transferring negative to positive sentiment (see Appendix A.3 for examples). It is not surprising that such a trivial output has low perplexity, high accuracy, and low BLEU score. On the other hand, our system obtains reasonably competitive PPL, and our approach achieves the highest accuracy and higher BLEU score than the UNMT baseline.
+
+# 5.3 FURTHER ABLATIONS AND ANALYSIS
+
+Parameter Sharing. We also conducted an experiment on the word substitution decipherment task, where we remove parameter sharing (as explained in Section 3.2) between two directions of transduction distributions, and optimize two encoder-decoder instead. We found that the model only obtained an extremely low BLEU score and failed to generate any meaningful outputs.
+
+Performance vs. Domain Divergence. Figure 3 plots the relative improvement of our method over UNMT with respect to accuracy of a naive Bayes’ classifier trained to predict the domain of test sentences. Tasks with high classification accuracy likely have more divergent domains. We can see that for decipherment and en-de translation, where the domains have different vocabularies and thus are easily distinguished, our method yields a smaller gain over UNMT This likely indicates that the (discrimination) regularization effect of the LM priors is less importan or necessary when the two domains are very different.
+
+![](images/6aa4e4f10b2de0917d9d783c828a8253cd750d1fcca6b0c6f71251a7ffedc9ff.jpg)  
+Figure 3: Improvement over UNMT vs. classification accuracy.
+
+Why does the proposed model outperform UNMT? Finally, we examine in detail the output of our model and UNMT for the author imitation task. We pick this task because the reference outputs for the test set are provided, aiding analysis. Examples shown in Table 3 demonstrate that UNMT tends to make overly large changes to the source so that the original meaning is lost, while our method is better at preserving the content of the source sentence. Next, we quantitatively examine the outputs from UNMT and our method by comparing the F1 measure of words bucketed by their syntactic tags. We use the open-sourced compare-mt tool (Neubig et al., 2019), and the results are shown in Figure 4. Our system has outperforms UNMT in all word categories. In particular, our system is much better at generating nouns, which likely leads to better content preservation.
+
+Table 3: Examples for author imitation task   
+
+<table><tr><td>Methods</td><td>Shakespeare to Modern</td></tr><tr><td>Source</td><td>Not to his father&#x27;s .</td></tr><tr><td>Reference</td><td>Not to his father&#x27;s house.</td></tr><tr><td>UNMT</td><td>Not to his brother .</td></tr><tr><td>Ours</td><td>Not to his father&#x27;s house .</td></tr><tr><td>Source</td><td>Send thy man away .</td></tr><tr><td>Reference</td><td>Send your man away.</td></tr><tr><td>UNMT</td><td>Send an excellent word .</td></tr><tr><td>Ours</td><td>Send your man away.</td></tr><tr><td>Source</td><td>Why should you fall into so deep an O ?</td></tr><tr><td>Reference</td><td>Why should you fall into so deep a moan ?</td></tr><tr><td>UNMT</td><td>Why should you carry so nicely,but have your legs ？</td></tr><tr><td>Ours</td><td>Why should you fall into so deep a sin ?</td></tr></table>
+
+![](images/77998449f70906451fe5613ae7e9933a82e30c20a2ca545eabe27b26da8c75ef.jpg)  
+Figure 4: Word F1 score by POS tag.
+
+Table 4: Comparison of gradient approximation on the sentiment transfer task.   
+
+<table><tr><td>Method</td><td>train ELBO个</td><td>test ELBO个</td><td>Acc.</td><td>BLEUr</td><td>BLEUs</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td>Sample-based</td><td>-3.51</td><td>-3.79</td><td>87.90</td><td>13.34</td><td>33.19</td><td>24.55</td><td>25.67</td></tr><tr><td>Greedy</td><td>-2.05</td><td>-2.07</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr></table>
+
+Table 5: Comparison of gradient propagation method on the sentiment transfer task.   
+
+<table><tr><td>Method</td><td>train ELBO↑</td><td>test ELBO个</td><td>Acc.</td><td>BLEUr</td><td>BLEUs</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td>Gumbel Softmax</td><td>-2.96</td><td>-2.98</td><td>81.30</td><td>16.17</td><td>40.47</td><td>22.70</td><td>23.88</td></tr><tr><td>REINFORCE</td><td>-6.07</td><td>-6.48</td><td>95.10</td><td>4.08</td><td>9.74</td><td>6.31</td><td>4.08</td></tr><tr><td>Stop Gradient</td><td>-2.05</td><td>-2.07</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr></table>
+
+Greedy vs. Sample-based Gradient Approximation. In our experiments, we use greedy decoding from the inference network to approximate the expectation required by ELBO, which is a biased estimator. The main purpose of this approach is to reduce the variance of the gradient estimator during training, especially in the early stages when the variance of sample-based approaches is quite high. As an ablation experiment on the sentiment transfer task we compare greedy and sample-based gradient approximations in terms of both train and test ELBO, as well as task performance corresponding to best test ELBO. After the model is fully trained, we find that the sample-based approximation has low variance. With a single sample, the standard deviation of the EBLO is less than 0.3 across 10 different test repetitions. All final reported ELBO values are all computed with this approach, regardless of whether the greedy approximation was used during training. The reported ELBO values are the evidence lower bound per word. Results are shown in Table 4, where the sampling-based training underperforms on both ELBO and task evaluations.
+
+# 5.4 COMPARISON OF GRADIENT PROPAGATION METHODS
+
+As noted above, to stabilize the training process, we stop gradients from propagating to the inference network from the reconstruction loss. Does this approach indeed better optimize the actual probabilistic objective (i.e. ELBO) or only indirectly lead to improved task evaluations? In this section we use sentiment transfer as an example task to compare different methods for propagating gradients and evaluate both ELBO and task evaluations.
+
+Specifically, we compare three different methods:
+
+• Stop Gradient: The gradients from reconstruction loss are not propagated to the inference network. This is the method we use in all previous experiments.   
+• Gumbel Softmax (Jang et al., 2017): Gradients from the reconstruction loss are propagated to the inference network with the straight-through Gumbel estimator.   
+• REINFORCE (Sutton et al., 2000): Gradients from reconstruction loss are propagated to the inference network with ELBO as a reward function. This method has been used in previous work for semi-supervised sequence generation (Miao & Blunsom, 2016; Yin et al., 2018), but often suffers from instability issues.
+
+We report the train and test ELBO along with task evaluations in Table 5, and plot the learning curves on validation set in Figure 5.9 While being much simpler, we show that the stop-gradient trick produces superior ELBO over Gumbel Softmax and REINFORCE. This result suggests that stopping gradient helps better optimize the likelihood objective under our probabilistic formulation in comparison with other optimization techniques that propagate gradients, which is counter-intuitive. A likely explanation is that as a gradient estimator, while clearly biased, stop-gradient has substantially reduced variance. In comparison with other techniques that offer reduced bias but extremely high variance when applied to our model class (which involves discrete sequences as latent variables), stop-gradient actually leads to better optimization of our objective because it achieves better balance of bias and variance overall.
+
+![](images/d795400be20ee935fa9f0e734c9f8151789443d1144ec02f23fde88102bcb2d4.jpg)  
+Figure 5: ELBO on the validation set v.s. the number training steps.
+
+# 6 CONCLUSION
+
+We propose a probabilistic generative forumalation that unites past work on unsupervised text style transfer. We show that this probabilistic formulation provides a different way to reason about unsupervised objectives in this domain. Our model leads to substantial improvements on five text style transfer tasks, yielding bigger gains when the styles considered are more difficult to distinguish.
+
+# ACKNOWLEDGEMENT
+
+The work of Junxian He and Xinyi Wang is supported by the DARPA GAILA project (award HR00111990063) and the Tang Family Foundation respectively. The authors would like to thank Zichao Yang for helpful feedback about the project.
+
+# REFERENCES
+
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+Colin Bannard and Chris Callison-Burch. Paraphrasing with bilingual parallel corpora. In Proceedings of ACL, 2005.
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+Harsh Jhamtani, Varun Gangal, Edward Hovy, and Eric Nyberg. Shakespearizing modern language using copy-enriched sequence-to-sequence models. Proceedings of EMNLP, 2017.
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+Melvin Johnson, Mike Schuster, Quoc V Le, Maxim Krikun, Yonghui Wu, Zhifeng Chen, Nikhil Thorat, Fernanda Viégas, Martin Wattenberg, Greg Corrado, et al. Google’s multilingual neural machine translation system: Enabling zero-shot translation. Transactions of the Association for Computational Linguistics, 2017.
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+Guillaume Lample, Myle Ott, Alexis Conneau, Ludovic Denoyer, and Marc’Aurelio Ranzato. Phrasebased & neural unsupervised machine translation. arXiv preprint arXiv:1804.07755, 2018.
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+Guillaume Lample, Sandeep Subramanian, Eric Smith, Ludovic Denoyer, Marc’Aurelio Ranzato, and Y-Lan Boureau. Multiple-attribute text rewriting. In Proceedings of ICLR, 2019.
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+Juncen Li, Robin Jia, He He, and Percy Liang. Delete, retrieve, generate: A simple approach to sentiment and style transfer. arXiv preprint arXiv:1804.06437, 2018.
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+Masahiro Mizukami, Graham Neubig, Sakriani Sakti, Tomoki Toda, and Satoshi Nakamura. Linguistic individuality transformation for spoken language. In Natural Language Dialog Systems and Intelligent Assistants. 2015.
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+Graham Neubig, Zi-Yi Dou, Junjie Hu, Paul Michel, Danish Pruthi, and Xinyi Wang. compare-mt: A tool for holistic comparison of language generation systems. In Meeting of the North American Chapter of the Association for Computational Linguistics (NAACL) Demo Track, Minneapolis, USA, June 2019. URL http://arxiv.org/abs/1903.07926.
+
+Nima Pourdamghani and Kevin Knight. Deciphering related languages. Proceedings of EMNLP, 2017.
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+Sudha Rao and Joel Tetreault. Dear sir or madam, may i introduce the gyafc dataset: Corpus, benchmarks and metrics for formality style transfer. arXiv preprint arXiv:1803.06535, 2018.
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+Sujith Ravi and Kevin Knight. Deciphering foreign language. In Proceedings of ACL, 2011.
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+Alexander M Rush, Sumit Chopra, and Jason Weston. A neural attention model for abstractive sentence summarization. In Proceedings of EMNLP, 2015.
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+Rico Sennrich, Barry Haddow, and Alexandra Birch. Improving neural machine translation models with monolingual data. In Proceedings of ACL, 2016.
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+Claude Elwood Shannon. A mathematical theory of communication. Bell system technical journal, 27(3):379–423, 1948.
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+Tianxiao Shen, Tao Lei, Regina Barzilay, and Tommi Jaakkola. Style transfer from non-parallel text by cross-alignment. In Proceeings of NIPS, 2017.
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+
+# A APPENDIX
+
+# A.1 MODEL CONFIGURATIONS.
+
+We adopt the following attentional encoder-decoder architecture for UNMT, $_ { \mathrm { B T + N L L } }$ , and our method across all the experiments:
+
+• We use word embeddings of size 128.   
+• We use 1 layer LSTM with hidden size of 512 as both the encoder and decoder.   
+• We apply dropout to the readout states before softmax with a rate of 0.3.   
+• Following Lample et al. (2019), we add a max pooling operation over the encoder hidden states before feeding it to the decoder. Intuitively the pooling window size would control how much information is preserved during transduction. A window size of 1 is equivalent to standard attention mechanism, and a large window size corresponds to no attention. See Appendix A.2 for how to select the window size. There is a noise function for UNMT baseline in its denoising autoencoder loss (Lample et al., 2017; 2019), which is critical for its success. We use the default noise function and noise hyperparameters in Lample et al. (2017) when running the UNMT model. For $_ { \mathrm { B T + N L L } }$ and our method we found that adding the extra noise into the self-reconstruction loss (Eq. 4) is only helpful when the two domains are relatively divergent (decipherment and related language translation tasks) where the language models play a less important role. Therefore, we add the default noise from UNMT to Eq. 4 for decipherment and related language translation tasks only, and do not use any noise for sentiment, author imitation, and formality tasks.
+
+# A.2 HYPERPARAMETER TUNING.
+
+We vary pooling windows size as $\{ 1 , 5 \}$ , the decaying patience hyperparameter $k$ for selfreconstruction loss (Eq. 4) as $\{ 1 , 2 , 3 \}$ . For the baseliens UNMT and $_ { \mathrm { B T + N L L } }$ , we also try the option of not annealing the self-reconstruction loss at all as in the unsupervised machine translation task (Lample et al., 2018). We vary the weight $\lambda$ for the NLL term $_ \mathrm { B T + N L L } )$ or the KL term (our method) as $\{ 0 . 0 0 1 , 0 . 0 1 , 0 . 0 3 , 0 . 0 5 , 0 . 1 \}$ .
+
+# A.3 SENTIMENT TRANSFER EXAMPLE OUTPUTS
+
+We list some examples of the sentiment transfer task in Table 6. Notably, the $_ { \mathrm { B T + N L L } }$ method tends to produce extremely short and simple sentences.
+
+# A.4 REPETITIVE EXAMPLES OF BT $^ +$ NLL
+
+In Section 5 we mentioned that the baseline $_ { \mathrm { B T + N L L } }$ has a low perplexity for some tasks because it tends to generate overly simple and repetitive sentences. From Table 1 we see that two representative tasks are sentiment transfer and formatliy transfer. In Appendix A.3 we have demonstrated some examples for sentiment transfer, next we show some repetitive samples of $_ { \mathrm { B T + N L L } }$ in Table 7.
+
+Table 6: Random Sentiment Transfer Examples   
+
+<table><tr><td>Methods</td><td>negative to positive</td></tr><tr><td>Original</td><td>the cake portion was extremely light and a bit dry .</td></tr><tr><td>UNMT</td><td>the cake portion was extremely light and a bit spicy .</td></tr><tr><td>BT+NLL</td><td>the cake portion was extremely light and a bit dry .</td></tr><tr><td>Ours</td><td>the cake portion was extremely light and a bit fresh .</td></tr><tr><td>Original</td><td>the “ chicken ” strip were paper thin oddly flavored strips .</td></tr><tr><td>UNMT</td><td>the“ chicken ”were extra crispy noodles were fresh and incredible .</td></tr><tr><td>BT+NLL</td><td>the service was great .</td></tr><tr><td>Ours</td><td>the“ chicken ”strip were paper sweet &amp; juicy flavored .</td></tr><tr><td>Original</td><td>if i could give them a zero star review i would !</td></tr><tr><td>UNMT</td><td> if i could give them a zero star review i would !</td></tr><tr><td>BT+NLL</td><td>i love this place .</td></tr><tr><td>Ours</td><td>i love the restaurant and give a great review i would !</td></tr><tr><td></td><td>positive to negative</td></tr><tr><td>Original</td><td> great food,staff is unbelievably nice .</td></tr><tr><td>UNMT BT+NLL</td><td>no ,food is n&#x27;t particularly friendly .</td></tr><tr><td>Ours</td><td>i will not be back .</td></tr><tr><td></td><td>no apologies,staff is unbelievably poor .</td></tr><tr><td>Original</td><td>my wife and i love coming here !</td></tr><tr><td>UNMT</td><td>my wife and i do n&#x27;t come here !</td></tr><tr><td>BT+NLL</td><td>i will not be back.</td></tr><tr><td>Ours</td><td>my wife and i walked out the last time .</td></tr><tr><td>Original</td><td>my wife and i love coming here !</td></tr><tr><td>UNMT</td><td>my wife and i do n&#x27;t come here !</td></tr><tr><td>BT+NLL</td><td>i will not be back .</td></tr><tr><td>Ours</td><td>my wife and i walked out the last time .</td></tr><tr><td>Original</td><td>the premier hookah lounge of las vegas !</td></tr><tr><td>UNMT</td><td>the worst museum of las vegas !</td></tr><tr><td>BT+NLL</td><td>the worst frame shop of las vegas !</td></tr><tr><td>Ours</td><td>the hallways scam lounge of las vegas !</td></tr></table>
+
+Table 7: Repetitive examples of $\mathrm { B T + N L L }$ baseline on Formality transfer.   
+
+<table><tr><td>Original</td><td>Transferred</td></tr><tr><td colspan="2">formal to informal</td></tr><tr><td>I like Rhythm and Blue music .</td><td>I like her and I don&#x27;t know .</td></tr><tr><td>There&#x27;s nothing he needs to change .</td><td>I don&#x27;t know,but Idon&#x27;t know .</td></tr><tr><td>Ienjoy watching my companion attempt to role @-@ play with them.</td><td>Idon&#x27;tknow,but Idon&#x27;t know.</td></tr><tr><td>Iam watching it right now</td><td>Idon&#x27;t know,but Idon&#x27;t know .</td></tr><tr><td>That is the key point,that you fell asleep .</td><td>I don&#x27;t know,but Idon&#x27;t know.</td></tr><tr><td colspan="2">informal to formal</td></tr><tr><td>its a great source just download it .</td><td>I do not know,but Ido not know .</td></tr><tr><td>Happy Days,it was the coolest ！</td><td>I do not know,butIdo not know.</td></tr><tr><td>I used to play flute but once I started sax,I got hooked .</td><td>I do not know,butIdo not know.</td></tr><tr><td>The word you are  looking  foris.... strengths</td><td>The word you are looking for is :)</td></tr><tr><td>Plus you can tell she really cared about her crew .</td><td>Plus you can tell she really cared about her crew.</td></tr></table>

parse/train/HJlA0C4tPS/HJlA0C4tPS_content_list.json

@@ -0,0 +1,1518 @@
+[
+    {
+        "type": "text",
+        "text": "A PROBABILISTIC FORMULATION OF UNSUPERVISED TEXT STYLE TRANSFER ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            99,
+            658,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Junxian $\\mathbf { H e } ^ { * }$ , Xinyi Wang∗, Graham Neubig Carnegie Mellon University {junxianh,xinyiw1,gneubig}@cs.cmu.edu ",
+        "bbox": [
+            183,
+            169,
+            545,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Taylor Berg-Kirkpatrick University of California San Diego tberg@eng.ucsd.edu ",
+        "bbox": [
+            575,
+            170,
+            805,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
+            544,
+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present a deep generative model for unsupervised text style transfer that unifies previously proposed non-generative techniques. Our probabilistic approach models non-parallel data from two domains as a partially observed parallel corpus. By hypothesizing a parallel latent sequence that generates each observed sequence, our model learns to transform sequences from one domain to another in a completely unsupervised fashion. In contrast with traditional generative sequence models (e.g. the HMM), our model makes few assumptions about the data it generates: it uses a recurrent language model as a prior and an encoder-decoder as a transduction distribution. While computation of marginal data likelihood is intractable in this model class, we show that amortized variational inference admits a practical surrogate. Further, by drawing connections between our variational objective and other recent unsupervised style transfer and machine translation techniques, we show how our probabilistic view can unify some known non-generative objectives such as backtranslation and adversarial loss. Finally, we demonstrate the effectiveness of our method on a wide range of unsupervised style transfer tasks, including sentiment transfer, formality transfer, word decipherment, author imitation, and related language translation. Across all style transfer tasks, our approach yields substantial gains over state-of-the-art non-generative baselines, including the state-of-the-art unsupervised machine translation techniques that our approach generalizes. Further, we conduct experiments on a standard unsupervised machine translation task and find that our unified approach matches the current state-of-the-art.1 ",
+        "bbox": [
+            232,
+            284,
+            766,
+            575
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            609,
+            334,
+            626
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Text sequence transduction systems convert a given text sequence from one domain to another. These techniques can be applied to a wide range of natural language processing applications such as machine translation (Bahdanau et al., 2015), summarization (Rush et al., 2015), and dialogue response generation (Zhao et al., 2017). In many cases, however, parallel corpora for the task at hand are scarce. Therefore, unsupervised sequence transduction methods that require only non-parallel data are appealing and have been receiving growing attention (Bannard & Callison-Burch, 2005; Ravi & Knight, 2011; Mizukami et al., 2015; Shen et al., 2017; Lample et al., 2018; 2019). This trend is most pronounced in the space of text style transfer tasks where parallel data is particularly challenging to obtain (Hu et al., 2017; Shen et al., 2017; Yang et al., 2018). Style transfer has historically referred to sequence transduction problems that modify superficial properties of text – i.e. style rather than content.2 We focus on a standard suite of style transfer tasks, including formality transfer (Rao & Tetreault, 2018), author imitation (Xu et al., 2012), word decipherment (Shen et al., 2017), sentiment transfer (Shen et al., 2017), and related language translation (Pourdamghani & Knight, 2017). General unsupervised translation has not typically been considered style transfer, but for the purpose of comparison we also conduct evaluation on this task (Lample et al., 2017). ",
+        "bbox": [
+            174,
+            645,
+            826,
+            852
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent work on unsupervised text style transfer mostly employs non-generative or non-probabilistic modeling approaches. For example, Shen et al. (2017) and Yang et al. (2018) design adversarial discriminators to shape their unsupervised objective – an approach that can be effective, but often introduces training instability. Other work focuses on directly designing unsupervised training objectives by incorporating intuitive loss terms (e.g. backtranslation loss), and demonstrates state-ofthe-art performance on unsupervised machine translation (Lample et al., 2018; Artetxe et al., 2019) and style transfer (Lample et al., 2019). However, the space of possible unsupervised objectives is extremely large and the underlying modeling assumptions defined by each objective can only be reasoned about indirectly. As a result, the process of designing such systems is often heuristic. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            229
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In contrast, probabilistic models (e.g. the noisy channel model (Shannon, 1948)) define assumptions about data more explicitly and allow us to reason about these assumptions during system design. Further, the corresponding objectives are determined naturally by principles of probabilistic inference, reducing the need for empirical search directly in the space of possible objectives. That said, classical probabilistic models for unsupervised sequence transduction (e.g. the HMM or semi-HMM) typically enforce overly strong independence assumptions about data to make exact inference tractable (Knight et al., 2006; Ravi & Knight, 2011; Pourdamghani & Knight, 2017). This has restricted their development and caused their performance to lag behind unsupervised neural objectives on complex tasks. Luckily, in recent years, powerful variational approximation techniques have made it more practical to train probabilistic models without strong independence assumptions (Miao & Blunsom, 2016; Yin et al., 2018). Inspired by this, we take a new approach to unsupervised style transfer. ",
+        "bbox": [
+            174,
+            236,
+            825,
+            388
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We directly define a generative probabilistic model that treats a non-parallel corpus in two domains as a partially observed parallel corpus. Our model makes few independence assumptions and its true posterior is intractable. However, we show that by using amortized variational inference (Kingma & Welling, 2013), a principled probabilistic technique, a natural unsupervised objective falls out of our modeling approach that has many connections with past work, yet is different from all past work in specific ways. In experiments across a suite of unsupervised text style transfer tasks, we find that the natural objective of our model actually outperforms all manually defined unsupervised objectives from past work, supporting the notion that probabilistic principles can be a useful guide even in deep neural systems. Further, in the case of unsupervised machine translation, our model matches the current state-of-the-art non-generative approach. ",
+        "bbox": [
+            174,
+            395,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 UNSUPERVISED TEXT STYLE TRANSFER ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            574,
+            542,
+            592
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first overview text style transfer, which aims to transfer a text (typically a single sentence or a short paragraph – for simplicity we refer to simply “sentences” below) from one domain to another while preserving underlying content. For example, formality transfer (Rao & Tetreault, 2018) is the task of transforming the tone of text from informal to formal without changing its content. Other examples include sentiment transfer (Shen et al., 2017), word decipherment (Knight et al., 2006), and author imitation (Xu et al., 2012). If parallel examples were available from each domain (i.e. the training data is a bitext consisting of pairs of sentences from each domain), supervised techniques could be used to perform style transfer (e.g. attentional Seq2Seq (Bahdanau et al., 2015) and Transformer (Vaswani et al., 2017)). However, for most style transfer problems, only non-parallel corpora (one corpus from each domain) can be easily collected. Thus, work on style transfer typically focuses on the more difficult unsupervised setting where systems must learn from non-parallel data alone. ",
+        "bbox": [
+            174,
+            618,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The model we propose treats an observed non-parallel text corpus as a partially observed parallel corpus. Thus, we introduce notation for both observed text inputs and those that we will treat as latent variables. Specifically, we let $X = \\{ x ^ { ( 1 ) } , x ^ { ( 2 ) } , \\cdot \\cdot \\cdot , x ^ { ( \\bar { m } ) } \\}$ represent observed data from domain $\\mathcal { D } _ { 1 }$ , while we let $Y = \\{ y ^ { ( m + 1 ) } , y ^ { ( m + \\overset { \\cdot } { 2 } ) } , \\cdot \\cdot \\cdot , y ^ { ( n ) } \\}$ represent observed data from domain $\\mathcal { D } _ { 2 }$ . Corresponding indices represent parallel sentences. Thus, none of the observed sentences share indices. In our model, we introduce latent sentences to complete the parallel corpus. Specifically, $\\bar { X } = \\{ \\bar { x } ^ { ( m + 1 ) } , \\bar { x } ^ { ( m + 2 ) } , \\cdot \\cdot \\cdot , \\bar { x } ^ { ( n ) } \\}$ represents the set of latent parallel sentences in $\\mathcal { D } _ { 1 }$ , while $\\bar { Y } = \\{ \\bar { y } ^ { ( 1 ) } , \\bar { y } ^ { ( 2 ) } , \\cdot \\cdot \\cdot , \\bar { y } ^ { ( m ) } \\}$ represents the set of latent parallel sentences in $\\mathcal { D } _ { 2 }$ . Then the goal of unsupervised text transduction is to infer these latent variables conditioned the observed non-parallel corpora; that is, to learn $p ( { \\bar { y } } | x )$ and $p ( { \\bar { x } } | y )$ . ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/41384ec1945473ca58fdedb371d1e2b9339b296d94ddeac4f8b18385ad392414.jpg",
+        "image_caption": [
+            "Figure 1: Proposed graphical model for style transfer via bitext completion. Shaded circles denote the observed variables and unshaded circles denote the latents. The generator is parameterized as an encoder-decoder architecture and the prior on the latent variable is a pretrained language model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            250,
+            85,
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+    {
+        "type": "text",
+        "text": "3 THE DEEP LATENT SEQUENCE MODEL ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "First we present our generative model of bitext, which we refer to as a deep latent sequence model.   \nWe then describe unsupervised learning and inference techniques for this model class. ",
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+        "type": "text",
+        "text": "3.1 MODEL STRUCTURE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Directly modeling $p ( { \\bar { y } } | x )$ and $p ( { \\bar { x } } | y )$ in the unsupervised setting is difficult because we never directly observe parallel data. Instead, we propose a generative model of the complete data that defines a joint likelihood, $p ( X , { \\bar { X } } , Y , { \\bar { Y } } )$ . In order to perform text transduction, the unobserved halves can be treated as latent variables: they will be marginalized out during learning and inferred via posterior inference at test time. ",
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+        "text": "Our model assumes that each observed sentence is generated from an unobserved parallel sentence in the opposite domain, as depicted in Figure 1. Specifically, each sentence $\\boldsymbol { x } ^ { ( i ) }$ in domain $\\mathcal { D } _ { 1 }$ is generated as follows: First, a latent sentence $\\bar { y } ^ { ( i ) }$ in domain $\\mathcal { D } _ { 2 }$ is sampled from a prior, $p _ { { D _ { 2 } } } ( \\bar { y } ^ { ( i ) } )$ . Then, $x ^ { ( i ) }$ is sampled conditioned on $\\bar { y } ^ { ( i ) }$ from a transduction model, $p ( \\boldsymbol { x } ^ { ( i ) } | \\bar { y } ^ { ( i ) } )$ . Similarly, each observed sentence $y ^ { ( j ) }$ in domain $\\mathcal { D } _ { 2 }$ is generated conditioned on a latent sentence, $\\bar { x } ^ { ( j ) }$ , in domain $\\mathcal { D } _ { 1 }$ via the opposite transduction model, $p ( \\boldsymbol { y } ^ { ( j ) } | \\bar { x } ^ { ( j ) } )$ , and prior, $p _ { \\mathcal { D } _ { 1 } } ( \\bar { x } ^ { ( j ) } )$ . We let $\\theta _ { x | \\bar { y } }$ and $\\theta _ { y | \\bar { x } }$ represent the parameters of the two transduction distributions respectively. We assume the prior distributions are pretrained on the observed data in their respective domains and therefore omit their parameters for simplicity of notation. Together, this gives the following joint likelihood: ",
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+        "type": "equation",
+        "img_path": "images/06718adcb603231ab8ecc7a010ef4805be851cf8f956d135d1fc5328140c8634.jpg",
+        "text": "$$\np ( X , \\bar { X } , Y , \\bar { Y } ; \\theta _ { x | \\bar { y } } , \\theta _ { y | \\bar { x } } ) = \\left( \\prod _ { i = 1 } ^ { m } p \\big ( x ^ { ( i ) } | \\bar { y } ^ { ( i ) } ; \\theta _ { x | \\bar { y } } \\big ) p _ { \\mathcal { D } _ { 2 } } \\big ( \\bar { y } ^ { ( i ) } \\big ) \\right) \\left( \\prod _ { j = m + 1 } ^ { n } p \\big ( y ^ { ( j ) } | \\bar { x } ^ { ( j ) } ; \\theta _ { y | \\bar { x } } \\big ) p _ { \\mathcal { D } _ { 1 } } \\big ( \\bar { x } ^ { ( j ) } \\big ) \\right)\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "The log marginal likelihood of the data, which we will approximate during training, is: ",
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+        "type": "equation",
+        "img_path": "images/5c66b8696425f416d6decd056afafbbf2f7de68453e4d564061add0730ac52e1.jpg",
+        "text": "$$\n\\log p ( X , Y ; \\theta _ { x | \\bar { y } } , \\theta _ { y | \\bar { x } } ) = \\log \\sum _ { \\bar { X } } \\sum _ { \\bar { Y } } p ( X , \\bar { X } , Y , \\bar { Y } ; \\theta _ { x | \\bar { y } } , \\theta _ { y | \\bar { x } } )\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "Note that if the two transduction models share no parameters, the training problems for each observed domain are independent. Critically, we introduce parameter sharing through our variational inference procedure, which we describe in more detail in Section 3.2. ",
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+        "text": "Architecture: Since we would like to be able to model a variety of transfer tasks, we choose a parameterization for our transduction distributions that makes no independence assumptions. Specifically, we employ an encoder-decoder architecture based on the standard attentional Seq2Seq model which has been shown to be successful across various tasks (Bahdanau et al., 2015; Rush et al., 2015). Similarly, our prior distributions for each domain are parameterized as recurrent language models which, again, make no independence assumptions. In contrast, traditional unsupervised generative sequence models typically make strong independence assumptions to enable exact inference (e.g. the HMM makes a Markov assumption on the latent sequence and emissions are one-to-one). Our model is more flexible, but exact inference via dynamic programming will be intractable. We address this problem in the next section. ",
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+        "img_path": "images/465557888fae2116dee1e4e4dd348b9e4d1230bed6a6f3b67479bcd78b680d54.jpg",
+        "image_caption": [
+            "Figure 2: Depiction of amortized variational approximation. Distributions $q ( { \\bar { y } } | x )$ and $q ( { \\bar { x } } | y )$ represent inference networks that approximate the model’s true posterior. Critically, parameters are shared between the generative model and inference networks to tie the learning problems for both domains. "
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+        "text": "3.2 LEARNING ",
+        "text_level": 1,
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+        "text": "Ideally, learning should directly optimize the log data likelihood, which is the marginal of our model shown in Eq. 2. However, due to our model’s neural parameterization which does not factorize, computing the data likelihood cannot be accomplished using dynamic programming as can be done with simpler models like the HMM. To overcome the intractability of computing the true data likelihood, we adopt amortized variational inference (Kingma & Welling, 2013) in order to derive a surrogate objective for learning, the evidence lower bound (ELBO) on log marginal likelihood3 : ",
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+        "img_path": "images/266cfec56cc0b2fe4d405d38b4ad01d44e63719324212b79b21a3b231ca37277.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\log p ( X , Y ; \\theta _ { x | \\bar { y } } , \\theta _ { y | \\bar { x } } ) } \\\\ & { \\ge \\mathcal { L } _ { \\mathrm { E L B O } } ( X , Y ; \\theta _ { x | \\bar { y } } , \\theta _ { y | \\bar { x } } , \\phi _ { \\bar { x } | y } , \\phi _ { \\bar { y } | x } ) } \\\\ & { = \\sum _ { i } \\Big [ \\mathbb { E } _ { q ( \\bar { y } | x ^ { ( i ) } ; \\phi _ { \\bar { y } | x } ) } [ \\log p ( x ^ { ( i ) } | \\bar { y } ; \\theta _ { x | \\bar { y } } ) ] - D _ { \\mathrm { K L } } \\big ( q ( \\bar { y } | x ^ { ( i ) } ; \\phi _ { \\bar { y } | x } ) | | p _ { \\mathcal { D } _ { 2 } } ( \\bar { y } ) \\big ) \\Big ] } \\\\ & { + \\sum _ { j } \\underbrace { \\Big [ \\mathbb { E } _ { q ( \\bar { x } | y ^ { ( j ) } ; \\phi _ { \\bar { x } | y } ) } [ \\log p ( y ^ { ( j ) } | \\bar { x } ; \\theta _ { y | \\bar { x } } ) ] } _ { \\mathrm { R e c o n s t u c i o n ~ l i k e l i h o o d } } - \\underbrace { D _ { \\mathrm { K L } } \\big ( q ( \\bar { x } | y ^ { ( j ) } ; \\phi _ { \\bar { x } | y } ) \\big ) | p _ { \\bar { D } _ { 1 } } ( \\bar { x } ) \\big ) } _ { \\mathrm { K L ~ r e g u l a r i z e r } } \\Big ] } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The surrogate objective introduces $q ( \\bar { y } | x ^ { ( i ) } ; \\phi _ { \\bar { y } | x } )$ and $q ( \\bar { x } | y ^ { ( j ) } ; \\phi _ { \\bar { x } | y } )$ , which represent two separate inference network distributions that approximate the model’s true posteriors, $p ( \\bar { y } | x ^ { ( i ) } ; \\theta _ { x | \\bar { y } } )$ and $p ( \\bar { x } | y ^ { ( j ) } ; \\theta _ { y | \\bar { x } } )$ , respectively. Learning operates by jointly optimizing the lower bound over both variational and model parameters. Once trained, the variational posterior distributions can be used directly for style transfer. The KL terms in Eq. 3, that appear naturally in the ELBO objective, can be intuitively viewed as regularizers that use the language model priors to bias the induced sentences towards the desired domains. Amortized variational techniques have been most commonly applied to continuous latent variables, as in the case of the variational autoencoder (VAE) (Kingma & Welling, 2013). Here, we use this approach for inference over discrete sequences, which has been shown to be effective in related work on a semi-supervised task (Miao & Blunsom, 2016). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Inference Network and Parameter Sharing: Note that the approximate posterior on one domain aims to learn the reverse style transfer distribution, which is exactly the goal of the generative distribution in the opposite domain. For example, the inference network $\\bar { q } ( \\bar { y } | x ^ { ( i ) } ; \\phi _ { \\bar { y } | x } )$ and the generative distribution $p ( y | \\bar { x } ^ { ( i ) } ; \\theta _ { y | \\bar { x } } )$ both aim to transform $\\mathcal { D } _ { 1 }$ to $\\mathcal { D } _ { 2 }$ . Therefore, we use the same architecture for each inference network as used in the transduction models, and tie their parameters: $\\phi _ { \\bar { x } | y } = \\theta _ { x | \\bar { y } } , \\phi _ { \\bar { y } | x } = \\theta _ { y | \\bar { x } }$ . This means we learn only two encoder-decoders overall – which are parameterized by $\\theta _ { x | \\bar { y } }$ and $\\theta _ { y | \\bar { x } }$ respectively – to represent two directions of transfer. In addition to reducing the number of learnable parameters, this parameter tying couples the learning problems for both domains and allows us to jointly learn from the full data. Moreover, inspired by recent work that builds a universal Seq2Seq model to translate between different language pairs (Johnson et al., 2017), we introduce further parameter tying between the two directions of transduction: the same encoder is employed for both $x$ and $y$ , and a domain embedding $c$ is provided to the same decoder to specify the transfer direction, as shown in Figure 2. Ablation analysis in Section 5.3 suggests that parameter sharing is important to achieve good performance. ",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Approximating Gradients of ELBO: The reconstruction and KL terms in Eq. 3 still involve intractable expectations due to the marginalization over the latent sequence, thus we need to approximate their gradients. Gumbel-softmax (Jang et al., 2017) and REINFORCE (Sutton et al., 2000) are often used as stochastic gradient estimators in the discrete case. Since the latent text variables have an extremely large domain, we find that REINFORCE-based gradient estimates result in high variance. Thus, we use the Gumbel-softmax straight-through estimator to backpropagate gradients from the KL terms.4 However, we find that approximating gradients of the reconstruction loss is much more challenging – both the Gumbel-softmax estimator and REINFORCE are unable to outperform a simple stop-gradient method that does not back-propagate the gradient of the latent sequence to the inference network. This confirms a similar observation in previous work on unsupervised machine translation (Lample et al., 2018). Therefore, we use greedy decoding without recording gradients to approximate the reconstruction term.5 Note that the inference networks still receive gradients from the prior through the KL term, and their parameters are shared with the decoders which do receive gradients from reconstruction. We consider this to be the best empirical compromise at the moment. ",
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+        "type": "text",
+        "text": "Initialization. Good initialization is often necessary for successful optimization of unsupervised learning objectives. In preliminary experiments, we find that the encoder-decoder structure has difficulty generating realistic sentences during the initial stages of training, which usually results in a disastrous local optimum. This is mainly because the encoder-decoder is initialized randomly and there is no direct training signal to specify the desired latent sequence in the unsupervised setting. Therefore, we apply a self-reconstruction loss $\\mathcal { L } _ { \\mathrm { r e c } }$ at the initial epochs of training. We denote the output the encoder as $e ( \\cdot )$ and the decoder distribution as $p _ { \\mathrm { d e c } }$ , then ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/313771fe28f95292088ac1d8557b2eaa1785b63e80edc65d27cb3cc96f46f2f6.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { { r e c } } } = - \\alpha \\cdot \\sum _ { i } [ p _ { \\mathrm { d e c } } ( e ( x ^ { ( i } ) , c _ { x } ) ] - \\alpha \\cdot \\sum _ { j } [ p _ { \\mathrm { d e c } } ( e ( y ^ { ( j } ) , c _ { y } ) ] ,\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "$\\alpha$ decays from 1.0 to 0.0 linearly in the first $k$ epochs. $k$ is a tunable parameter and usually less than 3 in all our experiments. ",
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+    {
+        "type": "text",
+        "text": "4 CONNECTION TO RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our probabilistic formulation can be connected with recent advances in unsupervised text transduction methods. For example, back translation loss (Sennrich et al., 2016) plays an important role in recent unsupervised machine translation (Artetxe et al., 2018; Lample et al., 2018; Artetxe et al., 2019) and unsupervised style transfer systems (Lample et al., 2019). In order to incorporate back translation loss the source language $x$ is translated to the target language $y$ to form a pseudo-parallel corpus, then a translation model from $y$ to $x$ can be learned on this pseudo bitext just as in supervised setting. While back translation was often explained as a data augmentation technique, in our probabilistic formulation it appears naturally with the ELBO objective as the reconstruction loss term. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Some previous work has incorporated a pretrained language models into neural semi-supervised or unsupervised objectives. He et al. (2016) uses the log likelihood of a pretrained language model as the reward to update a supervised machine translation system with policy gradient. Artetxe et al. (2019) utilize a similar idea for unsupervised machine translation. Yang et al. (2018) employed a similar approach, but interpret the LM as an adversary, training the generator to fool the LM. We show how our ELBO objective is connected with these more heuristic LM regularizers by expanding the KL loss term (assume $x$ is observed): ",
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+        "img_path": "images/3e95c454b7d21323b3ea99b526be97f7cb36c35fd441dabffa252f2bcb0c780b.jpg",
+        "text": "$$\nD _ { \\mathrm { K L } } ( q ( \\bar { y } | x ) | | p _ { \\mathcal { D } _ { 2 } } ( \\bar { y } ) ) = - H _ { q } - \\mathbb { E } _ { q } [ \\log p _ { \\mathcal { D } _ { 2 } } ( \\bar { y } ) ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that the loss used in previous work does not include the negative entropy term, $- H _ { q }$ . Our objective results in this additional “regularizer”, the negative entropy of the transduction distribution, $- H _ { q }$ . Intuitively, $- H _ { q }$ helps avoid a peaked transduction distribution, preventing the transduction from constantly generating similar sentences to satisfy the language model. In experiments we will show that this additional regularization is important and helps bypass bad local optima and improve performance. These important differences with past work suggest that a probabilistic view of the unsupervised sequence transduction may provide helpful guidance in determining effective training objectives. ",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We test our model on five style transfer tasks: sentiment transfer, word substitution decipherment, formality transfer, author imitation, and related language translation. For completeness, we also evaluate on the task of general unsupervised machine translation using standard benchmarks. ",
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+        "type": "text",
+        "text": "We compare with the unsupervised machine translation model (UNMT) which recently demonstrated state-of-the-art performance on transfer tasks such as sentiment and gender transfer (Lample et al., 2019).6 To validate the effect of the negative entropy term in the KL loss term Eq. 5, we remove it and train the model with a back-translation loss plus a language model negative log likelihood loss (which we denote as $_ { \\mathrm { B T + N L L } }$ ) as an ablation baseline. For each task, we also include strong baseline numbers from related work if available. For our method we select the model with the best validation ELBO, and for UNMT or $_ { \\mathrm { B T + N L L } }$ we select the model with the best back-translation loss. Complete model configurations and hyperparameters can be found in Appendix A.1. ",
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+    {
+        "type": "text",
+        "text": "5.1 DATASETS AND EXPERIMENT SETUP ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Word Substitution Decipherment. Word decipherment aims to uncover the plain text behind a corpus that was enciphered via word substitution where word in the vocabulary is mapped to a unique type in a cipher dictionary (Dou & Knight, 2012; Shen et al., 2017; Yang et al., 2018). In our formulation, the model is presented with a non-parallel corpus of English plaintext and the ciphertext. We use the data in (Yang et al., 2018) which provides 200K sentences from each domain. While previous work (Shen et al., 2017; Yang et al., 2018) controls the difficulty of this task by varying the percentage of words that are ciphered, we directly evaluate on the most difficult version of this task $- 1 0 0 \\%$ of the words are enciphered (i.e. no vocabulary sharing in the two domains). We select the model with the best unsupervised reconstruction loss, and evaluate with BLEU score on the test set which contains 100K parallel sentences. Results are shown in Table 2. ",
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+    {
+        "type": "text",
+        "text": "Sentiment Transfer. Sentiment transfer is a task of paraphrasing a sentence with a different sentiment while preserving the original content. Evaluation of sentiment transfer is difficult and is still an open research problem (Mir et al., 2019). Evaluation focuses on three aspects: attribute control, content preservation, and fluency. A successful system needs to perform well with respect to all three aspects. We follow prior work by using three automatic metrics (Yang et al., 2018; Lample et al., 2019): classification accuracy, self-BLEU (BLEU of the output with the original sentence as the reference), and the perplexity (PPL) of each system’s output under an external language model. We pretrain a convolutional classifier (Kim, 2014) to assess classification accuracy, and use an LSTM language model pretrained on each domain to compute the PPL of system outputs. ",
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+    {
+        "type": "text",
+        "text": "We use the Yelp reviews dataset collected by Shen et al. (2017) which contains 250K negative sentences and 380K positive sentences. We also use a small test set that has 1000 human-annotated parallel sentences introduced in Li et al. (2018). We denote the positive sentiment as domain $\\mathcal { D } _ { 1 }$ and the negative sentiment as domain $\\mathcal { D } _ { 2 }$ . We use Self-BLEU and BLEU to represent the BLEU score of the output against the original sentence and the reference respectively. Results are shown in Table 1. ",
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+    {
+        "type": "text",
+        "text": "Formality Transfer. Next, we consider a harder task of modifying the formality of a sequence. We use the GYAFC dataset (Rao & Tetreault, 2018), which contains formal and informal sentences from two different domains. In this paper, we use the Entertainment and Music domain, which has about 52K training sentences, 5K development sentences, and 2.5K test sentences. This dataset actually contains parallel data between formal and informal sentences, which we use only for evaluation. We follow the evaluation of sentiment transfer task and test models on three axes. Since the test set is a parallel corpus, we only compute reference BLEU and ignore self-BLEU. We use $\\mathcal { D } _ { 1 }$ to denote formal text, and $\\mathcal { D } _ { 2 }$ to denote informal text. Results are shown in Table 1. ",
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+    {
+        "type": "table",
+        "img_path": "images/29bd00bc1da68626a7c72f619008f31f00fbcfcec482e280bfe9f2c3240ba3ae.jpg",
+        "table_caption": [
+            "Table 1: Results on the sentiment transfer, author imitation, and formality transfer. We list the PPL of pretrained LMs on the test sets of both domains. We only report Self-BLEU on the sentiment task to compare with existing work. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Task</td><td>Model</td><td>Acc.</td><td>BLEU</td><td>Self-BLEU</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td rowspan=\"7\">Sentiment</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>31.97</td><td>21.87</td></tr><tr><td>Shen et al. (2017)</td><td>79.50</td><td>6.80</td><td>12.40</td><td>50.40</td><td>52.70</td></tr><tr><td>Hu et al. (2017)</td><td>87.70</td><td>-</td><td>65.60</td><td>115.60</td><td>239.80</td></tr><tr><td>Yang et al. (2018)</td><td>83.30</td><td>13.40</td><td>38.60</td><td>30.30</td><td>42.10</td></tr><tr><td>UNMT</td><td>87.17</td><td>16.99</td><td>44.88</td><td>26.53</td><td>35.72</td></tr><tr><td>BT+NLL</td><td>88.36</td><td>12.36</td><td>31.48</td><td>8.75</td><td>12.82</td></tr><tr><td>Ours</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr><tr><td rowspan=\"4\">AuthorImitation</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>132.95</td><td>85.25</td></tr><tr><td>UNMT</td><td>80.23</td><td>7.13</td><td>=</td><td>40.11</td><td>39.38</td></tr><tr><td>BT+NLL</td><td>76.98</td><td>10.80</td><td>=</td><td>61.70</td><td>65.51</td></tr><tr><td>Ours</td><td>81.43</td><td>10.81</td><td>=</td><td>49.62</td><td>44.86</td></tr><tr><td rowspan=\"4\">Formality</td><td>Test Set</td><td>-</td><td>-</td><td>-</td><td>71.30</td><td>135.50</td></tr><tr><td>UNMT</td><td>78.06</td><td>16.11</td><td>-</td><td>26.70</td><td>10.38</td></tr><tr><td>BT+NLL</td><td>82.43</td><td>8.57</td><td></td><td>6.57</td><td>8.21</td></tr><tr><td>Ours</td><td>80.46</td><td>18.54</td><td>-</td><td>22.65</td><td>17.23</td></tr></table>",
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+        "text": "Author Imitation. Author imitation is the task of paraphrasing a sentence to match another author’s style. The dataset we use is a collection of Shakespeare’s plays translated line by line into modern English. It was collected by $\\mathrm { X u }$ et al. $( 2 0 1 2 ) ^ { 7 }$ and used in prior work on supervised style transfer (Jhamtani et al., 2017). This is a parallel corpus and thus we follow the setting in the formality transfer task. We use $\\mathcal { D } _ { 1 }$ to denote modern English, and $\\mathcal { D } _ { 2 }$ to denote Shakespeare-style English. Results are shown in Table 1. ",
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+        "type": "text",
+        "text": "Related Language Translation. Next, we test our method on a challenging related language translation task (Pourdamghani & Knight, 2017; Yang et al., 2018). This task is a natural test bed for unsupervised sequence transduction since the goal is to preserve the meaning of the source sentence while rewriting it into the target language. For our experiments, we choose Bosnian (bs) and Serbian (sr) as the related language pairs. We follow Yang et al. (2018) to report BLEU-1 score on this task since BLEU-4 score is close to zero. Results are shown in Table 2. ",
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+        "type": "text",
+        "text": "Unsupervised MT. In order to draw connections with a related work on general unsupervised machine translation, we also evaluate on the WMT’16 German English translation task. This task is substantially more difficult than the style transfer tasks considered so far. We compare with the state-of-the-art UNMT system using the existing implementation from the XLM codebase,8 and implement our approach in the same framework with XLM initialization for fair comparison. We train both systems on 5M non-parallel sentences from each language. Results are shown in Table 2. ",
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+    {
+        "type": "text",
+        "text": "In Tables 1 we also list the PPL of the test set under the external LM for both the source and target domain. PPL of system outputs should be compared to PPL of the test set itself because extremely low PPL often indicates that the generated sentences are short or trivial. ",
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+        "table_caption": [
+            "Table 2: BLEU for decipherment, related language translation (Sr-Bs), and general unsupervised translation (En-De). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Decipher</td><td>Sr-Bs</td><td>Bs-Sr</td><td>En-De</td><td>De-En</td></tr><tr><td>Shen et al. (2017)</td><td>50.8</td><td>1</td><td>-</td><td></td><td>1</td></tr><tr><td>Yang et al. (2018)</td><td>49.3</td><td>31.0</td><td>33.4</td><td>1</td><td>-</td></tr><tr><td>UNMT</td><td>76.4</td><td>31.4</td><td>33.4</td><td>26.5</td><td>32.2</td></tr><tr><td>BT+NLL</td><td>78.0</td><td>29.6</td><td>31.4</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>78.4</td><td>36.2</td><td>38.3</td><td>26.9</td><td>32.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.2 RESULTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Tables 1 and 2 demonstrate some general trends. First, UNMT is able to outperform ",
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+        "type": "text",
+        "text": "other prior methods in unsupervised text style transfer, such as (Yang et al., 2018; Hu et al., 2017; Shen et al., 2017). The performance improvements of UNMT indicate that flexible and powerful architectures are crucial (prior methods generally do not have an attention mechanism). Second, our model achieves comparable classification accuracy to UNMT but outperforms it in all style transfer tasks in terms of the reference-BLEU, which is the most important metric since it directly measures the quality of the final generations against gold parallel data. This indicates that our method is both effective and consistent across many different tasks. Finally, the $_ { \\mathrm { B T + N L L } }$ baseline is sometimes quite competitive, which indicates that the addition of a language model alone can be beneficial. However, our method consistently outperforms the simple $_ { \\mathrm { B T + N L L } }$ method, which indicates the effectiveness of the additional entropy regularizer in Eq. 5 that is the byproduct of our probabilistic formulation. ",
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+    {
+        "type": "text",
+        "text": "Next, we examine the PPL of the system outputs under pretrained domain LMs, which should be evaluated in comparison with the PPL of the test set itself. For both the sentiment transfer and the formality transfer tasks in Table 1, $_ { \\mathrm { B T + N L L } }$ achieves extremely low PPL, lower than the PPL of the test corpus in the target domain. After a close examination of the output, we find that it contains many repeated and overly simple outputs. For example, the system generates many examples of “I love this place” when transferring negative to positive sentiment (see Appendix A.3 for examples). It is not surprising that such a trivial output has low perplexity, high accuracy, and low BLEU score. On the other hand, our system obtains reasonably competitive PPL, and our approach achieves the highest accuracy and higher BLEU score than the UNMT baseline. ",
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+    {
+        "type": "text",
+        "text": "5.3 FURTHER ABLATIONS AND ANALYSIS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Parameter Sharing. We also conducted an experiment on the word substitution decipherment task, where we remove parameter sharing (as explained in Section 3.2) between two directions of transduction distributions, and optimize two encoder-decoder instead. We found that the model only obtained an extremely low BLEU score and failed to generate any meaningful outputs. ",
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+    {
+        "type": "text",
+        "text": "Performance vs. Domain Divergence. Figure 3 plots the relative improvement of our method over UNMT with respect to accuracy of a naive Bayes’ classifier trained to predict the domain of test sentences. Tasks with high classification accuracy likely have more divergent domains. We can see that for decipherment and en-de translation, where the domains have different vocabularies and thus are easily distinguished, our method yields a smaller gain over UNMT This likely indicates that the (discrimination) regularization effect of the LM priors is less importan or necessary when the two domains are very different. ",
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+        "image_caption": [
+            "Figure 3: Improvement over UNMT vs. classification accuracy. "
+        ],
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+    {
+        "type": "text",
+        "text": "Why does the proposed model outperform UNMT? Finally, we examine in detail the output of our model and UNMT for the author imitation task. We pick this task because the reference outputs for the test set are provided, aiding analysis. Examples shown in Table 3 demonstrate that UNMT tends to make overly large changes to the source so that the original meaning is lost, while our method is better at preserving the content of the source sentence. Next, we quantitatively examine the outputs from UNMT and our method by comparing the F1 measure of words bucketed by their syntactic tags. We use the open-sourced compare-mt tool (Neubig et al., 2019), and the results are shown in Figure 4. Our system has outperforms UNMT in all word categories. In particular, our system is much better at generating nouns, which likely leads to better content preservation. ",
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+    {
+        "type": "table",
+        "img_path": "images/3da4f608c862633a065a041efda15be9391dfaff45649da46bcb01cf8217e988.jpg",
+        "table_caption": [
+            "Table 3: Examples for author imitation task "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Shakespeare to Modern</td></tr><tr><td>Source</td><td>Not to his father&#x27;s .</td></tr><tr><td>Reference</td><td>Not to his father&#x27;s house.</td></tr><tr><td>UNMT</td><td>Not to his brother .</td></tr><tr><td>Ours</td><td>Not to his father&#x27;s house .</td></tr><tr><td>Source</td><td>Send thy man away .</td></tr><tr><td>Reference</td><td>Send your man away.</td></tr><tr><td>UNMT</td><td>Send an excellent word .</td></tr><tr><td>Ours</td><td>Send your man away.</td></tr><tr><td>Source</td><td>Why should you fall into so deep an O ?</td></tr><tr><td>Reference</td><td>Why should you fall into so deep a moan ?</td></tr><tr><td>UNMT</td><td>Why should you carry so nicely,but have your legs ？</td></tr><tr><td>Ours</td><td>Why should you fall into so deep a sin ?</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/77998449f70906451fe5613ae7e9933a82e30c20a2ca545eabe27b26da8c75ef.jpg",
+        "image_caption": [
+            "Figure 4: Word F1 score by POS tag. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5f6740e1341881c2803294dccfe4db8d55c306e1c070bd1cb1f40421d9fb7517.jpg",
+        "table_caption": [
+            "Table 4: Comparison of gradient approximation on the sentiment transfer task. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>train ELBO个</td><td>test ELBO个</td><td>Acc.</td><td>BLEUr</td><td>BLEUs</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td>Sample-based</td><td>-3.51</td><td>-3.79</td><td>87.90</td><td>13.34</td><td>33.19</td><td>24.55</td><td>25.67</td></tr><tr><td>Greedy</td><td>-2.05</td><td>-2.07</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/64efa0127d8fef70a9ab7c8e6fa2e0ce146bb553af8190d53e1eed20c5e50950.jpg",
+        "table_caption": [
+            "Table 5: Comparison of gradient propagation method on the sentiment transfer task. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>train ELBO↑</td><td>test ELBO个</td><td>Acc.</td><td>BLEUr</td><td>BLEUs</td><td>PPLD1</td><td>PPLD2</td></tr><tr><td>Gumbel Softmax</td><td>-2.96</td><td>-2.98</td><td>81.30</td><td>16.17</td><td>40.47</td><td>22.70</td><td>23.88</td></tr><tr><td>REINFORCE</td><td>-6.07</td><td>-6.48</td><td>95.10</td><td>4.08</td><td>9.74</td><td>6.31</td><td>4.08</td></tr><tr><td>Stop Gradient</td><td>-2.05</td><td>-2.07</td><td>87.90</td><td>18.67</td><td>48.38</td><td>27.75</td><td>35.61</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Greedy vs. Sample-based Gradient Approximation. In our experiments, we use greedy decoding from the inference network to approximate the expectation required by ELBO, which is a biased estimator. The main purpose of this approach is to reduce the variance of the gradient estimator during training, especially in the early stages when the variance of sample-based approaches is quite high. As an ablation experiment on the sentiment transfer task we compare greedy and sample-based gradient approximations in terms of both train and test ELBO, as well as task performance corresponding to best test ELBO. After the model is fully trained, we find that the sample-based approximation has low variance. With a single sample, the standard deviation of the EBLO is less than 0.3 across 10 different test repetitions. All final reported ELBO values are all computed with this approach, regardless of whether the greedy approximation was used during training. The reported ELBO values are the evidence lower bound per word. Results are shown in Table 4, where the sampling-based training underperforms on both ELBO and task evaluations. ",
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+    {
+        "type": "text",
+        "text": "5.4 COMPARISON OF GRADIENT PROPAGATION METHODS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As noted above, to stabilize the training process, we stop gradients from propagating to the inference network from the reconstruction loss. Does this approach indeed better optimize the actual probabilistic objective (i.e. ELBO) or only indirectly lead to improved task evaluations? In this section we use sentiment transfer as an example task to compare different methods for propagating gradients and evaluate both ELBO and task evaluations. ",
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+    {
+        "type": "text",
+        "text": "Specifically, we compare three different methods: ",
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+    {
+        "type": "text",
+        "text": "• Stop Gradient: The gradients from reconstruction loss are not propagated to the inference network. This is the method we use in all previous experiments.   \n• Gumbel Softmax (Jang et al., 2017): Gradients from the reconstruction loss are propagated to the inference network with the straight-through Gumbel estimator.   \n• REINFORCE (Sutton et al., 2000): Gradients from reconstruction loss are propagated to the inference network with ELBO as a reward function. This method has been used in previous work for semi-supervised sequence generation (Miao & Blunsom, 2016; Yin et al., 2018), but often suffers from instability issues. ",
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+    {
+        "type": "text",
+        "text": "We report the train and test ELBO along with task evaluations in Table 5, and plot the learning curves on validation set in Figure 5.9 While being much simpler, we show that the stop-gradient trick produces superior ELBO over Gumbel Softmax and REINFORCE. This result suggests that stopping gradient helps better optimize the likelihood objective under our probabilistic formulation in comparison with other optimization techniques that propagate gradients, which is counter-intuitive. A likely explanation is that as a gradient estimator, while clearly biased, stop-gradient has substantially reduced variance. In comparison with other techniques that offer reduced bias but extremely high variance when applied to our model class (which involves discrete sequences as latent variables), stop-gradient actually leads to better optimization of our objective because it achieves better balance of bias and variance overall. ",
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+    {
+        "type": "image",
+        "img_path": "images/d795400be20ee935fa9f0e734c9f8151789443d1144ec02f23fde88102bcb2d4.jpg",
+        "image_caption": [
+            "Figure 5: ELBO on the validation set v.s. the number training steps. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We propose a probabilistic generative forumalation that unites past work on unsupervised text style transfer. We show that this probabilistic formulation provides a different way to reason about unsupervised objectives in this domain. Our model leads to substantial improvements on five text style transfer tasks, yielding bigger gains when the styles considered are more difficult to distinguish. ",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENT ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The work of Junxian He and Xinyi Wang is supported by the DARPA GAILA project (award HR00111990063) and the Tang Family Foundation respectively. The authors would like to thank Zichao Yang for helpful feedback about the project. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            303,
+            117
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.1 MODEL CONFIGURATIONS. ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            133,
+            408,
+            148
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We adopt the following attentional encoder-decoder architecture for UNMT, $_ { \\mathrm { B T + N L L } }$ , and our method across all the experiments: ",
+        "bbox": [
+            174,
+            160,
+            825,
+            188
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "• We use word embeddings of size 128.   \n• We use 1 layer LSTM with hidden size of 512 as both the encoder and decoder.   \n• We apply dropout to the readout states before softmax with a rate of 0.3.   \n• Following Lample et al. (2019), we add a max pooling operation over the encoder hidden states before feeding it to the decoder. Intuitively the pooling window size would control how much information is preserved during transduction. A window size of 1 is equivalent to standard attention mechanism, and a large window size corresponds to no attention. See Appendix A.2 for how to select the window size. There is a noise function for UNMT baseline in its denoising autoencoder loss (Lample et al., 2017; 2019), which is critical for its success. We use the default noise function and noise hyperparameters in Lample et al. (2017) when running the UNMT model. For $_ { \\mathrm { B T + N L L } }$ and our method we found that adding the extra noise into the self-reconstruction loss (Eq. 4) is only helpful when the two domains are relatively divergent (decipherment and related language translation tasks) where the language models play a less important role. Therefore, we add the default noise from UNMT to Eq. 4 for decipherment and related language translation tasks only, and do not use any noise for sentiment, author imitation, and formality tasks. ",
+        "bbox": [
+            215,
+            199,
+            825,
+            455
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.2 HYPERPARAMETER TUNING. ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            473,
+            421,
+            487
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We vary pooling windows size as $\\{ 1 , 5 \\}$ , the decaying patience hyperparameter $k$ for selfreconstruction loss (Eq. 4) as $\\{ 1 , 2 , 3 \\}$ . For the baseliens UNMT and $_ { \\mathrm { B T + N L L } }$ , we also try the option of not annealing the self-reconstruction loss at all as in the unsupervised machine translation task (Lample et al., 2018). We vary the weight $\\lambda$ for the NLL term $_ \\mathrm { B T + N L L } )$ or the KL term (our method) as $\\{ 0 . 0 0 1 , 0 . 0 1 , 0 . 0 3 , 0 . 0 5 , 0 . 1 \\}$ . ",
+        "bbox": [
+            174,
+            498,
+            825,
+            569
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.3 SENTIMENT TRANSFER EXAMPLE OUTPUTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            585,
+            529,
+            599
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We list some examples of the sentiment transfer task in Table 6. Notably, the $_ { \\mathrm { B T + N L L } }$ method tends to produce extremely short and simple sentences. ",
+        "bbox": [
+            176,
+            611,
+            823,
+            640
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4 REPETITIVE EXAMPLES OF BT $^ +$ NLL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            656,
+            478,
+            671
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In Section 5 we mentioned that the baseline $_ { \\mathrm { B T + N L L } }$ has a low perplexity for some tasks because it tends to generate overly simple and repetitive sentences. From Table 1 we see that two representative tasks are sentiment transfer and formatliy transfer. In Appendix A.3 we have demonstrated some examples for sentiment transfer, next we show some repetitive samples of $_ { \\mathrm { B T + N L L } }$ in Table 7. ",
+        "bbox": [
+            174,
+            683,
+            825,
+            739
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/4e355d046bbaa50661dcbfa3a77a1e58c6830e0e5233faba22720dfbe87da62b.jpg",
+        "table_caption": [
+            "Table 6: Random Sentiment Transfer Examples "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>negative to positive</td></tr><tr><td>Original</td><td>the cake portion was extremely light and a bit dry .</td></tr><tr><td>UNMT</td><td>the cake portion was extremely light and a bit spicy .</td></tr><tr><td>BT+NLL</td><td>the cake portion was extremely light and a bit dry .</td></tr><tr><td>Ours</td><td>the cake portion was extremely light and a bit fresh .</td></tr><tr><td>Original</td><td>the “ chicken ” strip were paper thin oddly flavored strips .</td></tr><tr><td>UNMT</td><td>the“ chicken ”were extra crispy noodles were fresh and incredible .</td></tr><tr><td>BT+NLL</td><td>the service was great .</td></tr><tr><td>Ours</td><td>the“ chicken ”strip were paper sweet &amp; juicy flavored .</td></tr><tr><td>Original</td><td>if i could give them a zero star review i would !</td></tr><tr><td>UNMT</td><td> if i could give them a zero star review i would !</td></tr><tr><td>BT+NLL</td><td>i love this place .</td></tr><tr><td>Ours</td><td>i love the restaurant and give a great review i would !</td></tr><tr><td></td><td>positive to negative</td></tr><tr><td>Original</td><td> great food,staff is unbelievably nice .</td></tr><tr><td>UNMT BT+NLL</td><td>no ,food is n&#x27;t particularly friendly .</td></tr><tr><td>Ours</td><td>i will not be back .</td></tr><tr><td></td><td>no apologies,staff is unbelievably poor .</td></tr><tr><td>Original</td><td>my wife and i love coming here !</td></tr><tr><td>UNMT</td><td>my wife and i do n&#x27;t come here !</td></tr><tr><td>BT+NLL</td><td>i will not be back.</td></tr><tr><td>Ours</td><td>my wife and i walked out the last time .</td></tr><tr><td>Original</td><td>my wife and i love coming here !</td></tr><tr><td>UNMT</td><td>my wife and i do n&#x27;t come here !</td></tr><tr><td>BT+NLL</td><td>i will not be back .</td></tr><tr><td>Ours</td><td>my wife and i walked out the last time .</td></tr><tr><td>Original</td><td>the premier hookah lounge of las vegas !</td></tr><tr><td>UNMT</td><td>the worst museum of las vegas !</td></tr><tr><td>BT+NLL</td><td>the worst frame shop of las vegas !</td></tr><tr><td>Ours</td><td>the hallways scam lounge of las vegas !</td></tr></table>",
+        "bbox": [
+            223,
+            143,
+            771,
+            662
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/f3fb3cd89abb0a245b4f41de665660ee7e4c4fde63a5f12a0eb0e714ad4eeda0.jpg",
+        "table_caption": [
+            "Table 7: Repetitive examples of $\\mathrm { B T + N L L }$ baseline on Formality transfer. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Original</td><td>Transferred</td></tr><tr><td colspan=\"2\">formal to informal</td></tr><tr><td>I like Rhythm and Blue music .</td><td>I like her and I don&#x27;t know .</td></tr><tr><td>There&#x27;s nothing he needs to change .</td><td>I don&#x27;t know,but Idon&#x27;t know .</td></tr><tr><td>Ienjoy watching my companion attempt to role @-@ play with them.</td><td>Idon&#x27;tknow,but Idon&#x27;t know.</td></tr><tr><td>Iam watching it right now</td><td>Idon&#x27;t know,but Idon&#x27;t know .</td></tr><tr><td>That is the key point,that you fell asleep .</td><td>I don&#x27;t know,but Idon&#x27;t know.</td></tr><tr><td colspan=\"2\">informal to formal</td></tr><tr><td>its a great source just download it .</td><td>I do not know,but Ido not know .</td></tr><tr><td>Happy Days,it was the coolest ！</td><td>I do not know,butIdo not know.</td></tr><tr><td>I used to play flute but once I started sax,I got hooked .</td><td>I do not know,butIdo not know.</td></tr><tr><td>The word you are  looking  foris.... strengths</td><td>The word you are looking for is :)</td></tr><tr><td>Plus you can tell she really cared about her crew .</td><td>Plus you can tell she really cared about her crew.</td></tr></table>",
+        "bbox": [
+            176,
+            736,
+            825,
+            895
+        ],
+        "page_idx": 13
+    }
+]

parse/train/S1Q79heRW/S1Q79heRW.md

@@ -0,0 +1,209 @@
+# UNSUPERVISED LEARNING OF ENTAILMENT-VECTOR WORD EMBEDDINGS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Entailment vectors are a principled way to encode in a vector what information is known and what is unknown. They are designed to model relations where one vector should include all the information in another vector, called entailment. This paper investigates the unsupervised learning of entailment vectors for the semantics of words. Using simple entailment-based models of the semantics of words in text (distributional semantics), we induce entailment-vector word embeddings which outperform the best previous results for predicting entailment between words, in unsupervised and semi-supervised experiments on hyponymy.
+
+# 1 INTRODUCTION
+
+Modelling entailment, is a fundamental issue in the semantics of natural language, and there has been a lot of interest in modelling entailment using vector-space representations. But, until recently, unsupervised models such as word embeddings have performed surprisingly poorly at detecting entailment Weeds et al. (2014); Shwartz et al. (2017), not beating a frequency baseline Weeds et al. (2014). Entailment is the relation of information inclusion, meaning that $y$ entails $x$ if and only if everything that is known given $x$ is also known given $y$ . As such, representations which support entailment need to encode not just what information is known, but also what information is unknown. The results on lexical entailment seem to indicate that standard word embeddings, such as Word2Vec, do not reflect the relative abstractness of words, and in this sense do not reflect how much information is left unspecified by a word.
+
+In contrast with the majority of the work in this area, which simply uses existing vector-space embeddings of words in their models of entailment, recent work has addressed this issue by proposing new vector-space models which are specifically designed to capture entailment. In particular, Vilnis & McCallum (2015) use variances to represent the uncertainty in values in a continuous space, and Henderson & Popa (2016) use probabilities to represent uncertainty about a discrete space. We will refer to the latter as the “entailment-vectors” framework. In this work, we use this framework from Henderson & Popa (2016) to develop new entailment-based models for the unsupervised learning of word embeddings, and demonstrate that these embeddings achieve unprecedented results in predicting entailment between words.
+
+Our unsupervised models use the distribution of words in a large text corpus to induce vector-space representations of the meaning of words. This approach to word meaning is called distributional semantics. The distributional semantic hypothesis (Harris, 1954) says that the meaning of a word is reflected in the distribution of text contexts which it appears in. Many methods (e.g. (Deerwester et al., 1990; Schutze, 1993; Mikolov et al., 2013a) and this paper) have been proposed for inducing ¨ vector representations of the meaning of words (word embeddings) from the distribution of wordcontext pairs found in large corpora of text.
+
+In the framework of Henderson & Popa (2016), each dimension of the vector-space represents something that might be known, and continuous vectors represent probabilities of these features being known or unknown. Henderson & Popa (2016) illustrate their framework by proposing a reinterpretation of existing Word2Vec (Mikolov et al., 2013a) word embeddings which maps them into entailment vectors, which in turn successfully predict entailment between words (hyponymy). To motivate this reinterpretation of existing word embeddings, they propose a model of distributional semantics and argue that the Word2Vec training objective approximates the training objective of this distributional semantic model given the mapping.
+
+In this paper, we implement this distributional semantic model and train new word embeddings using the exact objective. Based on our analysis of this model, we propose that this implementation can be done in several ways, including the one which motivates Henderson & Popa (2016)’s reinterpretation of Word2Vec embeddings. In each case, training results in entailment vector embeddings, which directly encode what is known and unknown given a word, and thus do not require any reinterpretation to predict hyponymy.
+
+To model the semantic relationship between a word and its context, the distributional semantic model postulates a latent pseudo-phrase vector for the unified semantics of the word and its neighbouring context word. This latent vector must entail the features in both words’ vectors and must be consistent with a prior over semantic vectors, thereby modelling the redundancy and consistency between the semantics of two neighbouring words.
+
+Based on our analysis of this entailment-based distributional semantic model, we hypothesise that the word embeddings suggested by Henderson & Popa (2016) are in fact not the best way to extract information about the semantics of a word from this model. They propose using a vector which represents the evidence about known features given the word (henceforth called the likelihood vectors). We propose to instead use a vector which represents the posterior distribution of known features for a phrase containing only the word. This posterior vector includes both the evidence from the word and its indirect consequences via the constraints imposed by the prior. Our efficient implementation of this model allows us to test this hypothesis by outputting either the likelihood vectors or the posterior vectors as word embeddings.
+
+To evaluate these word embeddings, we predict hyponymy between words, in both an unsupervised and semi-supervised setting. Given the word embeddings for two words, we measure whether they are a hypernym-hyponym pair using an entailment operator from (Henderson & Popa, 2016) applied to the two embeddings. We find that using the likelihood vectors performs as well as reinterpreting Word2Vec embeddings, confirming the claims of equivalence by Henderson & Popa (2016). But we also find that using the posterior vectors performs significantly better, confirming our hypothesis that posterior vectors are better, and achieving the best published results on this benchmark dataset. In addition to these unsupervised experiments, we evaluate in a semi-supervised setting and find a similar pattern of results, again achieving state-of-the-art performance.
+
+In the rest of this paper, section 2 presents the formal framework we use for modelling entailment in a vector space, the distributional semantic models, and how these are used to predict hyponymy. Section 3 discusses additional related work, and then section 4 presents the empirical evaluation on hyponymy detection, in both unsupervised and semi-supervised experiments. Some additional analysis of the induced vectors is presented in section 4.4.
+
+# 2 DISTRIBUTIONAL SEMANTIC ENTAILMENT
+
+Distributional semantics uses the distribution of contexts in which a word occurs to induce the semantics of the word (Harris, 1954; Deerwester et al., 1990; Schutze, 1993). The Word2Vec model ¨ (Mikolov et al., 2013a) introduced a set of refinements and computational optimisations of this idea which allowed the learning of vector-space embeddings for words from very large corpora with very good semantic generalisation. Henderson & Popa (2016) motivate their reinterpretation the Word2Vec Skipgram (Mikolov et al., 2013a) distributional semantic model with an entailment-based model of the semantic relationship between a word and its context words. We start by explaining our interpretation of the distributional semantic model proposed by Henderson & Popa (2016), and then propose our alternative models.
+
+Henderson & Popa (2016) postulate a latent vector $y$ which is the consistent unification of the features of the middle word $x _ { e } ^ { \prime }$ and the neighbouring context word $x _ { e }$ , illustrated on the left in figure 1.1 We can think of the latent vector $y$ as representing the semantics of a pseudo-phrase consisting of the two words. The unification requirement is defined as requiring that $y$ entail both words, written $y \Rightarrow x _ { e } ^ { \prime }$ and ${ y } \Rightarrow x _ { e }$ . The consistency requirement is defined as $y$ satisfying a prior $\theta ( y )$ , which embodies all the the constraints and correlations between features in the vector. This approach models the relationship between the semantics of a word and its context as being redundant and consistent.
+
+![](images/2e409103eb26df57b85087dde2856086923e32a2453e6248891724d852ffcf69.jpg)  
+Figure 1: The distributional semantic model of a word and its context (left), and its approximation in the word2hyp models (right).
+
+If $x _ { e } ^ { \prime }$ and $x _ { e }$ share features, then it will be easier for $y$ to satisfy both $y \Rightarrow x _ { e } ^ { \prime }$ and $y { \Rightarrow } x _ { e }$ . If the features of $x _ { e } ^ { \prime }$ and $x _ { e }$ are consistent, then it will be easier for $y$ to satisfy the prior $\theta ( y )$ .
+
+# 2.1 THE REINTERPRETATION OF WORD2VEC
+
+Henderson & Popa (2016) formalise the above model using their entailment-vectors framework. This framework models distributions over discrete vectors where a 1 in position $i$ means feature $i$ is known and a 0 means it is unknown. Entailment $y \Rightarrow x$ requires that the 1s in $x$ are a subset of the 1s in $y$ , so $1 \Rightarrow 1$ , $0 { \Rightarrow } 0$ and $1 { \Rightarrow } 0$ , but $0 { \neq } 1$ . Distributions over these discrete vectors are represented as continuous vectors of log-odds $X$ , so $P ( x _ { i } { = } 1 ) = \sigma ( X _ { i } )$ , where $\sigma$ is the logistic sigmoid. The probability of entailment $y \Rightarrow x$ between two such “entailment vectors” $Y , X$ can be measured using the operator $\bigcirc$ :2
+
+$$
+\begin{array} { c } { { \log P ( y { \Rightarrow } x \mid Y , X ) \approx } } \\ { { Y { \otimes } X \equiv \sigma ( - Y ) \cdot \log \sigma ( - X ) } } \end{array}
+$$
+
+For each feature $i$ in the vector, it calculates the expectation according to $P ( y _ { i } )$ that, either $y _ { i } { = } 1$ and thus the log-probability is zero, or $y _ { i } { = } 0$ and thus the log-probability is $\log P ( x _ { i } { = } 0 )$ (noting that $\sigma ( - X _ { i } ) = ( 1 - \sigma ( X _ { i } ) ) \approx P ( x _ { i } { = } 0 ) )$ .
+
+Henderson & Popa (2016) formalise the model on the left in figure 1 by first inferring the optimal latent vector distribution $Y$ (equation (3)), and then scoring how well the entailment and prior constraints have been satisfied (equation (2)).
+
+$$
+\begin{array} { r l } & { \underset { Y } { \operatorname* { m a x } } \big ( E _ { Y , X _ { e } ^ { \prime } , X _ { e } } \log P ( y \Rightarrow x _ { e } ^ { \prime } , y \Rightarrow x _ { e } , y ) \big ) } \\ & { \quad \approx Y \otimes X _ { e } ^ { \prime } + Y \otimes X _ { e } + ( - \sigma ( - Y ) ) \cdot \theta ( Y ) } \end{array}
+$$
+
+where
+
+$$
+Y = - \log \sigma ( - X _ { e } ^ { \prime } ) + - \log \sigma ( - X _ { e } ) + \theta ( Y )
+$$
+
+where $E _ { Y , X _ { e } ^ { \prime } , X _ { e } }$ is the expectation over the distribution defined by the log-odds vectors $Y , X _ { e } ^ { \prime } , X _ { e }$ , and log and $\sigma$ are applied componentwise. The term $\theta ( Y )$ is used to indicate the net effect of the prior on the vector $Y$ . Note that, in the formula (3) for inferring $Y$ , the contribution $- \log \sigma ( - X )$ of each word vector is also a component of the definition of $Y \odot X$ from equation (1). In this way, the score for measuring how well the entailment has been satisfied is using the same approximation as used in the inference to satisfy the entailment constraint. This function $- \log \sigma ( - X )$ is a nonnegative transform of $X$ , as shown in figure 2. Intuitively, for an entailed vector $x$ , we only care about the probability that $x _ { i } { = } 1$ (positive log-odds $X _ { i }$ ), because that constrains the entailing vector $y$ to have $y _ { i } { = } 1$ (adding to the log-odds $Y _ { i }$ ).
+
+The above model cannot be mapped directly to the Word2Vec model because Word2Vec has no way to model the prior $\theta ( Y )$ . On the other hand, the Word2Vec model postulates two vectors for every word, compared to one in the above model. Henderson & Popa (2016) propose an approximation to the above model which incorporates the prior into one of the two vectors, resulting in each word having one vector $X _ { e }$ as above plus another vector $X _ { p }$ with the prior incorporated.
+
+$$
+X _ { p } \approx - \log \sigma ( - X _ { e } ) + \theta ( Y )
+$$
+
+![](images/7431319ff0ba44d4033a6901d56a88b7a22ee12a3ce07fa20460fac547eb6697.jpg)  
+Figure 2: The function $- \log \sigma ( - X )$ used in inference and the $\bigcirc$ operator, versus $X$
+
+Both vectors $X _ { e }$ and $X _ { p }$ are parameters of the model, which need to be learned. Thus, there is no need to explicitly model the prior, thereby avoiding the need to choose a particular form for the prior $\theta$ , which in general may be very complex.
+
+This gives us the following score for how well the constraints of this model can be satisfied.
+
+$$
+\begin{array} { r l } & { \underset { Y } { \operatorname* { m a x } } \big ( E _ { Y , X _ { e } ^ { \prime } , X _ { p } } \log P ( y \Rightarrow x _ { e } ^ { \prime } , y \Rightarrow x _ { e } , y ) \big ) } \\ & { \quad \approx Y \otimes X _ { e } ^ { \prime } + ( - \sigma ( - Y ) ) \cdot X _ { p } } \end{array}
+$$
+
+where
+
+$$
+Y = - \log \sigma ( - X _ { e } ^ { \prime } ) + X _ { p }
+$$
+
+In (Henderson & Popa, 2016), score (5) is only used to provide a reinterpretation of Word2Vec word embeddings. They show that a transformation of the vectors output by Word2Vec (“W2V u.d.
+
+# 2.2 NEW DISTRIBUTIONAL SEMANTIC MODELS
+
+In this paper, we implement distributional semantic models based on score (5) and use them to train new word embeddings. We call these models the Word2Hyp models, because they are based on Word2Vec but are designed to predict hyponymy.
+
+To motivate our models, we provide a better understanding of the model behind score (5). In particular, we note that although we want $X _ { p }$ to approximate the effects $\theta ( Y )$ of the prior as in equation 4, in fact $X _ { p }$ is only dependent on one of the two words, and thus can only incorporate the portion of $\theta ( Y )$ which arises from that one word. Thus, a better understanding of $X _ { p }$ is provided by equation (7).
+
+$$
+X _ { p } \approx - \log \sigma ( - X _ { e } ) + \theta ( X _ { p } )
+$$
+
+In this framework, equation (7) is exactly the same formula as would be used to infer the vector for a single-word phrase (analogously to equation (3)).
+
+This interpretation of the approximate model in equation 5 is given on the right side of figure 1. As shown, $X _ { p }$ is interpreted as the posterior vector for a single-word phrase, which incorporates the likelihood and the prior for that word. In contrast, $X _ { e } ^ { \prime }$ is just the likelihood, which provides the evidence about the features of $Y$ from the other word, without including the indirect consequences of this information. This model, as argued above, approximates the model on the left side in Figure 1. But the grey part of the figure does not need to be explicitly modelled because $X _ { p }$ is trained directly.
+
+This interpretation suggests that the posterior vector $X _ { p }$ should be a better reflection of the semantics of the word than the likelihood vector $X _ { e }$ , since it includes both the direct evidence for some features and their indirect consequences for other features. We test this hypothesis empirically in Section 4.
+
+To implement our distributional semantic models, we define new versions of the Word2Vec code (Mikolov et al., 2013a;b). The Word2Vec code trains two vectors for each word, where negative sampling is applied to one of these vectors, and the other is the output vector. This applies to both the Skipgram and CBOW versions of training. Both versions also use a dot product between vectors to try to predict whether the example is a positive or negative sample. We simply replace this dot product with score (5) directly in the Word2Vec code, leaving the rest of the algorithm unchanged. We make this change in one of two ways, one where the output vector corresponds to the likelihood vector $X _ { e }$ , and one where the output vector corresponds to the posterior vector $X _ { p }$ . We will refer to the model where $X _ { p }$ is output as the “posterior” model, and the model where $X _ { e }$ is output as the “likelihood” model. Both these methods can be applied to both the Skipgram and CBOW models, giving us four different models to evaluate.
+
+# 2.3 MODELLING HYPONYMY
+
+The proposed distributional semantic models output a word embedding vector for every word in the vocabulary, which are directly interpretable as entailment vectors in the entailment-vectors framework. Thus, to predict lexical entailment between two words, we can simply apply the $\bigcirc$ operator to their vectors, to get an approximation of the log-probability of entailment.
+
+We evaluate these entailment predictions on hyponymy detection. Hyponym-hypernym pairs should have associated embeddings $Y , X$ which have a higher entailment scores $Y \odot X$ than other pairs. We rank the word pairs by the entailment scores for their embeddings, and evaluate this ranked list against the gold hyponymy annotations. We evaluate on hyponymy detection because it reflects a direct form of lexical entailment; the semantic features of a hypernym (e.g. “animal”) should be included in the semantic features of the hyponym (e.g. “cat”). Other forms of lexical entailment would benefit from some kind of reasoning or world knowledge, which we leave to future work on compositional models.
+
+# 3 RELATED WORK
+
+In this paper we propose a distributional semantic model which is based on entailment. Most of the work on modelling entailment with vector space embeddings has simply used distributional semantic vectors within a model of entailment, and is therefore not directly relevant here. See (Shwartz et al., 2017) for a comprehensive review of such measures. Shwartz et al. (2017) evaluate these measures as unsupervised models of hyponymy detection and run experiments on a number of hyponymy datasets. We report their best comparable result in Table 1.
+
+Vilnis & McCallum (2015) propose an unsupervised model of entailment in a vector space, and evaluate it on hyponymy detection. Instead of representing words as a point in a vector space, they represent words as a Gaussian distribution over points in a vector space. The variance of this distribution in a given dimension indicates the extent to which the dimension’s feature is unknown, so they use KL-divergence to detect hyponymy relations. Although this model has a nice theoretical motivation, the word representations are more complex and training appears to be more computationally expensive than the method proposed here. We empirically compare our models to their hyponymy detection accuracy and find equivalent results.
+
+The semi-supervised model of Kruszewski et al. (2015) learns a discrete Boolean vector space for predicting hyponymy. But they do not propose any unsupervised method for learning these vectors.
+
+Weeds et al. (2014) report hyponymy detection results for a number of unsupervised and semisupervised models. They propose a semi-supervised evaluation methodology where the words in the training and test sets are disjoint, so that the supervised component must learn about the unsupervised vector space and not about the individual words. Following Henderson & Popa (2016), we replicate their experimental setup in our evaluations, for both unsupervised and semi-supervised models, and compare to the best results among the models evaluated by Weeds et al. (2014), Shwartz et al. (2017) and Henderson & Popa (2016).
+
+# 4 EVALUATION OF WORD EMBEDDINGS
+
+We evaluate on hyponymy detection in both a fully unsupervised setup and a semi-supervised setup. In the semi-supervised setup, we use labelled hyponymy data to train a linear mapping from the unsupervised vector space to a new vector space with the objective of correctly predicting hyponymy relations in the new vector space. This prediction is done with the same (or equivalent) entailment operator as for the unsupervised experiments (called “map $\bigcirc$ ” in Table 2).
+
+Table 1: Hyponymy detection accuracies $( 5 0 \% A c c )$ and average precision $( A \nu e P r e c )$ , in the unsupervised experiments. For the accuracies, \* marks a significant improvement over the higher rows.   
+
+<table><tr><td>embeddings</td><td>operator</td><td>50% Acc AvePrec</td></tr><tr><td>Weeds et.al., 2014 Shwartz et.al., 2017</td><td></td><td>58% 1 44.1% 1</td></tr><tr><td>W2V GoogleNews</td><td>u.d.</td><td>64.5%* 1</td></tr><tr><td>W2V CBOW W2H Skip likelihood</td><td>u.d. ② ③</td><td>53.2% 55.2% 59.5% 57.8%</td></tr><tr><td>W2H CBOW] likelihood</td><td>③</td><td>61.8% 66.4%</td></tr><tr><td>W2V Skip</td><td>u.d.</td><td>62.1% 67.6%</td></tr><tr><td>W2H CBOW</td><td>posterior ③</td><td>68.1%* 70.8%</td></tr><tr><td>W2H [Skip</td><td>posterior 国</td><td>69.6% 68.9%</td></tr></table>
+
+We replicate the experimental setup of Weeds et al. (2014), using their selection of hyponymhypernym pairs from the BLESS dataset (Baroni & Lenci, 2011), which consists of noun-noun pairs, including $50 \%$ positive hyponymy pairs plus $50 \%$ negative pairs consisting of some other hyponymy pairs reversed, some pairs in other semantic relations, and some random pairs. As in (Weeds et al., 2014), our semi-supervised experiments use ten-fold cross validation, where each fold has items removed from the training set if they contain a word that also occurs in the testing set.
+
+The word embedding vectors which we train have 200 dimensions and were trained using our Word2Hyp modification of the Word2Vec code (with default settings), trained on a corpus of half a billion words of Wikipedia. We also replicate the approach of Henderson & Popa (2016) by training Word2Vec embeddings on this data.
+
+To quantify performance on hyponymy detection, for each model we rank the list of pairs according to the score given by the model, and report two measures of performance for this ranked lists. The “ $50 \%$ Acc” measure treats the first half of the list as labelled positive and the second half as labelled negative. This is motivated by the fact that we know a priori that the proportion of positive examples has been artificially set to (approximately) $50 \%$ . Average precision is a measure of the accuracy for ranked lists, used in Information Retrieval and advocated as a measure of hyponymy detection by Vilnis & McCallum (2015). For each positive example, precision is measured at the threshold just below that example, and these precision scores are averaged over positive examples. For cross validation, we average over the union of positive examples in all the test sets. Both these measures are reported (when available) in Tables 1 and 2.
+
+# 4.1 UNSUPERVISED HYPONYMY DETECTION
+
+The first set of experiments evaluate the different embeddings in their unsupervised models of hyponymy detection. Results are shown in Table 1. Our principal point of comparison is the best results from (Henderson & Popa, 2016) (called “W2V GoogleNews” in Table 1). They use the preexisting publicly available GoogleNews word embeddings, which were trained with the Word2Vec software on 100 billion words of the GoogleNews dataset, and have 300 dimensions. To provide a more direct comparison, we replicate the model of Henderson & Popa (2016) but using the same embedding training setup as for our Word2Hyp model (“W2V Skip”). Both cases use their proposed reinterpretation of these vectors for predicting entailment $( ^ { 6 } u . d . \odot ^ { 7 } )$ . We also report the best results from Weeds et al. (2014) and the best comparable results from (Shwartz et al., 2017). For our proposed Word2Hyp distributional semantic models (“W2H”), we report results for the four combinations of using the CBOW or Skipgram (“Skip”) model to train the likelihood or posterior vectors.
+
+The two Word2Hyp models with likelihood vectors perform slightly better than the best unsupervised model of Weeds et al. (2014), but similarly. The reinterpretation of Word2Vec vectors (“W2V GoogleNews $u . d . \odot ^ { \ ' } )$ ) performs significantly better, but when the same method is applied to the smaller Wikipedia corpus (“W2V Skip $u . d . \odot ^ { \ ' } ,$ ), this difference all but disappears. This confirms the hypothesis of Henderson & Popa (2016) that the reinterpretation of Word2Vec vectors and the likelihood vectors from Word2Hyp are approximately equivalent.
+
+Table 2: Hyponymy detection accuracies $50 \%$ Acc) and average precision (Ave Prec), in the semisupervised experiments.   
+
+<table><tr><td rowspan=1 colspan=2>embeddings     operator</td><td rowspan=1 colspan=1>50% AccAvePrec</td></tr><tr><td rowspan=1 colspan=2>Weeds et.al., 2014</td><td rowspan=1 colspan=1>75%    1</td></tr><tr><td rowspan=1 colspan=2>W2VGoogleNews    map①</td><td rowspan=1 colspan=1>80.1%  1</td></tr><tr><td rowspan=2 colspan=2>W2VSkip             map③W2H【CBOW】/ likelihoodmap②W2VCBOW           map②W2HSkip likelihoodmap①W2HSkip  posteriormap③W2HCBOW posteriormap③</td><td rowspan=2 colspan=1>81.9%  88.3%83.3% 90.3%84.6%  91.5%84.8%  90.9%85.5% 91.3%86.0% 92.8%</td></tr><tr><td rowspan=1 colspan=1>map②map①</td></tr></table>
+
+However, even with this smaller corpus, using the proposed posterior vectors from the Word2Hyp model are significantly more accurate than the reinterpretation of Word2Vec vectors. This confirms the hypothesis that the posterior vectors from the Word2Hyp model are a better model of the semantics of a word than the likelihood vectors suggested by Henderson & Popa (2016).
+
+Using the CBOW model or the Skipgram model makes only a small difference. The average precision score shows the same pattern as the accuracy.
+
+To allow a direct comparison to the model of Vilnis & McCallum (2015), we also evaluated the unsupervised models on the hyponymy data from (Baroni et al., 2012), which is not as carefully designed to evaluate hyponymy as the (Weeds et al., 2014) data. Both the likelihood and posterior vectors of the Word2Hyp CBOW model achieved average precision $( 8 1 \% , 8 0 \% )$ which is not significantly different from the best model of Vilnis & McCallum (2015) $( 8 0 \% )$ .
+
+# 4.2 SEMI-SUPERVISED HYPONYMY DETECTION
+
+The semi-supervised experiments train a linear mapping from each unsupervised vector space to a new vector space, where the entailment operator $\bigcirc$ is used to predict hyponymy (“map $\odot ^ { \prime \prime }$ ).
+
+The semi-supervised results (shown in Table 2)3 no longer show an advantage of GoogleNews vectors over Wikipedia vectors for the reinterpretation of Word2Vec vectors. And the advantage of posterior vectors over the likelihood vectors is less pronounced. However, the two posterior vectors still perform much better than all the previously proposed models, achieving $86 \%$ accuracy and nearly $93 \%$ average precision. These semi-supervised results confirm the results from the unsupervised experiments, that Word2Vec embeddings and Word2Hyp likelihood embeddings perform similarly, but that using the posterior vectors of the Word2Hyp model perform better.
+
+# 4.3 TRAINING TIMES
+
+Because the similarity measure in equation 5 is more complex than a simple dot product, training a new distributional semantic model is slower than with the original Word2Vec code. In our experiments, training took about 8 times longer for the CBOW model and about 15 times longer for the Skipgram model. This meant that Word2Hyp CBOW trained about 8 times faster than Word2Hyp Skipgram. As in the Word2Vec code, we used a quadrature approximation (i.e. a look-up table) to speed up the computation of the sigmoid function, and we added the same technique for computing the log-sigmoid function.
+
+# 4.4 DISCUSSION
+
+The relative success of our distributional semantic models at unsupervised hyponymy detection indicates that they are capturing some aspects of lexical entailment. But the gap between the unsupervised and semi-supervised results indicates that other features are also being captured. This is not surprising, since many other factors influence the co-occurrence statistics of words.
+
+Table 3: Ranking of the abstractness $( \mathbf { 0 } \otimes X )$ of frequent words from the hyponymy dataset, using Word2Hyp-Skipgram-posterior embeddings.   
+
+<table><tr><td colspan="2">most abstract</td><td colspan="2">least abstract</td></tr><tr><td>something</td><td>necessity</td><td></td><td>fork</td></tr><tr><td>anything</td><td>sense</td><td>hockey</td><td>&#x27;housing</td></tr><tr><td>end</td><td>back</td><td>republican</td><td>elm</td></tr><tr><td>inside</td><td>saw</td><td>hull</td><td>primate</td></tr><tr><td>good</td><td>：</td><td>cricket</td><td>fur</td></tr></table>
+
+To get a better understanding of these word embeddings, we ranked them by degree of abstractness. Table 3 shows the most abstract and least abstract frequent words that occur in the hyponymy data. To measure abstractness, we used our best unsupervised embeddings and measured how well they are entailed by the zero log-odds vector, which represents a uniform half probability of knowing each feature. For a vector to be entailed by the zero vector, it must be that its features are mostly probably unknown. The less you know given a word, the more abstract it is.
+
+An initial ranking found that six of the top ten abstract words had frequency less than 300 in the Wikipedia data, but none of the ten least abstract terms were infrequent. This indicates a problem with the current method, since infrequent words are generally very specific (as was the case for these low-frequency words, submissiveness, implementer, overdraft, ruminant, warplane, and londoner). Although this is an interesting characteristic of the method, the terms themselves seem to be noise, so we rank only terms with frequency greater than 300.
+
+The most abstract terms in table 3 include some clearly semantically abstract terms, in particular something and anything are ranked highest. Others may be affected by lexical ambiguity, since the model does not disambiguate words by part-of-speech (such as end, good, sense, back, and saw). The least abstract terms are mostly very semantically specific, but it is indicative that this list includes primate, which is an abstract term in Zoology but presumably occurs in very specific contexts in Wikipedia.
+
+# 5 CONCLUSIONS
+
+In this paper, we propose unsupervised methods for efficiently training word embeddings which capture semantic entailment. This work builds on the work of Henderson & Popa (2016), who propose the entailment-vectors framework for modelling entailment in a vector-space, and a distributional semantic model for reinterpreting Word2Vec word embeddings. Our contribution differs from theirs in that we provide a better understanding of their distributional semantic model, we choose different vectors in the model to use as word embeddings, and we train new word embeddings using our modification of the Word2Vec code. Empirical results on unsupervised and semi-supervised hyponymy detection confirm that the model’s likelihood vectors, which Henderson & Popa (2016) suggest to use, do indeed perform equivalently to their reinterpretation of Word2Vec vectors. But these experiments also show that the model’s posterior vectors, which we propose to use, perform significantly better, outperforming all previous results on this benchmark dataset.
+
+The success of these unsupervised models demonstrates that the proposed distributional semantic models are effective at extracting information about lexical entailment from the redundancy and consistency of words with their contexts in large text corpora. The use of the entailment-vectors framework to efficiently model entailment relations has been crucial to this success. This result suggests future work using the entailment-vectors framework in unsupervised models that leverage other distributional evidence about semantics, particularly in models of compositional semantics. The merger of word embeddings with compositional semantics to get representation learning for larger units of text is currently an important challenge in the semantics of natural language, and the work presented in this paper makes a significant contribution towards solving it.
+
+# REFERENCES
+
+Marco Baroni and Alessandro Lenci. How we blessed distributional semantic evaluation. In Proceedings of the GEMS 2011 Workshop on GEometrical Models of Natural Language Semantics,
+
+GEMS ’11, pp. 1–10. Association for Computational Linguistics, 2011. ISBN 978-1-937284-16- 9. URL http://dl.acm.org/citation.cfm?id=2140490.2140491.
+
+Marco Baroni, Raffaella Bernardi, Ngoc-Quynh Do, and Chung-chieh Shan. Entailment above the word level in distributional semantics. In Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics (EACL), pp. 23–32, Avignon, France, 2012. Association for Computational Linguistics. URL http://www.aclweb.org/ anthology/E12-1004.
+
+Scott Deerwester, Susan T. Dumais, George W. Furnas, Thomas K. Landauer, and Richard Harshman. Indexing by latent semantic analysis. Journal of the American Society for Information Science, 41(6):391–407, 1990.
+
+Zellig S. Harris. Distributional structure. ${ ; i \zeta W O R D ; / i \zeta }$ , 10(2-3):146–162, 1954. doi: 10.1080/ 00437956.1954.11659520. URL http://dx.doi.org/10.1080/00437956.1954. 11659520.
+
+James Henderson and Diana Popa. A vector space for distributional semantics for entailment. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 2052–2062, Berlin, Germany, August 2016. Association for Computational Linguistics. URL http://www.aclweb.org/anthology/P16-1193.
+
+Germn Kruszewski, Denis Paperno, and Marco Baroni. Deriving boolean structures from distributional vectors. Transactions of the Association for Computational Linguistics, 3:375–388, 2015. ISSN 2307-387X. URL https://tacl2013.cs.columbia.edu/ojs/index.php/ tacl/article/view/616.
+
+Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient estimation of word representations in vector space. CoRR, abs/1301.3781, 2013a. URL http://arxiv.org/abs/ 1301.3781.
+
+Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality. In C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger (eds.), Advances in Neural Information Processing Systems 26, pp. 3111–3119. Curran Associates, Inc., 2013b. URL http://papers.nips.cc/paper/ 5021-distributed-representations-of-words-and-phrases-and-their-compositionalit pdf.
+
+Hinrich Schutze. Word space. In ¨ Advances in Neural Information Processing Systems 5, pp. 895– 902. Morgan Kaufmann, 1993.
+
+Vered Shwartz, Enrico Santus, and Dominik Schlechtweg. Hypernyms under siege: Linguisticallymotivated artillery for hypernymy detection. In Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics: Volume 1, Long Papers, pp. 65–75, Valencia, Spain, April 2017. Association for Computational Linguistics. URL http://www.aclweb.org/anthology/E17-1007.
+
+Luke Vilnis and Andrew McCallum. Word representations via Gaussian embedding. In Proceedings of the International Conference on Learning Representations 2015 (ICLR), 2015. URL http: //arxiv.org/abs/1412.6623.
+
+Julie Weeds, Daoud Clarke, Jeremy Reffin, David Weir, and Bill Keller. Learning to distinguish hypernyms and co-hyponyms. In Proceedings of COLING 2014, the 25th International Conference on Computational Linguistics: Technical Papers, pp. 2249–2259, Dublin, Ireland, 2014. Dublin City University and Association for Computational Linguistics. URL http: //www.aclweb.org/anthology/C14-1212.

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+        "type": "text",
+        "text": "ABSTRACT ",
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+        "text": "Entailment vectors are a principled way to encode in a vector what information is known and what is unknown. They are designed to model relations where one vector should include all the information in another vector, called entailment. This paper investigates the unsupervised learning of entailment vectors for the semantics of words. Using simple entailment-based models of the semantics of words in text (distributional semantics), we induce entailment-vector word embeddings which outperform the best previous results for predicting entailment between words, in unsupervised and semi-supervised experiments on hyponymy. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Modelling entailment, is a fundamental issue in the semantics of natural language, and there has been a lot of interest in modelling entailment using vector-space representations. But, until recently, unsupervised models such as word embeddings have performed surprisingly poorly at detecting entailment Weeds et al. (2014); Shwartz et al. (2017), not beating a frequency baseline Weeds et al. (2014). Entailment is the relation of information inclusion, meaning that $y$ entails $x$ if and only if everything that is known given $x$ is also known given $y$ . As such, representations which support entailment need to encode not just what information is known, but also what information is unknown. The results on lexical entailment seem to indicate that standard word embeddings, such as Word2Vec, do not reflect the relative abstractness of words, and in this sense do not reflect how much information is left unspecified by a word. ",
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+        "text": "In contrast with the majority of the work in this area, which simply uses existing vector-space embeddings of words in their models of entailment, recent work has addressed this issue by proposing new vector-space models which are specifically designed to capture entailment. In particular, Vilnis & McCallum (2015) use variances to represent the uncertainty in values in a continuous space, and Henderson & Popa (2016) use probabilities to represent uncertainty about a discrete space. We will refer to the latter as the “entailment-vectors” framework. In this work, we use this framework from Henderson & Popa (2016) to develop new entailment-based models for the unsupervised learning of word embeddings, and demonstrate that these embeddings achieve unprecedented results in predicting entailment between words. ",
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+        "type": "text",
+        "text": "Our unsupervised models use the distribution of words in a large text corpus to induce vector-space representations of the meaning of words. This approach to word meaning is called distributional semantics. The distributional semantic hypothesis (Harris, 1954) says that the meaning of a word is reflected in the distribution of text contexts which it appears in. Many methods (e.g. (Deerwester et al., 1990; Schutze, 1993; Mikolov et al., 2013a) and this paper) have been proposed for inducing ¨ vector representations of the meaning of words (word embeddings) from the distribution of wordcontext pairs found in large corpora of text. ",
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+        "type": "text",
+        "text": "In the framework of Henderson & Popa (2016), each dimension of the vector-space represents something that might be known, and continuous vectors represent probabilities of these features being known or unknown. Henderson & Popa (2016) illustrate their framework by proposing a reinterpretation of existing Word2Vec (Mikolov et al., 2013a) word embeddings which maps them into entailment vectors, which in turn successfully predict entailment between words (hyponymy). To motivate this reinterpretation of existing word embeddings, they propose a model of distributional semantics and argue that the Word2Vec training objective approximates the training objective of this distributional semantic model given the mapping. ",
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+        "type": "text",
+        "text": "In this paper, we implement this distributional semantic model and train new word embeddings using the exact objective. Based on our analysis of this model, we propose that this implementation can be done in several ways, including the one which motivates Henderson & Popa (2016)’s reinterpretation of Word2Vec embeddings. In each case, training results in entailment vector embeddings, which directly encode what is known and unknown given a word, and thus do not require any reinterpretation to predict hyponymy. ",
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+        "type": "text",
+        "text": "To model the semantic relationship between a word and its context, the distributional semantic model postulates a latent pseudo-phrase vector for the unified semantics of the word and its neighbouring context word. This latent vector must entail the features in both words’ vectors and must be consistent with a prior over semantic vectors, thereby modelling the redundancy and consistency between the semantics of two neighbouring words. ",
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+        "text": "Based on our analysis of this entailment-based distributional semantic model, we hypothesise that the word embeddings suggested by Henderson & Popa (2016) are in fact not the best way to extract information about the semantics of a word from this model. They propose using a vector which represents the evidence about known features given the word (henceforth called the likelihood vectors). We propose to instead use a vector which represents the posterior distribution of known features for a phrase containing only the word. This posterior vector includes both the evidence from the word and its indirect consequences via the constraints imposed by the prior. Our efficient implementation of this model allows us to test this hypothesis by outputting either the likelihood vectors or the posterior vectors as word embeddings. ",
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+        "type": "text",
+        "text": "To evaluate these word embeddings, we predict hyponymy between words, in both an unsupervised and semi-supervised setting. Given the word embeddings for two words, we measure whether they are a hypernym-hyponym pair using an entailment operator from (Henderson & Popa, 2016) applied to the two embeddings. We find that using the likelihood vectors performs as well as reinterpreting Word2Vec embeddings, confirming the claims of equivalence by Henderson & Popa (2016). But we also find that using the posterior vectors performs significantly better, confirming our hypothesis that posterior vectors are better, and achieving the best published results on this benchmark dataset. In addition to these unsupervised experiments, we evaluate in a semi-supervised setting and find a similar pattern of results, again achieving state-of-the-art performance. ",
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+        "text": "In the rest of this paper, section 2 presents the formal framework we use for modelling entailment in a vector space, the distributional semantic models, and how these are used to predict hyponymy. Section 3 discusses additional related work, and then section 4 presents the empirical evaluation on hyponymy detection, in both unsupervised and semi-supervised experiments. Some additional analysis of the induced vectors is presented in section 4.4. ",
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+        "type": "text",
+        "text": "2 DISTRIBUTIONAL SEMANTIC ENTAILMENT ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Distributional semantics uses the distribution of contexts in which a word occurs to induce the semantics of the word (Harris, 1954; Deerwester et al., 1990; Schutze, 1993). The Word2Vec model ¨ (Mikolov et al., 2013a) introduced a set of refinements and computational optimisations of this idea which allowed the learning of vector-space embeddings for words from very large corpora with very good semantic generalisation. Henderson & Popa (2016) motivate their reinterpretation the Word2Vec Skipgram (Mikolov et al., 2013a) distributional semantic model with an entailment-based model of the semantic relationship between a word and its context words. We start by explaining our interpretation of the distributional semantic model proposed by Henderson & Popa (2016), and then propose our alternative models. ",
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+        "type": "text",
+        "text": "Henderson & Popa (2016) postulate a latent vector $y$ which is the consistent unification of the features of the middle word $x _ { e } ^ { \\prime }$ and the neighbouring context word $x _ { e }$ , illustrated on the left in figure 1.1 We can think of the latent vector $y$ as representing the semantics of a pseudo-phrase consisting of the two words. The unification requirement is defined as requiring that $y$ entail both words, written $y \\Rightarrow x _ { e } ^ { \\prime }$ and ${ y } \\Rightarrow x _ { e }$ . The consistency requirement is defined as $y$ satisfying a prior $\\theta ( y )$ , which embodies all the the constraints and correlations between features in the vector. This approach models the relationship between the semantics of a word and its context as being redundant and consistent. ",
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+        "img_path": "images/2e409103eb26df57b85087dde2856086923e32a2453e6248891724d852ffcf69.jpg",
+        "image_caption": [
+            "Figure 1: The distributional semantic model of a word and its context (left), and its approximation in the word2hyp models (right). "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "If $x _ { e } ^ { \\prime }$ and $x _ { e }$ share features, then it will be easier for $y$ to satisfy both $y \\Rightarrow x _ { e } ^ { \\prime }$ and $y { \\Rightarrow } x _ { e }$ . If the features of $x _ { e } ^ { \\prime }$ and $x _ { e }$ are consistent, then it will be easier for $y$ to satisfy the prior $\\theta ( y )$ . ",
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+    {
+        "type": "text",
+        "text": "2.1 THE REINTERPRETATION OF WORD2VEC ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Henderson & Popa (2016) formalise the above model using their entailment-vectors framework. This framework models distributions over discrete vectors where a 1 in position $i$ means feature $i$ is known and a 0 means it is unknown. Entailment $y \\Rightarrow x$ requires that the 1s in $x$ are a subset of the 1s in $y$ , so $1 \\Rightarrow 1$ , $0 { \\Rightarrow } 0$ and $1 { \\Rightarrow } 0$ , but $0 { \\neq } 1$ . Distributions over these discrete vectors are represented as continuous vectors of log-odds $X$ , so $P ( x _ { i } { = } 1 ) = \\sigma ( X _ { i } )$ , where $\\sigma$ is the logistic sigmoid. The probability of entailment $y \\Rightarrow x$ between two such “entailment vectors” $Y , X$ can be measured using the operator $\\bigcirc$ :2 ",
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+    {
+        "type": "equation",
+        "img_path": "images/151e772ed0b638101e09c180bbd77ab7d3126104dbf7fd5b355080fd26990374.jpg",
+        "text": "$$\n\\begin{array} { c } { { \\log P ( y { \\Rightarrow } x \\mid Y , X ) \\approx } } \\\\ { { Y { \\otimes } X \\equiv \\sigma ( - Y ) \\cdot \\log \\sigma ( - X ) } } \\end{array}\n$$",
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+        "type": "text",
+        "text": "For each feature $i$ in the vector, it calculates the expectation according to $P ( y _ { i } )$ that, either $y _ { i } { = } 1$ and thus the log-probability is zero, or $y _ { i } { = } 0$ and thus the log-probability is $\\log P ( x _ { i } { = } 0 )$ (noting that $\\sigma ( - X _ { i } ) = ( 1 - \\sigma ( X _ { i } ) ) \\approx P ( x _ { i } { = } 0 ) )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Henderson & Popa (2016) formalise the model on the left in figure 1 by first inferring the optimal latent vector distribution $Y$ (equation (3)), and then scoring how well the entailment and prior constraints have been satisfied (equation (2)). ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/f7c2e2fff81b39c7d8b0962f10c5753857e5ecfef8d818b8d31eea83a591044e.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\underset { Y } { \\operatorname* { m a x } } \\big ( E _ { Y , X _ { e } ^ { \\prime } , X _ { e } } \\log P ( y \\Rightarrow x _ { e } ^ { \\prime } , y \\Rightarrow x _ { e } , y ) \\big ) } \\\\ & { \\quad \\approx Y \\otimes X _ { e } ^ { \\prime } + Y \\otimes X _ { e } + ( - \\sigma ( - Y ) ) \\cdot \\theta ( Y ) } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/0528f55410317d73787b259d5b4bf3a5430052d49a664d09452a23cebabd1242.jpg",
+        "text": "$$\nY = - \\log \\sigma ( - X _ { e } ^ { \\prime } ) + - \\log \\sigma ( - X _ { e } ) + \\theta ( Y )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $E _ { Y , X _ { e } ^ { \\prime } , X _ { e } }$ is the expectation over the distribution defined by the log-odds vectors $Y , X _ { e } ^ { \\prime } , X _ { e }$ , and log and $\\sigma$ are applied componentwise. The term $\\theta ( Y )$ is used to indicate the net effect of the prior on the vector $Y$ . Note that, in the formula (3) for inferring $Y$ , the contribution $- \\log \\sigma ( - X )$ of each word vector is also a component of the definition of $Y \\odot X$ from equation (1). In this way, the score for measuring how well the entailment has been satisfied is using the same approximation as used in the inference to satisfy the entailment constraint. This function $- \\log \\sigma ( - X )$ is a nonnegative transform of $X$ , as shown in figure 2. Intuitively, for an entailed vector $x$ , we only care about the probability that $x _ { i } { = } 1$ (positive log-odds $X _ { i }$ ), because that constrains the entailing vector $y$ to have $y _ { i } { = } 1$ (adding to the log-odds $Y _ { i }$ ). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The above model cannot be mapped directly to the Word2Vec model because Word2Vec has no way to model the prior $\\theta ( Y )$ . On the other hand, the Word2Vec model postulates two vectors for every word, compared to one in the above model. Henderson & Popa (2016) propose an approximation to the above model which incorporates the prior into one of the two vectors, resulting in each word having one vector $X _ { e }$ as above plus another vector $X _ { p }$ with the prior incorporated. ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/784353254b6371e089aac85c5b741f6f9b07b5dea301ef82f9e904c1d85dc275.jpg",
+        "text": "$$\nX _ { p } \\approx - \\log \\sigma ( - X _ { e } ) + \\theta ( Y )\n$$",
+        "text_format": "latex",
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+        "type": "image",
+        "img_path": "images/7431319ff0ba44d4033a6901d56a88b7a22ee12a3ce07fa20460fac547eb6697.jpg",
+        "image_caption": [
+            "Figure 2: The function $- \\log \\sigma ( - X )$ used in inference and the $\\bigcirc$ operator, versus $X$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Both vectors $X _ { e }$ and $X _ { p }$ are parameters of the model, which need to be learned. Thus, there is no need to explicitly model the prior, thereby avoiding the need to choose a particular form for the prior $\\theta$ , which in general may be very complex. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This gives us the following score for how well the constraints of this model can be satisfied. ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/6adff4f3c08edbf5c68709e575913db56fc241d1f384d06773e68d8d63556dc3.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\underset { Y } { \\operatorname* { m a x } } \\big ( E _ { Y , X _ { e } ^ { \\prime } , X _ { p } } \\log P ( y \\Rightarrow x _ { e } ^ { \\prime } , y \\Rightarrow x _ { e } , y ) \\big ) } \\\\ & { \\quad \\approx Y \\otimes X _ { e } ^ { \\prime } + ( - \\sigma ( - Y ) ) \\cdot X _ { p } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where ",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dcf16fea28f0250b3a26220f6fd0c866f84c7fd5c8878185f5f4ec8e98592b56.jpg",
+        "text": "$$\nY = - \\log \\sigma ( - X _ { e } ^ { \\prime } ) + X _ { p }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In (Henderson & Popa, 2016), score (5) is only used to provide a reinterpretation of Word2Vec word embeddings. They show that a transformation of the vectors output by Word2Vec (“W2V u.d.\r>” below) can be seen as an approximation to the likelihood vector $X _ { e }$ . In Section 4, we empirically test this hypothesis by directly training $X _ { e }$ (“W2H likelihood” below) and comparing the results to those with reinterpreted Word2Vec vectors. ",
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+    {
+        "type": "text",
+        "text": "2.2 NEW DISTRIBUTIONAL SEMANTIC MODELS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we implement distributional semantic models based on score (5) and use them to train new word embeddings. We call these models the Word2Hyp models, because they are based on Word2Vec but are designed to predict hyponymy. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "To motivate our models, we provide a better understanding of the model behind score (5). In particular, we note that although we want $X _ { p }$ to approximate the effects $\\theta ( Y )$ of the prior as in equation 4, in fact $X _ { p }$ is only dependent on one of the two words, and thus can only incorporate the portion of $\\theta ( Y )$ which arises from that one word. Thus, a better understanding of $X _ { p }$ is provided by equation (7). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b1f5f6784d1286d53b517437e42d63780be0c8b21a1a3a46d2013d15c853ede0.jpg",
+        "text": "$$\nX _ { p } \\approx - \\log \\sigma ( - X _ { e } ) + \\theta ( X _ { p } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            397,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this framework, equation (7) is exactly the same formula as would be used to infer the vector for a single-word phrase (analogously to equation (3)). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This interpretation of the approximate model in equation 5 is given on the right side of figure 1. As shown, $X _ { p }$ is interpreted as the posterior vector for a single-word phrase, which incorporates the likelihood and the prior for that word. In contrast, $X _ { e } ^ { \\prime }$ is just the likelihood, which provides the evidence about the features of $Y$ from the other word, without including the indirect consequences of this information. This model, as argued above, approximates the model on the left side in Figure 1. But the grey part of the figure does not need to be explicitly modelled because $X _ { p }$ is trained directly. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This interpretation suggests that the posterior vector $X _ { p }$ should be a better reflection of the semantics of the word than the likelihood vector $X _ { e }$ , since it includes both the direct evidence for some features and their indirect consequences for other features. We test this hypothesis empirically in Section 4. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To implement our distributional semantic models, we define new versions of the Word2Vec code (Mikolov et al., 2013a;b). The Word2Vec code trains two vectors for each word, where negative sampling is applied to one of these vectors, and the other is the output vector. This applies to both the Skipgram and CBOW versions of training. Both versions also use a dot product between vectors to try to predict whether the example is a positive or negative sample. We simply replace this dot product with score (5) directly in the Word2Vec code, leaving the rest of the algorithm unchanged. We make this change in one of two ways, one where the output vector corresponds to the likelihood vector $X _ { e }$ , and one where the output vector corresponds to the posterior vector $X _ { p }$ . We will refer to the model where $X _ { p }$ is output as the “posterior” model, and the model where $X _ { e }$ is output as the “likelihood” model. Both these methods can be applied to both the Skipgram and CBOW models, giving us four different models to evaluate. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "2.3 MODELLING HYPONYMY ",
+        "text_level": 1,
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "The proposed distributional semantic models output a word embedding vector for every word in the vocabulary, which are directly interpretable as entailment vectors in the entailment-vectors framework. Thus, to predict lexical entailment between two words, we can simply apply the $\\bigcirc$ operator to their vectors, to get an approximation of the log-probability of entailment. ",
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+        "type": "text",
+        "text": "We evaluate these entailment predictions on hyponymy detection. Hyponym-hypernym pairs should have associated embeddings $Y , X$ which have a higher entailment scores $Y \\odot X$ than other pairs. We rank the word pairs by the entailment scores for their embeddings, and evaluate this ranked list against the gold hyponymy annotations. We evaluate on hyponymy detection because it reflects a direct form of lexical entailment; the semantic features of a hypernym (e.g. “animal”) should be included in the semantic features of the hyponym (e.g. “cat”). Other forms of lexical entailment would benefit from some kind of reasoning or world knowledge, which we leave to future work on compositional models. ",
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+        "type": "text",
+        "text": "3 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper we propose a distributional semantic model which is based on entailment. Most of the work on modelling entailment with vector space embeddings has simply used distributional semantic vectors within a model of entailment, and is therefore not directly relevant here. See (Shwartz et al., 2017) for a comprehensive review of such measures. Shwartz et al. (2017) evaluate these measures as unsupervised models of hyponymy detection and run experiments on a number of hyponymy datasets. We report their best comparable result in Table 1. ",
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+    {
+        "type": "text",
+        "text": "Vilnis & McCallum (2015) propose an unsupervised model of entailment in a vector space, and evaluate it on hyponymy detection. Instead of representing words as a point in a vector space, they represent words as a Gaussian distribution over points in a vector space. The variance of this distribution in a given dimension indicates the extent to which the dimension’s feature is unknown, so they use KL-divergence to detect hyponymy relations. Although this model has a nice theoretical motivation, the word representations are more complex and training appears to be more computationally expensive than the method proposed here. We empirically compare our models to their hyponymy detection accuracy and find equivalent results. ",
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+        "type": "text",
+        "text": "The semi-supervised model of Kruszewski et al. (2015) learns a discrete Boolean vector space for predicting hyponymy. But they do not propose any unsupervised method for learning these vectors. ",
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+        "type": "text",
+        "text": "Weeds et al. (2014) report hyponymy detection results for a number of unsupervised and semisupervised models. They propose a semi-supervised evaluation methodology where the words in the training and test sets are disjoint, so that the supervised component must learn about the unsupervised vector space and not about the individual words. Following Henderson & Popa (2016), we replicate their experimental setup in our evaluations, for both unsupervised and semi-supervised models, and compare to the best results among the models evaluated by Weeds et al. (2014), Shwartz et al. (2017) and Henderson & Popa (2016). ",
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+    {
+        "type": "text",
+        "text": "4 EVALUATION OF WORD EMBEDDINGS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate on hyponymy detection in both a fully unsupervised setup and a semi-supervised setup. In the semi-supervised setup, we use labelled hyponymy data to train a linear mapping from the unsupervised vector space to a new vector space with the objective of correctly predicting hyponymy relations in the new vector space. This prediction is done with the same (or equivalent) entailment operator as for the unsupervised experiments (called “map $\\bigcirc$ ” in Table 2). ",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 1: Hyponymy detection accuracies $( 5 0 \\% A c c )$ and average precision $( A \\nu e P r e c )$ , in the unsupervised experiments. For the accuracies, \\* marks a significant improvement over the higher rows. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>embeddings</td><td>operator</td><td>50% Acc AvePrec</td></tr><tr><td>Weeds et.al., 2014 Shwartz et.al., 2017</td><td></td><td>58% 1 44.1% 1</td></tr><tr><td>W2V GoogleNews</td><td>u.d.</td><td>64.5%* 1</td></tr><tr><td>W2V CBOW W2H Skip likelihood</td><td>u.d. ② ③</td><td>53.2% 55.2% 59.5% 57.8%</td></tr><tr><td>W2H CBOW] likelihood</td><td>③</td><td>61.8% 66.4%</td></tr><tr><td>W2V Skip</td><td>u.d.</td><td>62.1% 67.6%</td></tr><tr><td>W2H CBOW</td><td>posterior ③</td><td>68.1%* 70.8%</td></tr><tr><td>W2H [Skip</td><td>posterior 国</td><td>69.6% 68.9%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "We replicate the experimental setup of Weeds et al. (2014), using their selection of hyponymhypernym pairs from the BLESS dataset (Baroni & Lenci, 2011), which consists of noun-noun pairs, including $50 \\%$ positive hyponymy pairs plus $50 \\%$ negative pairs consisting of some other hyponymy pairs reversed, some pairs in other semantic relations, and some random pairs. As in (Weeds et al., 2014), our semi-supervised experiments use ten-fold cross validation, where each fold has items removed from the training set if they contain a word that also occurs in the testing set. ",
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+    {
+        "type": "text",
+        "text": "The word embedding vectors which we train have 200 dimensions and were trained using our Word2Hyp modification of the Word2Vec code (with default settings), trained on a corpus of half a billion words of Wikipedia. We also replicate the approach of Henderson & Popa (2016) by training Word2Vec embeddings on this data. ",
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+    {
+        "type": "text",
+        "text": "To quantify performance on hyponymy detection, for each model we rank the list of pairs according to the score given by the model, and report two measures of performance for this ranked lists. The “ $50 \\%$ Acc” measure treats the first half of the list as labelled positive and the second half as labelled negative. This is motivated by the fact that we know a priori that the proportion of positive examples has been artificially set to (approximately) $50 \\%$ . Average precision is a measure of the accuracy for ranked lists, used in Information Retrieval and advocated as a measure of hyponymy detection by Vilnis & McCallum (2015). For each positive example, precision is measured at the threshold just below that example, and these precision scores are averaged over positive examples. For cross validation, we average over the union of positive examples in all the test sets. Both these measures are reported (when available) in Tables 1 and 2. ",
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+    {
+        "type": "text",
+        "text": "4.1 UNSUPERVISED HYPONYMY DETECTION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The first set of experiments evaluate the different embeddings in their unsupervised models of hyponymy detection. Results are shown in Table 1. Our principal point of comparison is the best results from (Henderson & Popa, 2016) (called “W2V GoogleNews” in Table 1). They use the preexisting publicly available GoogleNews word embeddings, which were trained with the Word2Vec software on 100 billion words of the GoogleNews dataset, and have 300 dimensions. To provide a more direct comparison, we replicate the model of Henderson & Popa (2016) but using the same embedding training setup as for our Word2Hyp model (“W2V Skip”). Both cases use their proposed reinterpretation of these vectors for predicting entailment $( ^ { 6 } u . d . \\odot ^ { 7 } )$ . We also report the best results from Weeds et al. (2014) and the best comparable results from (Shwartz et al., 2017). For our proposed Word2Hyp distributional semantic models (“W2H”), we report results for the four combinations of using the CBOW or Skipgram (“Skip”) model to train the likelihood or posterior vectors. ",
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+    {
+        "type": "text",
+        "text": "The two Word2Hyp models with likelihood vectors perform slightly better than the best unsupervised model of Weeds et al. (2014), but similarly. The reinterpretation of Word2Vec vectors (“W2V GoogleNews $u . d . \\odot ^ { \\ ' } )$ ) performs significantly better, but when the same method is applied to the smaller Wikipedia corpus (“W2V Skip $u . d . \\odot ^ { \\ ' } ,$ ), this difference all but disappears. This confirms the hypothesis of Henderson & Popa (2016) that the reinterpretation of Word2Vec vectors and the likelihood vectors from Word2Hyp are approximately equivalent. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8bc30d327f101808f952c562934f73f7a80dcc4f52606630d9c6d96a70ceb4ef.jpg",
+        "table_caption": [
+            "Table 2: Hyponymy detection accuracies $50 \\%$ Acc) and average precision (Ave Prec), in the semisupervised experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=2>embeddings     operator</td><td rowspan=1 colspan=1>50% AccAvePrec</td></tr><tr><td rowspan=1 colspan=2>Weeds et.al., 2014</td><td rowspan=1 colspan=1>75%    1</td></tr><tr><td rowspan=1 colspan=2>W2VGoogleNews    map①</td><td rowspan=1 colspan=1>80.1%  1</td></tr><tr><td rowspan=2 colspan=2>W2VSkip             map③W2H【CBOW】/ likelihoodmap②W2VCBOW           map②W2HSkip likelihoodmap①W2HSkip  posteriormap③W2HCBOW posteriormap③</td><td rowspan=2 colspan=1>81.9%  88.3%83.3% 90.3%84.6%  91.5%84.8%  90.9%85.5% 91.3%86.0% 92.8%</td></tr><tr><td rowspan=1 colspan=1>map②map①</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "However, even with this smaller corpus, using the proposed posterior vectors from the Word2Hyp model are significantly more accurate than the reinterpretation of Word2Vec vectors. This confirms the hypothesis that the posterior vectors from the Word2Hyp model are a better model of the semantics of a word than the likelihood vectors suggested by Henderson & Popa (2016). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Using the CBOW model or the Skipgram model makes only a small difference. The average precision score shows the same pattern as the accuracy. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To allow a direct comparison to the model of Vilnis & McCallum (2015), we also evaluated the unsupervised models on the hyponymy data from (Baroni et al., 2012), which is not as carefully designed to evaluate hyponymy as the (Weeds et al., 2014) data. Both the likelihood and posterior vectors of the Word2Hyp CBOW model achieved average precision $( 8 1 \\% , 8 0 \\% )$ which is not significantly different from the best model of Vilnis & McCallum (2015) $( 8 0 \\% )$ . ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 SEMI-SUPERVISED HYPONYMY DETECTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The semi-supervised experiments train a linear mapping from each unsupervised vector space to a new vector space, where the entailment operator $\\bigcirc$ is used to predict hyponymy (“map $\\odot ^ { \\prime \\prime }$ ). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The semi-supervised results (shown in Table 2)3 no longer show an advantage of GoogleNews vectors over Wikipedia vectors for the reinterpretation of Word2Vec vectors. And the advantage of posterior vectors over the likelihood vectors is less pronounced. However, the two posterior vectors still perform much better than all the previously proposed models, achieving $86 \\%$ accuracy and nearly $93 \\%$ average precision. These semi-supervised results confirm the results from the unsupervised experiments, that Word2Vec embeddings and Word2Hyp likelihood embeddings perform similarly, but that using the posterior vectors of the Word2Hyp model perform better. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.3 TRAINING TIMES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Because the similarity measure in equation 5 is more complex than a simple dot product, training a new distributional semantic model is slower than with the original Word2Vec code. In our experiments, training took about 8 times longer for the CBOW model and about 15 times longer for the Skipgram model. This meant that Word2Hyp CBOW trained about 8 times faster than Word2Hyp Skipgram. As in the Word2Vec code, we used a quadrature approximation (i.e. a look-up table) to speed up the computation of the sigmoid function, and we added the same technique for computing the log-sigmoid function. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.4 DISCUSSION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The relative success of our distributional semantic models at unsupervised hyponymy detection indicates that they are capturing some aspects of lexical entailment. But the gap between the unsupervised and semi-supervised results indicates that other features are also being captured. This is not surprising, since many other factors influence the co-occurrence statistics of words. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ebb097a5d716bb6a6612d79a5f548b61e7e187a599106981ddb46c2e088071da.jpg",
+        "table_caption": [
+            "Table 3: Ranking of the abstractness $( \\mathbf { 0 } \\otimes X )$ of frequent words from the hyponymy dataset, using Word2Hyp-Skipgram-posterior embeddings. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">most abstract</td><td colspan=\"2\">least abstract</td></tr><tr><td>something</td><td>necessity</td><td></td><td>fork</td></tr><tr><td>anything</td><td>sense</td><td>hockey</td><td>&#x27;housing</td></tr><tr><td>end</td><td>back</td><td>republican</td><td>elm</td></tr><tr><td>inside</td><td>saw</td><td>hull</td><td>primate</td></tr><tr><td>good</td><td>：</td><td>cricket</td><td>fur</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To get a better understanding of these word embeddings, we ranked them by degree of abstractness. Table 3 shows the most abstract and least abstract frequent words that occur in the hyponymy data. To measure abstractness, we used our best unsupervised embeddings and measured how well they are entailed by the zero log-odds vector, which represents a uniform half probability of knowing each feature. For a vector to be entailed by the zero vector, it must be that its features are mostly probably unknown. The less you know given a word, the more abstract it is. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "An initial ranking found that six of the top ten abstract words had frequency less than 300 in the Wikipedia data, but none of the ten least abstract terms were infrequent. This indicates a problem with the current method, since infrequent words are generally very specific (as was the case for these low-frequency words, submissiveness, implementer, overdraft, ruminant, warplane, and londoner). Although this is an interesting characteristic of the method, the terms themselves seem to be noise, so we rank only terms with frequency greater than 300. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The most abstract terms in table 3 include some clearly semantically abstract terms, in particular something and anything are ranked highest. Others may be affected by lexical ambiguity, since the model does not disambiguate words by part-of-speech (such as end, good, sense, back, and saw). The least abstract terms are mostly very semantically specific, but it is indicative that this list includes primate, which is an abstract term in Zoology but presumably occurs in very specific contexts in Wikipedia. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose unsupervised methods for efficiently training word embeddings which capture semantic entailment. This work builds on the work of Henderson & Popa (2016), who propose the entailment-vectors framework for modelling entailment in a vector-space, and a distributional semantic model for reinterpreting Word2Vec word embeddings. Our contribution differs from theirs in that we provide a better understanding of their distributional semantic model, we choose different vectors in the model to use as word embeddings, and we train new word embeddings using our modification of the Word2Vec code. Empirical results on unsupervised and semi-supervised hyponymy detection confirm that the model’s likelihood vectors, which Henderson & Popa (2016) suggest to use, do indeed perform equivalently to their reinterpretation of Word2Vec vectors. But these experiments also show that the model’s posterior vectors, which we propose to use, perform significantly better, outperforming all previous results on this benchmark dataset. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The success of these unsupervised models demonstrates that the proposed distributional semantic models are effective at extracting information about lexical entailment from the redundancy and consistency of words with their contexts in large text corpora. The use of the entailment-vectors framework to efficiently model entailment relations has been crucial to this success. This result suggests future work using the entailment-vectors framework in unsupervised models that leverage other distributional evidence about semantics, particularly in models of compositional semantics. The merger of word embeddings with compositional semantics to get representation learning for larger units of text is currently an important challenge in the semantics of natural language, and the work presented in this paper makes a significant contribution towards solving it. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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parse/train/SJHRf5nW93/SJHRf5nW93.md

@@ -0,0 +1,291 @@
+# Subgraph Federated Learning with Missing Neighbor Generation
+
+Ke Zhang1,4, Carl Yang1∗, Xiaoxiao $\mathbf { L i } ^ { 2 }$ , Lichao $\mathbf { S u n ^ { 3 } }$ , Siu Ming $\mathbf { Y i u ^ { 4 } }$
+
+1Emory University, 2University of British Columbia, 3Lehigh University, 4University of Hong Kon kzhang2@cs.hku.hk, j.carlyang@emory.edu, xiaoxiao.li@ece.ubc.ca, lis221@lehigh.edu, smyiu@cs.hku.hk
+
+# Abstract
+
+Graphs have been widely used in data mining and machine learning due to their unique representation of real-world objects and their interactions. As graphs are getting bigger and bigger nowadays, it is common to see their subgraphs separately collected and stored in multiple local systems. Therefore, it is natural to consider the subgraph federated learning setting, where each local system holds a small subgraph that may be biased from the distribution of the whole graph. Hence, the subgraph federated learning aims to collaboratively train a powerful and generalizable graph mining model without directly sharing their graph data. In this work, towards the novel yet realistic setting of subgraph federated learning, we propose two major techniques: (1) FedSage, which trains a GraphSage model based on FedAvg to integrate node features, link structures, and task labels on multiple local subgraphs; (2) FedSage+, which trains a missing neighbor generator along FedSage to deal with missing links across local subgraphs. Empirical results on four real-world graph datasets with synthesized subgraph federated learning settings demonstrate the effectiveness and efficiency of our proposed techniques. At the same time, consistent theoretical implications are made towards their generalization ability on the global graphs.
+
+# 1 Introduction
+
+Graph mining leverages links among connected nodes in graphs to conduct inference. Recently, graph neural networks (GNNs) have gained applause with impressing performance and generalizability in many graph mining tasks [29, 11, 16, 20, 32]. Similar to machine learning tasks in other domains, attaining a well-performed GNN model requires its training data to not only be sufficient but also follow the similar distribution as general queries. While in reality, data owners often collect limited and biased graphs and cannot observe the global distribution. With heterogeneous subgraphs separately stored in local data owners, accomplishing a globally applicable GNN requires collaboration.
+
+Federated learning (FL) [17, 35], targeting at training machine learning models with data distributed in multiple local systems to resolve the information-silo problem, has shown its advantage in enhancing the performance and generalizability of the collaboratively trained models without the need of sharing any actual data. For example, FL has been devised in computer vision (CV) and natural language processing (NLP) to allow the joint training of powerful and generalizable deep convolutional neural networks and language models on separately stored datasets of images and texts [19, 6, 18, 39, 13].
+
+Motivating Scenario. Taking the healthcare system as an example, as shown in Fig. 1, residents of a city may go to different hospitals for various reasons. As a result, their healthcare data, such as demographics and living conditions, as well as patient interactions, such as co-staying in a sickroom and co-diagnosis of a disease, are stored only within the hospitals they visit. When any healthcare problem is to be studied in the whole city, e.g., the prediction of infections when a pandemic occurs, a single powerful graph mining model is needed to conduct effective inference over the entire global patient network, which contains all subgraphs from different hospitals. However, it is rather difficult to let all hospitals share their patient networks with others to train the graph mining model due to conflicts of interests and privacy concerns.
+
+![](images/3db6f8e262d5f8e6077596e2a5ad0ce466e2079af4e964e11006ec52d9f282f4.jpg)  
+Figure 1: A toy example of the distributed subgraph storage system: In this example, there are four hospitals and a medical administration center. The global graph records, for a certain period, the city’s patients (nodes), their information (attributes), and interactions (links). Specifically, the left part of the figure shows how the global graph is stored in each hospital, where the grey solid lines are the links explicitly stored in each hospital, and the red dashed lines are the cross-hospital links that may exist but are not stored in any hospital. The right part of the figure indicates our goal that without sharing actual data, the system obtains a globally powerful graph mining model.
+
+In such scenarios, it is desirable to train a powerful and generalizable graph mining model over multiple distributed subgraphs without actual data sharing. However, this novel yet realistic setting brings two unique technical challenges, which have never been explored so far.
+
+Challenge 1: How to jointly learn from multiple local subgraphs? In our considered scenario, the global graph is distributed into a set of small subgraphs with heterogeneous feature and structure distributions. Training a separate graph mining model on each subgraph may not capture the global data distribution and is also prone to overfitting. Moreover, it is unclear how to integrate multiple graph mining models into a universally applicable one that can handle any queries from the underlying global graph.
+
+Solution 1: FedSage: Training GraphSage with FedAvg. To attain a powerful and generalizable graph mining model from small and biased subgraphs distributed in multiple local owners, we develop a framework of subgraph federated learning, specifically, with the vanilla mechanism of FedAvg [21]. As for the graph mining model, we resort to GraphSage [11], due to its advantages of inductiveness and scalability. We term this framework as FedSage.
+
+Challenge 2: How to deal with missing links across local subgraphs? Unlike distributed systems in other domains such as CV and NLP, whose data samples of images and texts are isolated and independent, data samples in graphs are connected and correlated. Most importantly, in a subgraph federated learning system, data samples in each subgraph can potentially have connections to those in other subgraphs. These connections carrying important information of node neighborhoods and serving as bridges among the data owners, however, are never directly captured by any data owner.
+
+Solution 2: FedSage+: Generating missing neighbors along FedSage. To deal with crosssubgraph missing links, we add a missing neighbor generator on top of FedSage and propose a novel FedSage+ model. Specifically, for each data owner, instead of training the GraphSage model on the original subgraph, it first mends the subgraph with generated cross-subgraph missing neighbors and then applies FedSage on the mended subgraph. To obtain the missing neighbor generator, each data owner impairs the subgraph by randomly holding out some nodes and related links and then trains the generator based on the held-out neighbors. Training the generator on an individual local subgraph enables it to generate potential missing links within the subgraph. Further training the generator in our subgraph FL setting allows it to generate missing neighbors across distributed subgraphs.
+
+We conduct experiments on four real-world datasets with different numbers of data owners to better simulate the application scenarios. According to our results, both of our models outperform locally trained classifiers in all scenarios. Compared to FedSage, FedSage+ further promotes the performance of the outcome classifier. Further in-depth model analysis shows the convergence and generalization ability of our frameworks, which is corroborated by our theoretical analysis in the end.
+
+# 2 Related works
+
+Graph mining. Graph mining emerges its significance in analyzing the informative graph data, which range from social networks to gene interaction networks [31, 33, 34, 24]. One of the most frequently applied tasks on graph data is node classification. Recently, graph neural networks (GNNs), e.g., graph convolutional networks (GCN) [16] and GraphSage [11], improved the state-of-the-art in node classification with their elegant yet powerful designs. However, as GNNs leverage the homophily of nodes in both node features and link structures to conduct the inference, they are vulnerable to the perturbation on graphs [4, 40, 41]. Robust GNNs, aiming at reducing the degeneration in GNNs caused by graph perturbation, are gaining attention these days. Current robust GNNs focus on the sensitivity towards modifications on node features [3, 42, 15] or adding/removing edges on the graph [37]. However, neither of these two types recapitulates the missing neighbor problem, which affects both the feature distribution and structure distribution.
+
+To obtain a node classifier with good generalizability, the development of domain adaptive GNN sheds light on adapting a GNN model trained on the source domain to the target domain by leveraging underlying structural consistency [38, 36, 28]. However, in the distributed system we consider, data owners have subgraphs with heterogeneous feature and structure distributions. Moreover, direct information exchanges among subgraphs, such as message passing, are fully blocked due to the missing cross-subgraph links. The violation of the domain adaptive GNNs’ assumptions on alignable nodes and cross-domain structural consistency denies their usage in the distributed subgraph system.
+
+Federated learning. FL is proposed for cross-institutional collaborative learning without sharing raw data [17, 35, 21]. FedAvg [21] is an efficient and well-studied FL method. Similar to most FL methods, it is originally proposed for traditional machine learning problems [35] to allow collaborative training on silo data through local updating and global aggregation. The ecently proposed meta-learning framework [9, 23, 14] that exploits information from different data sources to obtain a general model attracts FL researchers [8]. However, meta-learning aims to learn general models that easily adapt to different local tasks, while we learn a generalizable model from diverse data owners to assist in solving a global task. In the distributed subgraph system, to obtain a globally applicable model without sharing local graph data, we borrow the idea of FL to collaboratively train GNNs.
+
+Federated graph learning. Recent researchers have made some progress in federated graph learning. There are existing FL frameworks designed for the graph data learning task [12, 27, 30]. [12] design graph-level FL schemes with graph datasets dispersed over multiple data owners, which are inapplicable to our distributed subgraph system construction. [27] proposes an FL method for the recommendation problem with each data owner learning on a subgraph of the whole recommendation user-item graph. It considers a different scenario assuming subgraphs have overlapped items (nodes), and the user-item interactions (edges) are distributed but completely stored in the system, which ignores the possible cross-subgraph information lost in real-world scenarios. However, we study a more challenging yet realistic case in the distributed subgraph system, where cross-subgraph edges are totally missing.
+
+In this work, we consider the commonly existing yet not studied scenario, i.e., distributed subgraph system with missing cross-subgraph edges. Under this scenario, we focus on obtaining a globally applicable node classifier through FL on distributed subgraphs.
+
+# 3 FedSage
+
+In this section, we first illustrate the definition of the distributed subgraph system derived from real-world application scenarios. Based on this system, we then formulate our novel subgraph FL framework and a vanilla solution called FedSage.
+
+# 3.1 Subgraphs Distributed in Local Systems
+
+Notation. We denote a global graph as $G = \{ V , E , X \}$ , where $V$ is the node set, $X$ is the respective node feature set, and $E$ is the edge set. In the FL system, we have the central server $S$ , and $M$ data owners with distributed subgraphs. $G _ { i } = \{ V _ { i } , E _ { i } , X _ { i } \}$ is the subgraph owned by $D _ { i }$ , for $i \in [ M ]$ .
+
+Problem setup. For the whole system, we assume $V = V _ { 1 } \cup \cdots \cup V _ { M }$ . To simulate the scenario with most missing links, we assume no overlapping nodes shared across data owners, namely $V _ { i } \cap V _ { j } = \emptyset$ for $\forall i , j \in [ M ]$ and $i \neq j$ . Note that the central server $S$ only maintains a graph mining model with no actual graph data stored. Any data owner $D _ { i }$ cannot directly retrieve $u \in V _ { j }$ from another data owner $D _ { j }$ . Therefore, for an edge $e _ { v , u } \in E$ , where $v \in V _ { i }$ and $u \in V _ { j }$ , $e _ { v , u } \notin E _ { i } \cup E _ { j }$ , that is, $e _ { v , u }$ might exist in reality but is not stored anywhere in the whole system.
+
+For the global graph $G = \{ V , E , X \}$ , every node $v \in V$ has its features $x _ { v } \in X$ and one label $y _ { v } \in Y$ for the downstream task, e.g., node classification. Note that for $v \in V$ , $v$ ’s feature $x _ { v } \in \mathbb { R } ^ { d _ { x } }$ and respective label $y _ { v }$ is a $d _ { y }$ -dimensional one-hot vector. In a typical GNN, predicting a node’s label requires an ego-graph of the queried node. For a node $v$ from graph $G$ , we denote the queried ego-graph of $v$ as $G ( v )$ , and $( G ( v ) , y _ { v } ) \sim \mathcal { D } _ { G }$ .
+
+With subgraphs distributed in the system defined above, we formulate our goal as follows.
+
+Goal. The system exploits an $\mathrm { F L }$ framework to collaboratively learn on isolated subgraphs in all data owners, without raw graph data sharing, to obtain a global node classifier $F$ . The learnable weights $\phi$ in $F$ is optimized for queried ego-graphs following the distribution of ones drawn from the global graph $G$ . We formalize the problem as finding $\phi ^ { * }$ that minimizes the aggregated risk
+
+$$
+\boldsymbol { \phi } ^ { * } = \arg \operatorname* { m i n } _ { \mathbf { \phi } } \mathcal { R } ( \boldsymbol { F } ( \boldsymbol { \phi } ) ) = \frac { 1 } { M } \sum _ { i } ^ { M } \mathcal { R } _ { i } ( F _ { i } ( \boldsymbol { \phi } ) ) ) ,
+$$
+
+where $\mathcal { R } _ { i }$ is the local empirical risk defined as
+
+$$
+\begin{array} { r } { \mathcal { R } _ { i } \big ( F _ { i } ( \phi ) \big ) : = \mathbb { E } _ { ( G _ { i } , Y _ { i } ) \sim \mathcal { D } _ { G _ { i } } } [ \ell ( F _ { i } ( \phi ; G _ { i } ) , Y _ { i } ) ) ] , } \end{array}
+$$
+
+where $\ell$ is a task-specific loss function
+
+$$
+\ell : = \frac { 1 } { | V _ { i } | } \sum _ { v \in V _ { i } } l ( \phi ; G _ { i } ( v ) , y _ { v } ) .
+$$
+
+# 3.2 Collaborative Learning on Isolated Subgraphs
+
+To fulfill the system’s goal illustrated above, we leverage the simple and efficient FedAvg framework [21] and fix the node classifier $F$ as a GraphSage model. The inductiveness and scalability of the GraphSage model facilitate both the training on diverse subgraphs with heterogeneous query distributions and the later inference upon the global graph. We term the GraphSage model trained with the FedAvg framework as FedSage.
+
+r a queried node -hop neighborho $v \in V$ , a glraph ally shared  to conduct $K$ -layer GraphSage classifier ediction with learnable par $F$ integeters $v$ $K$ $G$ $\phi = \{ \phi ^ { k } \} _ { k = 1 } ^ { K }$ Taking a subgraph $G _ { i }$ as an example, for $v \in V _ { i }$ with features as $h _ { v } ^ { 0 } = x _ { v }$ , at each layer $k \in [ K ]$ , $F$ computes $v$ ’s representation $h _ { v } ^ { k }$ as
+
+$$
+h _ { v } ^ { k } = \sigma \left( \phi ^ { k } \cdot \left( h _ { v } ^ { k - 1 } | | A g g \left( \left\{ h _ { u } ^ { k - 1 } , \forall u \in \mathcal { N } _ { G _ { i } } ( v ) \right\} \right) \right) \right) ,
+$$
+
+where $\mathcal { N } _ { G _ { i } } ( v )$ is the set of $v$ ’s neighbors on graph $G _ { i } , | |$ is the concatenation operation, $A g g ( \cdot )$ is the aggregator (e.g., mean pooling) and $\sigma$ is the activation function (e.g., ReLU).
+
+With $F$ outputting the inference label $\widetilde { y } _ { v } = \mathrm { S o f t m a x } ( h _ { v } ^ { K } )$ for $v \in V _ { i }$ , the supervised loss function $l ( \phi | \cdot )$ is defined as follows
+
+$$
+\mathcal { L } ^ { c } = l ( \phi | G _ { i } ( v ) , y _ { v } ) = C E ( \widetilde { y } _ { v } , y _ { v } ) = - \left[ y _ { v } \log \widetilde { y } _ { v } + ( 1 - y _ { v } ) \log \left( 1 - \widetilde { y } _ { v } \right) \right] ,
+$$
+
+where $C E ( \cdot )$ is the cross entropy function, $G _ { i } ( v )$ is $v$ ’s K-hop ego-graph on $G _ { i }$ , which contains the information of $v$ and its K-hop neighbors on $G _ { i }$ .
+
+In FedSage, the distributed subgraph system obtains a shared global node classifier $F$ parameterized by $\phi$ through $e _ { c }$ epochs of training. During each epoch $t$ , every $D _ { i }$ first locally computes $\phi _ { i } \gets$ $\phi - \eta \nabla \ell ( \phi | \{ ( G _ { i } ( v ) , y _ { v } ) | v \in V _ { i } ^ { t } \} )$ , where $V _ { i } ^ { t } \subseteq V _ { i }$ contains the sampled training nodes for epoch $t$ , and $\eta$ is the learning rate; then the central server $S$ collects the latest $\{ \phi _ { i } | i \in [ \bar { M } ] \}$ ; next, through averaging over $\{ \phi _ { i } | \bar { i } \in [ M ] \}$ , $S$ sets $\phi$ as the averaged value; finally, $S$ broadcasts $\phi$ to data owners and finishes one round of training $F$ . After $e _ { c }$ epochs, the entire system retrieves $F$ as the outcome global classifier, which is not limited to or biased towards the queries in any specific data owner.
+
+Unlike FL on Euclidean data, nodes in the distributed subgraph system can have potential interactions with each other across subgraphs. However, as the cross-subgraph links cannot be captured by any data owner in the system, incomplete neighborhoods, compared to those on the global graph, commonly exist therein. Thus, directly aggregating incomplete queried ego-graph information through FedSage restricts the outcome $F$ from achieving the desideratum of capturing the global query distribution.
+
+![](images/3bcb77490b0c2ae8e863682998c4fd95fb5f8ae6d294a9c24fbf42bbce8fcbf8.jpg)  
+Figure 2: Joint training of missing neighbor generation and node classification.
+
+# 4 FedSage+
+
+In this section, we propose a novel framework of FedSage $^ +$ , i.e., subgraph FL with missing neighbor generation. We first design a missing neighbor generator (NeighGen) and its training schema via graph mending. Then, we describe the joint training of NeighGen and GraphSage to better achieve the goal in Section 3.1. Without loss of generality, in the following demonstration, we take NeighGeni, i.e., the missing neighbor generator of $D _ { i }$ , as an example, where $i \in [ M ]$ .
+
+# 4.1 Missing Neighbor Generator (NeighGen)
+
+Neural architecture of NeighGen. As shown in Fig. 2, NeighGen consists of two modules, i.e., an encoder $H ^ { e }$ and a generator $H ^ { g }$ . We describe their designs in details in the following.
+
+$H ^ { e }$ : A GNN model, i.e., a K-layer GraphSage encoder, with parameters $\theta ^ { e }$ . For node $v \in V _ { i }$ on the input graph $G _ { i }$ , $H ^ { e }$ computes node embeddings $Z _ { i } = \{ z _ { v } | z _ { v } \stackrel { \cdot } { = } h _ { v } ^ { K } , z _ { v } \in \mathbb { R } ^ { d _ { z } } , v \in V _ { i } \}$ according to Eq. (1) by substituting $\phi$ , $G$ with $\theta ^ { e }$ and $G _ { i }$ .
+
+$H ^ { g }$ : A generative model recovering missing neighbors for the input graph based on the node embedding. $H ^ { g }$ contains dGen and fGen, where dGen is a linear regression model parameterized by $\theta ^ { d }$ that predicts the numbers of missing neighbors $\widetilde { N } _ { i } = \{ \widetilde { n } _ { v } | \widetilde { n } _ { v } \in \mathbb { N } , v \in V _ { i } \}$ , and fGen is a feature generator parameterized by $\theta ^ { f }$ that generates a set of $\widetilde { N } _ { i }$ feature vectors $\widetilde { X } _ { i } = \{ \widetilde { x } _ { v } | \widetilde { x } _ { v } \in$ $\mathbb { R } ^ { \widetilde { n } _ { v } \times d _ { x } } , \widetilde { n } _ { v } \in \widetilde { N } _ { i } , v \in V _ { i } \}$ e e. Both dGen and fGen are constructed as fully connected neural networks e(FNNs), while fGen is further equipped with a Gaussian noise generator $\mathbf { N } ( 0 , 1 )$ that generates $d _ { z }$ -dimensional noise vectors and a random sampler $R$ . For node $v \in V _ { i }$ , fGen is variational, which generates the missing neighbors’ features for $v$ after inserting noises into the embedding $z _ { v }$ , while $R$ ensures fGen to output the features of a specific number of neighbors by sampling $\widetilde { n } _ { v }$ feature vectors from the feature generator’s output. Mathematically, we have
+
+$$
+\widetilde { n } _ { v } = \sigma ( ( { \boldsymbol { \theta } } ^ { d } ) ^ { T } \cdot { \boldsymbol { n } } _ { v } ) , \operatorname { a n d } \widetilde { x } _ { v } = R \left( \sigma \left( ( { \boldsymbol { \theta } } ^ { f } ) ^ { T } \cdot ( z _ { v } + \mathbf { N } ( 0 , 1 ) ) \right) , \widetilde { { \boldsymbol { n } } } _ { v } \right) .
+$$
+
+Graph mending simulation. For each data owner in our system, we assume that only a particular set of nodes have cross-subgraph missing neighbors. The assumption is realistic yet non-trivial for it both seizing the quiddity of the distributed subgraph system, and allowing us to locally simulate the missing neighbor situation through a graph impairing and mending process. Specifically, to simulate a graph mending process during the training of NeighGen, in each local subgraph $G _ { i }$ , we randomly hold out $h \%$ of its nodes $V _ { i } ^ { h } \subset V _ { i }$ and all links involving them $E _ { i _ { - } } ^ { h } = \{ e _ { u v } | u \stackrel { - } { \in } \bar { V } _ { i } ^ { h }$ or $v \in V _ { i } ^ { h } \} \subset \mathsf { \bar { E } } _ { i }$ , to form an impaired subgraph, denoted as $\bar { G } _ { i }$ . $\bar { G } _ { i } = \mathsf { \bar { \{ V } }  _ { i } , \bar { E } _ { i } , \bar { X } _ { i } \}$ contains the impaired set of nodes $\bar { V } _ { i } = V _ { i } \setminus V _ { i } ^ { h }$ , the corresponding nodes features ${ \bar { X } } _ { i } = X _ { i } \setminus X _ { i } ^ { h }$ and edges $\bar { E } _ { i } = E _ { i } \setminus E _ { i } ^ { h }$ .
+
+Accordingly, based on the ground-truth missing nodes $V _ { i } ^ { h }$ and links $E _ { i } ^ { h }$ , the training of NeighGen on the impaired graph $\bar { G } _ { i }$ boils down to jointly training dGen and fGen as below.
+
+$$
+\mathcal { L } ^ { n } = \lambda ^ { d } \mathcal { L } ^ { d } + \lambda ^ { f } \mathcal { L } ^ { f } = \lambda ^ { d } \frac { 1 } { | \bar { V } _ { i } | } \sum _ { v \in \bar { V } _ { i } } L _ { 1 } ^ { S } \big ( \widetilde { n } _ { v } - n _ { v } \big ) + \lambda ^ { f } \frac { 1 } { | \bar { V } _ { i } | } \sum _ { v \in \bar { V } _ { i } } \sum _ { p \in \{ \widetilde { n } _ { v } \} } \operatorname* { m i n } _ { u \in \mathcal { N } _ { G _ { i } } ( v ) \cap V _ { i } ^ { h } } ( | | \widetilde { x } _ { v } ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) ,
+$$
+
+where $L _ { 1 } ^ { S }$ is the smooth L1 distance [10] and $\mathcal { \widetilde { x } } _ { v } ^ { p } \in \mathbb { R } ^ { d _ { x } }$ is the $p$ -th predicted feature in $\widetilde { x } _ { v }$ . Note that, $\mathcal { N } _ { G _ { i } } ( v ) \cap V _ { i } ^ { h }$ contains $n _ { v }$ nodes that are $v$ e’s neighbors on $G _ { i }$ missing into $V _ { i } ^ { h }$ . $\mathcal { N } _ { G _ { i } } ( v ) \cap V _ { i } ^ { h }$ , which can be retrieved from $V _ { i } ^ { h }$ and $E _ { i } ^ { h }$ , provides ground-truth for training NeighGen.
+
+Neighbor Generation. To retrieve $G _ { i } ^ { \prime }$ from $G _ { i }$ , data owner $D _ { i }$ performs two steps, which are also shown in Fig. 2: 1) $D _ { i }$ trains NeighGen on the impaired graph $\bar { G } _ { i }$ w.r.t. the ground-true hidden neighbors ${ \bar { V } } _ { i } ^ { \breve { h } }$ ; 2) $D _ { i }$ exploits NeighGen to generate missing neighbors for nodes on $G _ { i }$ and then mends $G _ { i }$ into $G _ { i } ^ { \prime }$ with generated neighbors. On the local graph $G _ { i }$ alone, this process can be understood as a data augmentation that further generates potential missing neighbors within $G _ { i }$ . However, the actual goal is to allow NeighGen to generate the cross-subgraph missing neighbors, which can be achieved via training NeighGen with FL and will be discussed in Section 4.3.
+
+# 4.2 Local Joint Training of GraphSage and NeighGen
+
+While NeighGen is designed to recover missing neighbors, the final goal of our system is to train a node classifier. Therefore, we design the joint training of GraphSage and NeighGen, which leverages neighbors generated by NeighGen to assist the node classification by GraphSage. We term the integration of GraphSage and NeighGen on the local graphs as LocSage+.
+
+After NeighGen mends the graph $G _ { i }$ into $G _ { i } ^ { \prime }$ , the GraphSage classifier $F$ is applied on $G _ { i } ^ { \prime }$ , according to Eq. (1) (with $G _ { i }$ replaced by $G _ { i } ^ { \prime }$ ). Thus, the joint training of NeighGen and GraphSage is done by optimizing the following loss function
+
+$$
+\mathcal { L } = \mathcal { L } ^ { n } + \lambda ^ { c } \mathcal { L } ^ { c } = \lambda ^ { d } \mathcal { L } ^ { d } + \lambda ^ { f } \mathcal { L } ^ { f } + \lambda ^ { c } \mathcal { L } ^ { c } ,
+$$
+
+where ${ \mathcal { L } } ^ { d }$ and $\mathcal { L } ^ { f }$ are defined in Eq. (4), and $\mathcal { L } ^ { c }$ is defined in Eq. (2) (with $G _ { i }$ substituted by $G _ { i } ^ { \prime }$
+
+The local joint training of GraphSage and NeighGen allows NeighGen to generate missing neighbors in the local graph that are helpful for the classifications made by GraphSage. However, like GraphSage, the information encoded in the local NeighGen is limited to and biased towards the local graph, which does not enable it to really generate neighbors belonging to other data owners connected by the missing cross-subgraph links. To this end, it is natural to train NeighGen with $\mathrm { F L }$ as well.
+
+# 4.3 Federated Learning of GraphSage and NeighGen
+
+Similarly to GraphSage alone, as described in Section 3.2, we can apply FedAvg to the joint training of GraphSage and NeighGen, by setting the loss function to $\mathcal { L }$ and learnable parameters to $\{ \theta ^ { e } , \theta ^ { d } , \theta ^ { f } , \phi \}$ . However, we observe that cooperation through directly averaging weights of NeighGen across the system can negatively affect its performance, i.e., averaging the weights of a single NeighGen model does not really allow it to generate diverse neighbors from different subgraphs. Recalling our goal of constructing NeighGen, which is to facilitate the training of a centralized GraphSage classifier by generating diverse missing neighbors in each subgraph, we do not necessarily need a centralized NeighGen. Therefore, instead of training a single centralized NeighGen, we train a local NeighGeni for each data owner $D _ { i }$ . In order to allow each NeighGeni to generate diverse neighbors similar to those missed into other subgraphs $G _ { j } , j \in [ M ] \backslash \{ i \}$ , we add a cross-subgraph feature reconstruction loss into $\mathrm { f G e n } _ { i }$ as follows:
+
+$$
+\mathcal { L } _ { i } ^ { f } = \frac { 1 } { \lvert \overline { { V _ { i } } } \rvert } \sum _ { v \in \bar { V } _ { i } } \sum _ { p \in [ \tilde { n } _ { v } ] } \left( \operatorname* { m i n } _ { u \in N _ { G _ { i } } ( v ) \cap V _ { i } ^ { h } } ( \lvert | \widetilde { x } _ { v } ^ { p } - x _ { u } \rvert | _ { 2 } ^ { 2 } ) + \alpha \sum _ { j \in [ M ] / i } \operatorname* { m i n } _ { u \in V _ { j } } ( \lvert | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } \rvert | _ { 2 } ^ { 2 } ) \right) ,
+$$
+
+where $u \in V _ { j } , \forall j \in [ M ] \setminus \{ i \}$ is picked as the closest node from $G _ { j }$ other than $G _ { i }$ to simulate the neighbor of $v \in { \bar { V } } _ { i }$ missed into $G _ { j }$ .
+
+As shown above, to optimize Eq. (6), $D _ { i }$ needs to pick the closest $u$ from $G _ { j }$ . However, directly transmitting node features $X _ { j }$ in $D _ { j }$ to $D _ { i }$ not only violates our subgraph FL system constraints on no direct data sharing but also is impractical in reality, as it requires each $D _ { i }$ to hold the entire global graph’s node features throughout training ${ \mathrm { N e i g h G e n } } _ { i }$ . Therefore, to allow $D _ { i }$ to update ${ \mathrm { N e i g h G e n } } _ { i }$ using Eq. (6) without direct access to $X _ { j }$ , for $v \in { \bar { V } } _ { i }$ , $D _ { j }$ locally computes $\begin{array} { r } { \sum _ { p \in [ \widetilde { n } _ { v } ] } \operatorname* { m i n } _ { u \in V _ { j } } ( | | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) } \end{array}$ and sends the respective gradient back to $D _ { i }$ .
+
+During this process, for $v \in \bar { V } _ { i }$ , to federated optimize Eq. (6), only $H _ { i } ^ { g }$ , $H _ { i } ^ { g }$ ’s input $z _ { v }$ , and the $D _ { j }$ ’s locally computed model gradients of loss term $\begin{array} { r } { \sum _ { p \in [ \tilde { n } _ { v } ] } \operatorname* { m i n } _ { u \in V _ { j } } ( | | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) } \end{array}$ are transmitted among the system via the server $S$ e. For data owner $D _ { i }$ , the gradients received from $D _ { j }$ are then weighted by $\alpha$ and combined with the local gradients as in Eq. (6) to update the parameters of $H _ { i } ^ { g }$ of NeighGeni In this way, $D _ { i }$ achieves the federate training of ${ \mathrm { N e i g h G e n } } _ { i }$ without raw graph data sharing. Note that, due to NeighGen’s architecture of a concatenation of $H ^ { e }$ and $H ^ { g }$ , the locally preserved GNN $H _ { i } ^ { e }$ can prevent other data owners from inferring $x _ { v }$ by only seeing $z _ { v }$ . Through Eq. (6), NeighGen $_ { \cdot i }$ is expected to perceive diverse neighborhood information from all data owners, so as to generate more realistic cross-subgraph missing neighbors. The expectedly diverse and unbiased neighbors further assist the FedSage in training a globally applicable classifier that satisfies our goal in Section 3.1.
+
+Note that, to reduce communications and computation time incurred by Eq. (6), batch training can be applied. Appendix A shows the pseudo code of FedSage+.
+
+# 5 Experiments
+
+We conduct experiments on four datasets to verify the effectiveness of FedSage and FedSage+ under different testing scenarios. We further conduct case studies to visualize how FedSage and FedSage+ assist local data owners in accommodating queries from the global distribution. Finally, we also provide more in-depth studies on the effectiveness of NeighGen in Appendix D.
+
+# 5.1 Datasets and experimental settings
+
+We synthesize the distributed subgraph system with four widely used real-world graph datasets, i.e., Cora [25], Citeseer [25], PubMed [22], and MSAcademic [26]. To synthesize the distributed subgraph system, we find hierarchical graph clusters on each dataset with the Louvain algorithm [2] and use the clustering results with 3, 5, and 10 clusters of similar sizes to obtain subgraphs for data owners. The statistics of these datasets are presented in Table 1.
+
+Table 1: Statistics of the datasets and the synthesized distributed subgraph systems with $M = 3$ , 5, and $1 0 . \# \mathrm { C }$ row shows the number of classes, $| V _ { i } |$ and $| E _ { i } |$ rows show the averaged numbers of nodes and links in all subgraphs, and $\Delta E$ shows the total number of missing cross-subgraph links.   
+
+<table><tr><td>Data</td><td colspan="3">Cora</td><td colspan="3">Citeseer</td><td colspan="3">PubMed</td><td colspan="3">MSAcademic</td></tr><tr><td>#C |V</td><td colspan="3"></td><td colspan="3">6</td><td colspan="3">3</td><td colspan="3">15</td></tr><tr><td></td><td colspan="3"></td><td colspan="3">3312</td><td colspan="3">19717</td><td colspan="3">18333</td></tr><tr><td>|E</td><td colspan="3">5429</td><td colspan="3">4715</td><td colspan="3">44338</td><td colspan="3">81894</td></tr><tr><td>M</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td></tr><tr><td>Vil</td><td>903</td><td>542</td><td>271</td><td>1104</td><td>662</td><td>331</td><td>6572</td><td>3943</td><td>1972</td><td>6111</td><td>3667</td><td>1833</td></tr><tr><td>E</td><td>1675</td><td>968</td><td>450</td><td>1518</td><td>902</td><td>442</td><td>12932</td><td>7630</td><td>3789</td><td>23584</td><td>13949</td><td>5915</td></tr><tr><td>△E</td><td>403</td><td>589</td><td>929</td><td>161</td><td>206</td><td>300</td><td>5543</td><td>6189</td><td>6445</td><td>11141</td><td>12151</td><td>22743</td></tr></table>
+
+We implement GraphSage with two layers using the mean aggregator [5]. The number of nodes sampled in each layer of GraphSage is 5. We use batch size 64 and set training epochs to 50. The training-validation-testing ratio is $6 0 \% - 2 0 \% - 2 0 \%$ due to limited sizes of local subgraphs. Based on our observations in hyper-parameter studies for $\alpha$ and the graph impairing ratio $h$ , we set $h \% \in [ 3 . 4 \% , 2 7 . 8 \% ]$ and $\alpha { = } 1$ . All $\lambda s$ are simply set to 1. Optimization is done with Adam with a learning rate of 0.001. We implement FedSage and FedSage $^ +$ in Python and execute all experiments on a server with 8 NVIDIA GeForce GTX 1080 Ti GPUs.
+
+Since we are the first to study the novel yet important setting of subgraph federated learning, there are no existing baselines. We conduct comprehensive ablation evaluation by comparing FedSage and FedSage+ with three models, i.e., 1) GlobSage: the GraphSage model trained on the original global graph without missing links (as an upper bound for FL framework with GraphSage model alone), 2) LocSage: one GraphSage model trained solely on each subgraph, 3) LocSage+: the GraphSage plus NeighGen model jointly trained solely on each subgraph.
+
+The metric used in our experiments is the node classification accuracy on the queries sampled from the testing nodes on the global graph. For globally shared models of GlobSage, FedSage, and FedSage+, we report the average accuracy over five random repetitions, while for locally possessed models of LocSage and LocSage+, the scores are further averaged across local models.
+
+# 5.2 Experimental results
+
+Overall performance. We conduct comprehensive ablation experiments to verify the significant promotion brought by FedSage and FedSage $^ +$ for local owners in global node classification, as
+
+Table 2: Node classification results on four datasets with $M = 3 , 5$ , and 10. Besides averaged accuracy, we also provide the corresponding std.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Cora</td><td colspan="3">Citesser</td></tr><tr><td>M=3</td><td>M=5</td><td>M=10</td><td>M=3</td><td>M=5</td><td>M=10</td></tr><tr><td>LocSage</td><td>0.5762 (±0.0302)</td><td>0.4431 (±0.0847)</td><td>0.2798 (±0.0080)</td><td>0.6789 (±0.054)</td><td>0.5612 (±0.086)</td><td>0.4240 (±0.0859)</td></tr><tr><td>LocSage+</td><td>0.5644 (±0.0219)</td><td>0.4533 (±0.047)</td><td>0.2851 (±0.0080)</td><td>0.6848 (±0.0517)</td><td>0.5676 (±0.0714)</td><td>0.4323 (±0.0715)</td></tr><tr><td>FedSage</td><td>0.8656 (±0.0043)</td><td>0.8645 (±0.0050)</td><td>0.8626 (±0.0103)</td><td>0.7241 (±0.0022)</td><td>0.7226 ±0.0066)</td><td>0.7158 (±0.0053)</td></tr><tr><td>FedSage+</td><td>0.8686 (±0.0054)</td><td>0.8648 (±0.0051)</td><td>0.8632 (±0.0034)</td><td>0.7454 (±0.0038)</td><td>0.7440 (±0.0025)</td><td>0.7392 (±0.0041)</td></tr><tr><td>GlobSage</td><td colspan="3">0.8701 (±0.0042)</td><td colspan="3">0.7561 (±0.0031)</td></tr><tr><td></td><td colspan="3">PubMed</td><td colspan="3">MSAcademic</td></tr><tr><td>Model LocSage</td><td>M=3 0.8447</td><td>M=5 0.8039</td><td>M=10 0.7148</td><td>M=3 0.8188</td><td>M=5 0.7426</td><td>M=10 0.5918</td></tr><tr><td>LocSage+</td><td>(±0.0047) 0.8481</td><td>(±0.0337) 0.8046</td><td>(±0.0951) 0.7039</td><td>(±0.0331) 0.8393</td><td>(±0.0790) 0.7480</td><td>(±0.1005) 0.5927</td></tr><tr><td>FedSage</td><td>(±0.0041) 0.8708</td><td>(±0.0318) 0.8696</td><td>(±0.0925) 0.8692</td><td>(±0.0330) 0.9327</td><td>(±0.0810) 0.9391</td><td>(±0.1094) 0.9262</td></tr><tr><td>FedSage+</td><td>(±0.0014) 0.8775</td><td>(±0.0035) 0.8755</td><td>(±0.0010) 0.8749 (±0.0013)</td><td>(±0.0005) 0.9359</td><td>(±0.0007) 0.9414</td><td>(±0.0009) 0.9314</td></tr><tr><td>GlobSage</td><td colspan="3">(±0.0012) (±0.0047) 0.8776(±0.0011)</td><td colspan="3">(±0.0005) (±0.0006) (±0.0009) 0.9681(±0.0006)</td></tr></table>
+
+![](images/f5d09c56497904b9874f53707008c0a9fc33ff3d97d4bd643722125b8b83b440.jpg)  
+Figure 3: Node classification results on four datasets under different $\alpha$ and $h$ values with $M { = } 3$
+
+![](images/d8edc2a8c89aa1b7af1e5c37f6bdd3d4ca1a825535041dd7cb01087d1f167ea4.jpg)  
+(b) Hyper-parameter study for $h$ with $\alpha = 1$
+
+(a) Hyper-parameter study for $\alpha$ with $h = 1 5 \%$ .
+
+shown in Table 2. The most important observation emerging from the results is that FedSage+ not only clearly outperforms LocSage by an average of $2 3 . 1 8 \%$ , but also distinctly overcomes the cross-subgraph missing neighbor problem by reducing the average accuracy drop from the $2 . 1 1 \%$ of FedSage to $1 . 2 8 \%$ , when compared with GlobSage (absolute accuracy difference).
+
+The significant gaps between a locally obtained classifier, i.e., LocSage or LocSage+, and a federated trained classifier, i.e., FedSage or FedSage+, assay the benefits brought by the collaboration across data owners in our distributed subgraph system. Compared to FedSage, the further elevation brought by FedSage+ corroborates the assumed degeneration brought by missing cross-subgraph links and the effectiveness of our innovatively designed NeighGen module. Notably, when the graph is relatively sparse (e.g., see Citeseer in Table 1), FedSage $^ +$ significantly exhibits its robustness in resisting the cross-subgraph information loss compared to FedSage. Note that the gaps between LocSage and LocSage $^ +$ are comparatively smaller, indicating that our NeighGen serves more than a robust GNN trainer, but is rather uniquely crucial in the subgraph FL setting.
+
+![](images/340fed2f9eb7820c32f1356b372f58b89eaf0278e38ddb1d7e0e43f7fd227aa5.jpg)  
+Figure 4: Label distributions on the PubMed dataset with $M { = } 5$ .
+
+![](images/d9a0dba0d4f8b0360ca2fc6ffa8f34e11572c41664b2723573d2450a8cc02308.jpg)  
+Figure 5: Training curves of different frameworks (GlobSage provides an upper bound).
+
+Hyper-parameter studies. We compare the downstream task performance under different $\alpha$ and $h$ values with three data owners. Results are shown in Fig. 3, where Fig. 3 (a) shows results when $h$ is fixed as $15 \%$ , and Fig. 3 (b) shows results under $\alpha { = } 1$ .
+
+Fig. 3 (a) indicates that choosing a proper $\alpha$ , which brings the information from other subgraphs in the system, can constantly elevate the final testing accuracy. Across different datasets, the optimal $\alpha$ is constantly around 1, and the performance is not influenced much unless $\alpha$ is set to extreme values like 0.1 or 10. Referring to Fig. 3 (b), we can observe that either a too-small $( 1 \% )$ or a too-large $( 3 0 \% )$ hiding portion can degrade the learning process. A too-small $h$ can not provide sufficient data for training NeighGen, while a too-large $h$ can result in sparse local subgraphs that harm the effective training of GraphSage. Referring back to the graph statistics in Table 1 in the paper, the portion of actual missing edges compared to the global graph is within the range of $[ 3 . 4 \%$ , $2 7 . 8 \% ]$ , which explains why a value like $15 \%$ can mostly boost the performance of FedSage+.
+
+Case studies. To further understand how FedSage and ${ \mathrm { F e d S a g e } } +$ improve the global classifier over LocSage, we provide case study results on PubMed with five data owners in Fig. 4. For the studied scenario, each data owner only possesses about $20 \%$ of the nodes with rather biased label distributions, as shown in Fig. 4 (a). Such bias is due to the way we synthesize the distributed subgraph system with Louvain clustering, which is also realistic in real scenarios. Local bias essentially makes it hard for any local data owner with limited training samples to obtain a generalized classifier that is globally useful. Although with $1 3 . 9 \%$ of the links missing among the system, both FedSage and FedSage+ empower local data owners in predicting labels that closely follow the ground-true global label distribution as shown in Fig. 4 (b). The figure clearly evidences that our FL models exhibit their advantages in learning a more realistic label distribution as our goal in Section 3.1, which is consistent with the observed performances in Table 2 and our theoretical implications in Section 6.
+
+For Cora dataset with five data owners, we visualize testing accuracy, loss convergence, and runtime along 100 epochs in obtaining $F$ with FedSage, FedSage+, GlobSage, LocSage and LocSage+. The results are presented in Fig. 5. Both FedSage and FedSage+ can consistently achieve convergence with rapidly improved testing accuracy. Regarding runtime, even though the classifier from FedSage+ learns from distributed mended subgraphs, FedSage+ does not consume observable more training time compared to FedSage. Due to the additional communications and computations in subgraph FL, both FedSage and FedSage $^ +$ consume slightly more training time compared to GlobSage.
+
+# 6 Implications on Generalization Bound
+
+In this section, we provide a theoretical implication for the generalization error associated with number of training samples, i.e., nodes in the distributed subgraph system, following Graph Neural Tangent Kernel (GNTK) [7] on universal graph neural networks. Thus, we are motivated to promote the FedSage and FedSage+ algorithms that include more nodes in the global graph through collaborative training with FL.
+
+Setting. Our explanation builds on a generalized setting, where we assume a GNN $F$ with layerwise aggregation operations and fully-connected layers with ReLU activation functions, which includes GraphSage as a special case. The weights of $F$ , $\phi$ , is i.i.d. sampled from a multivariate Gaussian distribution $\mathbf { N } ( 0 , I )$ . For Graph $G = \{ \bar { V } , E , X \}$ , we define the kernel matrix of two nodes $u , v \in V$ as follows. Here we consider $F$ is in the GNTK format.
+
+Definition 6.1 (Informal version of GNTK on node classification (Definition B.2)) Considering in the overparameterized regime for an GNN $F$ , $F$ is trained using gradient descent with infinite small learning rate. Given n nodes with corresponding labels as training samples, we denote $\boldsymbol { \Theta } \in \mathbb { R } ^ { n \times n }$ as the the kernel matrix of GNTK. $\mathbf { \Theta } _ { \mathbf { \Theta } } \Theta _ { u v }$ is defined as
+
+$$
+\Theta _ { u v } = \mathbb { E } _ { \phi \sim { \bf N } ( 0 , I ) } \left[ \left. \frac { \partial F ( \phi , G , u ) } { \partial \phi } , \frac { F ( \phi , G , v ) } { \partial \phi } \right. \right] \in \mathbb { R } .
+$$
+
+Full expression of $\Theta$ is shown in the Appendix B. The generalization ability in the GNTK regime depends on the kernel matrix $\Theta$ . We present the generalization bound associated with the number of training samples $n$ in Theorem 6.2.
+
+Theorem 6.2 (Generalization bound) Given n training samples of nodes $\left( u _ { i } , y _ { i } \right) _ { i = 1 } ^ { n }$ drawn i.i.d. from the global graph $G$ , consider any loss function $l : \mathbb { R } \times \mathbb { R } \mapsto [ 0 , 1 ]$ that is $^ { l }$ -Lipschitz in the first argument such that $l ( y , y ) = 0$ . With probability at least $1 - \sigma$ and constant $c \in ( 0 , 1 )$ , the generalization error of GNTK for node classification can be upper-bounded by
+
+$$
+L _ { { \mathcal { D } } ( F ) } = \mathbb { E } _ { ( u ^ { \prime } , y ) \sim G } [ l ( F ( G , u ^ { \prime } ) , y ) ] \lesssim O ( 1 / n ^ { c } ) .
+$$
+
+Following the generalization bound analysis in [7], we use a standard generalization bound of kernel methods of [1], which shows the upper bound of our GNTK formation error depends on that of $\mathbf { y } ^ { \top } \Theta ^ { ( - 1 ) } \mathbf { y }$ and $\operatorname { t r } ( \Theta )$ , where $\mathbf { y }$ is the label vector. Appendix C shows the full version of the proofs.
+
+Implications. We show the error bound of GNTK on node classification corresponding to the number of training samples. Under the assumptions in Definition 6.1, our theoretical result indicates that more training samples bring down the generalization error , which provides plausible support for our goal of building a globally useful classifier through FL in Eq. (3.1). Such implications are also consistent with our experimental findings in Fig. 4 where our FedSage and FedSage+ models can learn more generalizable classifiers that follow the label distributions of the global graph through involving more training nodes across different subgraphs.
+
+# 7 Conclusion
+
+This work aims at obtaining a generalized node classification model in a distributed subgraph system without direct data sharing. To tackle the realistic yet unexplored issue of missing cross-subgraph links, we design a novel missing neighbor generator NeighGen with the corresponding local and federated training processes. Experimental results evidence the distinguished elevation brought by our FedSage and FedSage $^ +$ frameworks , which is consistent with our theoretical implications.
+
+Though FedSage manifests advantageous performance, it confronts additional communication cost and potential privacy concerns. As communications are vital for federated learning, properly reducing communication and rigorously guaranteeing privacy protection in the distributed subgraph system can both be promising future directions.
+
+# Acknowledgments and Disclosure of Funding
+
+This work is partially supported by the internal funding and GPU servers provided by the Computer Science Department of Emory University. We thank Dr. Pan Li from Purdue University for the suggestions on the design of our NeighGen mechanism.
+
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parse/train/SJHRf5nW93/SJHRf5nW93_content_list.json

@@ -0,0 +1,1318 @@
+[
+    {
+        "type": "text",
+        "text": "Subgraph Federated Learning with Missing Neighbor Generation ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ke Zhang1,4, Carl Yang1∗, Xiaoxiao $\\mathbf { L i } ^ { 2 }$ , Lichao $\\mathbf { S u n ^ { 3 } }$ , Siu Ming $\\mathbf { Y i u ^ { 4 } }$ ",
+        "bbox": [
+            266,
+            224,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1Emory University, 2University of British Columbia, 3Lehigh University, 4University of Hong Kon kzhang2@cs.hku.hk, j.carlyang@emory.edu, xiaoxiao.li@ece.ubc.ca, lis221@lehigh.edu, smyiu@cs.hku.hk ",
+        "bbox": [
+            186,
+            241,
+            833,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            318,
+            535,
+            334
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Graphs have been widely used in data mining and machine learning due to their unique representation of real-world objects and their interactions. As graphs are getting bigger and bigger nowadays, it is common to see their subgraphs separately collected and stored in multiple local systems. Therefore, it is natural to consider the subgraph federated learning setting, where each local system holds a small subgraph that may be biased from the distribution of the whole graph. Hence, the subgraph federated learning aims to collaboratively train a powerful and generalizable graph mining model without directly sharing their graph data. In this work, towards the novel yet realistic setting of subgraph federated learning, we propose two major techniques: (1) FedSage, which trains a GraphSage model based on FedAvg to integrate node features, link structures, and task labels on multiple local subgraphs; (2) FedSage+, which trains a missing neighbor generator along FedSage to deal with missing links across local subgraphs. Empirical results on four real-world graph datasets with synthesized subgraph federated learning settings demonstrate the effectiveness and efficiency of our proposed techniques. At the same time, consistent theoretical implications are made towards their generalization ability on the global graphs. ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+            608,
+            310,
+            626
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Graph mining leverages links among connected nodes in graphs to conduct inference. Recently, graph neural networks (GNNs) have gained applause with impressing performance and generalizability in many graph mining tasks [29, 11, 16, 20, 32]. Similar to machine learning tasks in other domains, attaining a well-performed GNN model requires its training data to not only be sufficient but also follow the similar distribution as general queries. While in reality, data owners often collect limited and biased graphs and cannot observe the global distribution. With heterogeneous subgraphs separately stored in local data owners, accomplishing a globally applicable GNN requires collaboration. ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Federated learning (FL) [17, 35], targeting at training machine learning models with data distributed in multiple local systems to resolve the information-silo problem, has shown its advantage in enhancing the performance and generalizability of the collaboratively trained models without the need of sharing any actual data. For example, FL has been devised in computer vision (CV) and natural language processing (NLP) to allow the joint training of powerful and generalizable deep convolutional neural networks and language models on separately stored datasets of images and texts [19, 6, 18, 39, 13]. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Motivating Scenario. Taking the healthcare system as an example, as shown in Fig. 1, residents of a city may go to different hospitals for various reasons. As a result, their healthcare data, such as demographics and living conditions, as well as patient interactions, such as co-staying in a sickroom and co-diagnosis of a disease, are stored only within the hospitals they visit. When any healthcare problem is to be studied in the whole city, e.g., the prediction of infections when a pandemic occurs, a single powerful graph mining model is needed to conduct effective inference over the entire global patient network, which contains all subgraphs from different hospitals. However, it is rather difficult to let all hospitals share their patient networks with others to train the graph mining model due to conflicts of interests and privacy concerns. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3db6f8e262d5f8e6077596e2a5ad0ce466e2079af4e964e11006ec52d9f282f4.jpg",
+        "image_caption": [
+            "Figure 1: A toy example of the distributed subgraph storage system: In this example, there are four hospitals and a medical administration center. The global graph records, for a certain period, the city’s patients (nodes), their information (attributes), and interactions (links). Specifically, the left part of the figure shows how the global graph is stored in each hospital, where the grey solid lines are the links explicitly stored in each hospital, and the red dashed lines are the cross-hospital links that may exist but are not stored in any hospital. The right part of the figure indicates our goal that without sharing actual data, the system obtains a globally powerful graph mining model. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In such scenarios, it is desirable to train a powerful and generalizable graph mining model over multiple distributed subgraphs without actual data sharing. However, this novel yet realistic setting brings two unique technical challenges, which have never been explored so far. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Challenge 1: How to jointly learn from multiple local subgraphs? In our considered scenario, the global graph is distributed into a set of small subgraphs with heterogeneous feature and structure distributions. Training a separate graph mining model on each subgraph may not capture the global data distribution and is also prone to overfitting. Moreover, it is unclear how to integrate multiple graph mining models into a universally applicable one that can handle any queries from the underlying global graph. ",
+        "bbox": [
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+            464,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Solution 1: FedSage: Training GraphSage with FedAvg. To attain a powerful and generalizable graph mining model from small and biased subgraphs distributed in multiple local owners, we develop a framework of subgraph federated learning, specifically, with the vanilla mechanism of FedAvg [21]. As for the graph mining model, we resort to GraphSage [11], due to its advantages of inductiveness and scalability. We term this framework as FedSage. ",
+        "bbox": [
+            174,
+            553,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Challenge 2: How to deal with missing links across local subgraphs? Unlike distributed systems in other domains such as CV and NLP, whose data samples of images and texts are isolated and independent, data samples in graphs are connected and correlated. Most importantly, in a subgraph federated learning system, data samples in each subgraph can potentially have connections to those in other subgraphs. These connections carrying important information of node neighborhoods and serving as bridges among the data owners, however, are never directly captured by any data owner. ",
+        "bbox": [
+            174,
+            628,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Solution 2: FedSage+: Generating missing neighbors along FedSage. To deal with crosssubgraph missing links, we add a missing neighbor generator on top of FedSage and propose a novel FedSage+ model. Specifically, for each data owner, instead of training the GraphSage model on the original subgraph, it first mends the subgraph with generated cross-subgraph missing neighbors and then applies FedSage on the mended subgraph. To obtain the missing neighbor generator, each data owner impairs the subgraph by randomly holding out some nodes and related links and then trains the generator based on the held-out neighbors. Training the generator on an individual local subgraph enables it to generate potential missing links within the subgraph. Further training the generator in our subgraph FL setting allows it to generate missing neighbors across distributed subgraphs. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on four real-world datasets with different numbers of data owners to better simulate the application scenarios. According to our results, both of our models outperform locally trained classifiers in all scenarios. Compared to FedSage, FedSage+ further promotes the performance of the outcome classifier. Further in-depth model analysis shows the convergence and generalization ability of our frameworks, which is corroborated by our theoretical analysis in the end. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related works ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            89,
+            325,
+            106
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Graph mining. Graph mining emerges its significance in analyzing the informative graph data, which range from social networks to gene interaction networks [31, 33, 34, 24]. One of the most frequently applied tasks on graph data is node classification. Recently, graph neural networks (GNNs), e.g., graph convolutional networks (GCN) [16] and GraphSage [11], improved the state-of-the-art in node classification with their elegant yet powerful designs. However, as GNNs leverage the homophily of nodes in both node features and link structures to conduct the inference, they are vulnerable to the perturbation on graphs [4, 40, 41]. Robust GNNs, aiming at reducing the degeneration in GNNs caused by graph perturbation, are gaining attention these days. Current robust GNNs focus on the sensitivity towards modifications on node features [3, 42, 15] or adding/removing edges on the graph [37]. However, neither of these two types recapitulates the missing neighbor problem, which affects both the feature distribution and structure distribution. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To obtain a node classifier with good generalizability, the development of domain adaptive GNN sheds light on adapting a GNN model trained on the source domain to the target domain by leveraging underlying structural consistency [38, 36, 28]. However, in the distributed system we consider, data owners have subgraphs with heterogeneous feature and structure distributions. Moreover, direct information exchanges among subgraphs, such as message passing, are fully blocked due to the missing cross-subgraph links. The violation of the domain adaptive GNNs’ assumptions on alignable nodes and cross-domain structural consistency denies their usage in the distributed subgraph system. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Federated learning. FL is proposed for cross-institutional collaborative learning without sharing raw data [17, 35, 21]. FedAvg [21] is an efficient and well-studied FL method. Similar to most FL methods, it is originally proposed for traditional machine learning problems [35] to allow collaborative training on silo data through local updating and global aggregation. The ecently proposed meta-learning framework [9, 23, 14] that exploits information from different data sources to obtain a general model attracts FL researchers [8]. However, meta-learning aims to learn general models that easily adapt to different local tasks, while we learn a generalizable model from diverse data owners to assist in solving a global task. In the distributed subgraph system, to obtain a globally applicable model without sharing local graph data, we borrow the idea of FL to collaboratively train GNNs. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Federated graph learning. Recent researchers have made some progress in federated graph learning. There are existing FL frameworks designed for the graph data learning task [12, 27, 30]. [12] design graph-level FL schemes with graph datasets dispersed over multiple data owners, which are inapplicable to our distributed subgraph system construction. [27] proposes an FL method for the recommendation problem with each data owner learning on a subgraph of the whole recommendation user-item graph. It considers a different scenario assuming subgraphs have overlapped items (nodes), and the user-item interactions (edges) are distributed but completely stored in the system, which ignores the possible cross-subgraph information lost in real-world scenarios. However, we study a more challenging yet realistic case in the distributed subgraph system, where cross-subgraph edges are totally missing. ",
+        "bbox": [
+            174,
+            511,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we consider the commonly existing yet not studied scenario, i.e., distributed subgraph system with missing cross-subgraph edges. Under this scenario, we focus on obtaining a globally applicable node classifier through FL on distributed subgraphs. ",
+        "bbox": [
+            176,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 FedSage ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            709,
+            276,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first illustrate the definition of the distributed subgraph system derived from real-world application scenarios. Based on this system, we then formulate our novel subgraph FL framework and a vanilla solution called FedSage. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Subgraphs Distributed in Local Systems ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            784,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Notation. We denote a global graph as $G = \\{ V , E , X \\}$ , where $V$ is the node set, $X$ is the respective node feature set, and $E$ is the edge set. In the FL system, we have the central server $S$ , and $M$ data owners with distributed subgraphs. $G _ { i } = \\{ V _ { i } , E _ { i } , X _ { i } \\}$ is the subgraph owned by $D _ { i }$ , for $i \\in [ M ]$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Problem setup. For the whole system, we assume $V = V _ { 1 } \\cup \\cdots \\cup V _ { M }$ . To simulate the scenario with most missing links, we assume no overlapping nodes shared across data owners, namely $V _ { i } \\cap V _ { j } = \\emptyset$ for $\\forall i , j \\in [ M ]$ and $i \\neq j$ . Note that the central server $S$ only maintains a graph mining model with no actual graph data stored. Any data owner $D _ { i }$ cannot directly retrieve $u \\in V _ { j }$ from another data owner $D _ { j }$ . Therefore, for an edge $e _ { v , u } \\in E$ , where $v \\in V _ { i }$ and $u \\in V _ { j }$ , $e _ { v , u } \\notin E _ { i } \\cup E _ { j }$ , that is, $e _ { v , u }$ might exist in reality but is not stored anywhere in the whole system. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the global graph $G = \\{ V , E , X \\}$ , every node $v \\in V$ has its features $x _ { v } \\in X$ and one label $y _ { v } \\in Y$ for the downstream task, e.g., node classification. Note that for $v \\in V$ , $v$ ’s feature $x _ { v } \\in \\mathbb { R } ^ { d _ { x } }$ and respective label $y _ { v }$ is a $d _ { y }$ -dimensional one-hot vector. In a typical GNN, predicting a node’s label requires an ego-graph of the queried node. For a node $v$ from graph $G$ , we denote the queried ego-graph of $v$ as $G ( v )$ , and $( G ( v ) , y _ { v } ) \\sim \\mathcal { D } _ { G }$ . ",
+        "bbox": [
+            173,
+            125,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With subgraphs distributed in the system defined above, we formulate our goal as follows. ",
+        "bbox": [
+            171,
+            202,
+            761,
+            218
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Goal. The system exploits an $\\mathrm { F L }$ framework to collaboratively learn on isolated subgraphs in all data owners, without raw graph data sharing, to obtain a global node classifier $F$ . The learnable weights $\\phi$ in $F$ is optimized for queried ego-graphs following the distribution of ones drawn from the global graph $G$ . We formalize the problem as finding $\\phi ^ { * }$ that minimizes the aggregated risk ",
+        "bbox": [
+            173,
+            223,
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+            280
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2e69cf1ef262bb6fbcc65c364e6407ceb23c5772f4da6a0cdf1532f4036ff701.jpg",
+        "text": "$$\n\\boldsymbol { \\phi } ^ { * } = \\arg \\operatorname* { m i n } _ { \\mathbf { \\phi } } \\mathcal { R } ( \\boldsymbol { F } ( \\boldsymbol { \\phi } ) ) = \\frac { 1 } { M } \\sum _ { i } ^ { M } \\mathcal { R } _ { i } ( F _ { i } ( \\boldsymbol { \\phi } ) ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            279,
+            651,
+            318
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { R } _ { i }$ is the local empirical risk defined as ",
+        "bbox": [
+            179,
+            320,
+            483,
+            335
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cf5abc8e880fbdcbb9c8db910151cdd444dd06c9c8deb25784aa0eb7a436b878.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { R } _ { i } \\big ( F _ { i } ( \\phi ) \\big ) : = \\mathbb { E } _ { ( G _ { i } , Y _ { i } ) \\sim \\mathcal { D } _ { G _ { i } } } [ \\ell ( F _ { i } ( \\phi ; G _ { i } ) , Y _ { i } ) ) ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            334,
+            651,
+            353
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\ell$ is a task-specific loss function ",
+        "bbox": [
+            179,
+            356,
+            431,
+            369
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e32bfe4480073abbecc3ad7beb2aa2887dd26f4113bb69b91ca2eda10d2e3a76.jpg",
+        "text": "$$\n\\ell : = \\frac { 1 } { | V _ { i } | } \\sum _ { v \\in V _ { i } } l ( \\phi ; G _ { i } ( v ) , y _ { v } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            398,
+            369,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Collaborative Learning on Isolated Subgraphs ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            420,
+            537,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To fulfill the system’s goal illustrated above, we leverage the simple and efficient FedAvg framework [21] and fix the node classifier $F$ as a GraphSage model. The inductiveness and scalability of the GraphSage model facilitate both the training on diverse subgraphs with heterogeneous query distributions and the later inference upon the global graph. We term the GraphSage model trained with the FedAvg framework as FedSage. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "r a queried node -hop neighborho $v \\in V$ , a glraph ally shared  to conduct $K$ -layer GraphSage classifier ediction with learnable par $F$ integeters $v$ $K$ $G$ $\\phi = \\{ \\phi ^ { k } \\} _ { k = 1 } ^ { K }$ Taking a subgraph $G _ { i }$ as an example, for $v \\in V _ { i }$ with features as $h _ { v } ^ { 0 } = x _ { v }$ , at each layer $k \\in [ K ]$ , $F$ computes $v$ ’s representation $h _ { v } ^ { k }$ as ",
+        "bbox": [
+            173,
+            520,
+            826,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cc089e230bf25f65bd4ea9b451eb0a0306fd6612ae1d8c376f7e3a1f6d107078.jpg",
+        "text": "$$\nh _ { v } ^ { k } = \\sigma \\left( \\phi ^ { k } \\cdot \\left( h _ { v } ^ { k - 1 } | | A g g \\left( \\left\\{ h _ { u } ^ { k - 1 } , \\forall u \\in \\mathcal { N } _ { G _ { i } } ( v ) \\right\\} \\right) \\right) \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            318,
+            583,
+            678,
+            602
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { N } _ { G _ { i } } ( v )$ is the set of $v$ ’s neighbors on graph $G _ { i } , | |$ is the concatenation operation, $A g g ( \\cdot )$ is the aggregator (e.g., mean pooling) and $\\sigma$ is the activation function (e.g., ReLU). ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With $F$ outputting the inference label $\\widetilde { y } _ { v } = \\mathrm { S o f t m a x } ( h _ { v } ^ { K } )$ for $v \\in V _ { i }$ , the supervised loss function $l ( \\phi | \\cdot )$ is defined as follows ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/759b1e3c806d06c0153a8a8c6e290ad93da00cf0d7a6fcaced9db00f2a9d28e3.jpg",
+        "text": "$$\n\\mathcal { L } ^ { c } = l ( \\phi | G _ { i } ( v ) , y _ { v } ) = C E ( \\widetilde { y } _ { v } , y _ { v } ) = - \\left[ y _ { v } \\log \\widetilde { y } _ { v } + ( 1 - y _ { v } ) \\log \\left( 1 - \\widetilde { y } _ { v } \\right) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $C E ( \\cdot )$ is the cross entropy function, $G _ { i } ( v )$ is $v$ ’s K-hop ego-graph on $G _ { i }$ , which contains the information of $v$ and its K-hop neighbors on $G _ { i }$ . ",
+        "bbox": [
+            176,
+            689,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In FedSage, the distributed subgraph system obtains a shared global node classifier $F$ parameterized by $\\phi$ through $e _ { c }$ epochs of training. During each epoch $t$ , every $D _ { i }$ first locally computes $\\phi _ { i } \\gets$ $\\phi - \\eta \\nabla \\ell ( \\phi | \\{ ( G _ { i } ( v ) , y _ { v } ) | v \\in V _ { i } ^ { t } \\} )$ , where $V _ { i } ^ { t } \\subseteq V _ { i }$ contains the sampled training nodes for epoch $t$ , and $\\eta$ is the learning rate; then the central server $S$ collects the latest $\\{ \\phi _ { i } | i \\in [ \\bar { M } ] \\}$ ; next, through averaging over $\\{ \\phi _ { i } | \\bar { i } \\in [ M ] \\}$ , $S$ sets $\\phi$ as the averaged value; finally, $S$ broadcasts $\\phi$ to data owners and finishes one round of training $F$ . After $e _ { c }$ epochs, the entire system retrieves $F$ as the outcome global classifier, which is not limited to or biased towards the queries in any specific data owner. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Unlike FL on Euclidean data, nodes in the distributed subgraph system can have potential interactions with each other across subgraphs. However, as the cross-subgraph links cannot be captured by any data owner in the system, incomplete neighborhoods, compared to those on the global graph, commonly exist therein. Thus, directly aggregating incomplete queried ego-graph information through FedSage restricts the outcome $F$ from achieving the desideratum of capturing the global query distribution. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/3bcb77490b0c2ae8e863682998c4fd95fb5f8ae6d294a9c24fbf42bbce8fcbf8.jpg",
+        "image_caption": [
+            "Figure 2: Joint training of missing neighbor generation and node classification. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4 FedSage+ ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we propose a novel framework of FedSage $^ +$ , i.e., subgraph FL with missing neighbor generation. We first design a missing neighbor generator (NeighGen) and its training schema via graph mending. Then, we describe the joint training of NeighGen and GraphSage to better achieve the goal in Section 3.1. Without loss of generality, in the following demonstration, we take NeighGeni, i.e., the missing neighbor generator of $D _ { i }$ , as an example, where $i \\in [ M ]$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Missing Neighbor Generator (NeighGen) ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Neural architecture of NeighGen. As shown in Fig. 2, NeighGen consists of two modules, i.e., an encoder $H ^ { e }$ and a generator $H ^ { g }$ . We describe their designs in details in the following. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$H ^ { e }$ : A GNN model, i.e., a K-layer GraphSage encoder, with parameters $\\theta ^ { e }$ . For node $v \\in V _ { i }$ on the input graph $G _ { i }$ , $H ^ { e }$ computes node embeddings $Z _ { i } = \\{ z _ { v } | z _ { v } \\stackrel { \\cdot } { = } h _ { v } ^ { K } , z _ { v } \\in \\mathbb { R } ^ { d _ { z } } , v \\in V _ { i } \\}$ according to Eq. (1) by substituting $\\phi$ , $G$ with $\\theta ^ { e }$ and $G _ { i }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$H ^ { g }$ : A generative model recovering missing neighbors for the input graph based on the node embedding. $H ^ { g }$ contains dGen and fGen, where dGen is a linear regression model parameterized by $\\theta ^ { d }$ that predicts the numbers of missing neighbors $\\widetilde { N } _ { i } = \\{ \\widetilde { n } _ { v } | \\widetilde { n } _ { v } \\in \\mathbb { N } , v \\in V _ { i } \\}$ , and fGen is a feature generator parameterized by $\\theta ^ { f }$ that generates a set of $\\widetilde { N } _ { i }$ feature vectors $\\widetilde { X } _ { i } = \\{ \\widetilde { x } _ { v } | \\widetilde { x } _ { v } \\in$ $\\mathbb { R } ^ { \\widetilde { n } _ { v } \\times d _ { x } } , \\widetilde { n } _ { v } \\in \\widetilde { N } _ { i } , v \\in V _ { i } \\}$ e e. Both dGen and fGen are constructed as fully connected neural networks e(FNNs), while fGen is further equipped with a Gaussian noise generator $\\mathbf { N } ( 0 , 1 )$ that generates $d _ { z }$ -dimensional noise vectors and a random sampler $R$ . For node $v \\in V _ { i }$ , fGen is variational, which generates the missing neighbors’ features for $v$ after inserting noises into the embedding $z _ { v }$ , while $R$ ensures fGen to output the features of a specific number of neighbors by sampling $\\widetilde { n } _ { v }$ feature vectors from the feature generator’s output. Mathematically, we have ",
+        "bbox": [
+            173,
+            455,
+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/79bc247abed1cc31ee0df1f00215aee30e5b001b4bb5a4ce3ee0c252b37d2fba.jpg",
+        "text": "$$\n\\widetilde { n } _ { v } = \\sigma ( ( { \\boldsymbol { \\theta } } ^ { d } ) ^ { T } \\cdot { \\boldsymbol { n } } _ { v } ) , \\operatorname { a n d } \\widetilde { x } _ { v } = R \\left( \\sigma \\left( ( { \\boldsymbol { \\theta } } ^ { f } ) ^ { T } \\cdot ( z _ { v } + \\mathbf { N } ( 0 , 1 ) ) \\right) , \\widetilde { { \\boldsymbol { n } } } _ { v } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            274,
+            613,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Graph mending simulation. For each data owner in our system, we assume that only a particular set of nodes have cross-subgraph missing neighbors. The assumption is realistic yet non-trivial for it both seizing the quiddity of the distributed subgraph system, and allowing us to locally simulate the missing neighbor situation through a graph impairing and mending process. Specifically, to simulate a graph mending process during the training of NeighGen, in each local subgraph $G _ { i }$ , we randomly hold out $h \\%$ of its nodes $V _ { i } ^ { h } \\subset V _ { i }$ and all links involving them $E _ { i _ { - } } ^ { h } = \\{ e _ { u v } | u \\stackrel { - } { \\in } \\bar { V } _ { i } ^ { h }$ or $v \\in V _ { i } ^ { h } \\} \\subset \\mathsf { \\bar { E } } _ { i }$ , to form an impaired subgraph, denoted as $\\bar { G } _ { i }$ . $\\bar { G } _ { i } = \\mathsf { \\bar { \\{ V } }  _ { i } , \\bar { E } _ { i } , \\bar { X } _ { i } \\}$ contains the impaired set of nodes $\\bar { V } _ { i } = V _ { i } \\setminus V _ { i } ^ { h }$ , the corresponding nodes features ${ \\bar { X } } _ { i } = X _ { i } \\setminus X _ { i } ^ { h }$ and edges $\\bar { E } _ { i } = E _ { i } \\setminus E _ { i } ^ { h }$ . ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Accordingly, based on the ground-truth missing nodes $V _ { i } ^ { h }$ and links $E _ { i } ^ { h }$ , the training of NeighGen on the impaired graph $\\bar { G } _ { i }$ boils down to jointly training dGen and fGen as below. ",
+        "bbox": [
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+            767,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ef49b9eeb87b61c156c2684751f387a8a2a0424ce5dc16f677e89bd55d24baed.jpg",
+        "text": "$$\n\\mathcal { L } ^ { n } = \\lambda ^ { d } \\mathcal { L } ^ { d } + \\lambda ^ { f } \\mathcal { L } ^ { f } = \\lambda ^ { d } \\frac { 1 } { | \\bar { V } _ { i } | } \\sum _ { v \\in \\bar { V } _ { i } } L _ { 1 } ^ { S } \\big ( \\widetilde { n } _ { v } - n _ { v } \\big ) + \\lambda ^ { f } \\frac { 1 } { | \\bar { V } _ { i } | } \\sum _ { v \\in \\bar { V } _ { i } } \\sum _ { p \\in \\{ \\widetilde { n } _ { v } \\} } \\operatorname* { m i n } _ { u \\in \\mathcal { N } _ { G _ { i } } ( v ) \\cap V _ { i } ^ { h } } ( | | \\widetilde { x } _ { v } ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            820,
+            794,
+            857
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $L _ { 1 } ^ { S }$ is the smooth L1 distance [10] and $\\mathcal { \\widetilde { x } } _ { v } ^ { p } \\in \\mathbb { R } ^ { d _ { x } }$ is the $p$ -th predicted feature in $\\widetilde { x } _ { v }$ . Note that, $\\mathcal { N } _ { G _ { i } } ( v ) \\cap V _ { i } ^ { h }$ contains $n _ { v }$ nodes that are $v$ e’s neighbors on $G _ { i }$ missing into $V _ { i } ^ { h }$ . $\\mathcal { N } _ { G _ { i } } ( v ) \\cap V _ { i } ^ { h }$ , which can be retrieved from $V _ { i } ^ { h }$ and $E _ { i } ^ { h }$ , provides ground-truth for training NeighGen. ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Neighbor Generation. To retrieve $G _ { i } ^ { \\prime }$ from $G _ { i }$ , data owner $D _ { i }$ performs two steps, which are also shown in Fig. 2: 1) $D _ { i }$ trains NeighGen on the impaired graph $\\bar { G } _ { i }$ w.r.t. the ground-true hidden neighbors ${ \\bar { V } } _ { i } ^ { \\breve { h } }$ ; 2) $D _ { i }$ exploits NeighGen to generate missing neighbors for nodes on $G _ { i }$ and then mends $G _ { i }$ into $G _ { i } ^ { \\prime }$ with generated neighbors. On the local graph $G _ { i }$ alone, this process can be understood as a data augmentation that further generates potential missing neighbors within $G _ { i }$ . However, the actual goal is to allow NeighGen to generate the cross-subgraph missing neighbors, which can be achieved via training NeighGen with FL and will be discussed in Section 4.3. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 Local Joint Training of GraphSage and NeighGen ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            204,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "While NeighGen is designed to recover missing neighbors, the final goal of our system is to train a node classifier. Therefore, we design the joint training of GraphSage and NeighGen, which leverages neighbors generated by NeighGen to assist the node classification by GraphSage. We term the integration of GraphSage and NeighGen on the local graphs as LocSage+. ",
+        "bbox": [
+            173,
+            229,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "After NeighGen mends the graph $G _ { i }$ into $G _ { i } ^ { \\prime }$ , the GraphSage classifier $F$ is applied on $G _ { i } ^ { \\prime }$ , according to Eq. (1) (with $G _ { i }$ replaced by $G _ { i } ^ { \\prime }$ ). Thus, the joint training of NeighGen and GraphSage is done by optimizing the following loss function ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/76964aabfba4b61b492d8ad6d90c870279bd7dda781e1fbe4d5ee7a1ab37dd2e.jpg",
+        "text": "$$\n\\mathcal { L } = \\mathcal { L } ^ { n } + \\lambda ^ { c } \\mathcal { L } ^ { c } = \\lambda ^ { d } \\mathcal { L } ^ { d } + \\lambda ^ { f } \\mathcal { L } ^ { f } + \\lambda ^ { c } \\mathcal { L } ^ { c } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            338,
+            640,
+            356
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathcal { L } } ^ { d }$ and $\\mathcal { L } ^ { f }$ are defined in Eq. (4), and $\\mathcal { L } ^ { c }$ is defined in Eq. (2) (with $G _ { i }$ substituted by $G _ { i } ^ { \\prime }$ ",
+        "bbox": [
+            171,
+            363,
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+            378
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The local joint training of GraphSage and NeighGen allows NeighGen to generate missing neighbors in the local graph that are helpful for the classifications made by GraphSage. However, like GraphSage, the information encoded in the local NeighGen is limited to and biased towards the local graph, which does not enable it to really generate neighbors belonging to other data owners connected by the missing cross-subgraph links. To this end, it is natural to train NeighGen with $\\mathrm { F L }$ as well. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 Federated Learning of GraphSage and NeighGen ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            469,
+            555,
+            486
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Similarly to GraphSage alone, as described in Section 3.2, we can apply FedAvg to the joint training of GraphSage and NeighGen, by setting the loss function to $\\mathcal { L }$ and learnable parameters to $\\{ \\theta ^ { e } , \\theta ^ { d } , \\theta ^ { f } , \\phi \\}$ . However, we observe that cooperation through directly averaging weights of NeighGen across the system can negatively affect its performance, i.e., averaging the weights of a single NeighGen model does not really allow it to generate diverse neighbors from different subgraphs. Recalling our goal of constructing NeighGen, which is to facilitate the training of a centralized GraphSage classifier by generating diverse missing neighbors in each subgraph, we do not necessarily need a centralized NeighGen. Therefore, instead of training a single centralized NeighGen, we train a local NeighGeni for each data owner $D _ { i }$ . In order to allow each NeighGeni to generate diverse neighbors similar to those missed into other subgraphs $G _ { j } , j \\in [ M ] \\backslash \\{ i \\}$ , we add a cross-subgraph feature reconstruction loss into $\\mathrm { f G e n } _ { i }$ as follows: ",
+        "bbox": [
+            173,
+            494,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/19b9cbadec4d5d1e0024391d82beafab0220d0ad072559a9cbb9191b94554267.jpg",
+        "text": "$$\n\\mathcal { L } _ { i } ^ { f } = \\frac { 1 } { \\lvert \\overline { { V _ { i } } } \\rvert } \\sum _ { v \\in \\bar { V } _ { i } } \\sum _ { p \\in [ \\tilde { n } _ { v } ] } \\left( \\operatorname* { m i n } _ { u \\in N _ { G _ { i } } ( v ) \\cap V _ { i } ^ { h } } ( \\lvert | \\widetilde { x } _ { v } ^ { p } - x _ { u } \\rvert | _ { 2 } ^ { 2 } ) + \\alpha \\sum _ { j \\in [ M ] / i } \\operatorname* { m i n } _ { u \\in V _ { j } } ( \\lvert | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } \\rvert | _ { 2 } ^ { 2 } ) \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            214,
+            661,
+            782,
+            707
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $u \\in V _ { j } , \\forall j \\in [ M ] \\setminus \\{ i \\}$ is picked as the closest node from $G _ { j }$ other than $G _ { i }$ to simulate the neighbor of $v \\in { \\bar { V } } _ { i }$ missed into $G _ { j }$ . ",
+        "bbox": [
+            176,
+            708,
+            821,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown above, to optimize Eq. (6), $D _ { i }$ needs to pick the closest $u$ from $G _ { j }$ . However, directly transmitting node features $X _ { j }$ in $D _ { j }$ to $D _ { i }$ not only violates our subgraph FL system constraints on no direct data sharing but also is impractical in reality, as it requires each $D _ { i }$ to hold the entire global graph’s node features throughout training ${ \\mathrm { N e i g h G e n } } _ { i }$ . Therefore, to allow $D _ { i }$ to update ${ \\mathrm { N e i g h G e n } } _ { i }$ using Eq. (6) without direct access to $X _ { j }$ , for $v \\in { \\bar { V } } _ { i }$ , $D _ { j }$ locally computes $\\begin{array} { r } { \\sum _ { p \\in [ \\widetilde { n } _ { v } ] } \\operatorname* { m i n } _ { u \\in V _ { j } } ( | | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) } \\end{array}$ and sends the respective gradient back to $D _ { i }$ . ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "During this process, for $v \\in \\bar { V } _ { i }$ , to federated optimize Eq. (6), only $H _ { i } ^ { g }$ , $H _ { i } ^ { g }$ ’s input $z _ { v }$ , and the $D _ { j }$ ’s locally computed model gradients of loss term $\\begin{array} { r } { \\sum _ { p \\in [ \\tilde { n } _ { v } ] } \\operatorname* { m i n } _ { u \\in V _ { j } } ( | | H _ { i } ^ { g } ( z _ { v } ) ^ { p } - x _ { u } | | _ { 2 } ^ { 2 } ) } \\end{array}$ are transmitted among the system via the server $S$ e. For data owner $D _ { i }$ , the gradients received from $D _ { j }$ are then weighted by $\\alpha$ and combined with the local gradients as in Eq. (6) to update the parameters of $H _ { i } ^ { g }$ of NeighGeni In this way, $D _ { i }$ achieves the federate training of ${ \\mathrm { N e i g h G e n } } _ { i }$ without raw graph data sharing. Note that, due to NeighGen’s architecture of a concatenation of $H ^ { e }$ and $H ^ { g }$ , the locally preserved GNN $H _ { i } ^ { e }$ can prevent other data owners from inferring $x _ { v }$ by only seeing $z _ { v }$ . Through Eq. (6), NeighGen $_ { \\cdot i }$ is expected to perceive diverse neighborhood information from all data owners, so as to generate more realistic cross-subgraph missing neighbors. The expectedly diverse and unbiased neighbors further assist the FedSage in training a globally applicable classifier that satisfies our goal in Section 3.1. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Note that, to reduce communications and computation time incurred by Eq. (6), batch training can be applied. Appendix A shows the pseudo code of FedSage+. ",
+        "bbox": [
+            174,
+            181,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            219,
+            312,
+            237
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on four datasets to verify the effectiveness of FedSage and FedSage+ under different testing scenarios. We further conduct case studies to visualize how FedSage and FedSage+ assist local data owners in accommodating queries from the global distribution. Finally, we also provide more in-depth studies on the effectiveness of NeighGen in Appendix D. ",
+        "bbox": [
+            174,
+            251,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1 Datasets and experimental settings ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            315,
+            454,
+            329
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We synthesize the distributed subgraph system with four widely used real-world graph datasets, i.e., Cora [25], Citeseer [25], PubMed [22], and MSAcademic [26]. To synthesize the distributed subgraph system, we find hierarchical graph clusters on each dataset with the Louvain algorithm [2] and use the clustering results with 3, 5, and 10 clusters of similar sizes to obtain subgraphs for data owners. The statistics of these datasets are presented in Table 1. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/323b180efc1821974e30e47553dfeeef4fecb7e673816dc52fcad63a161121c8.jpg",
+        "table_caption": [
+            "Table 1: Statistics of the datasets and the synthesized distributed subgraph systems with $M = 3$ , 5, and $1 0 . \\# \\mathrm { C }$ row shows the number of classes, $| V _ { i } |$ and $| E _ { i } |$ rows show the averaged numbers of nodes and links in all subgraphs, and $\\Delta E$ shows the total number of missing cross-subgraph links. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Data</td><td colspan=\"3\">Cora</td><td colspan=\"3\">Citeseer</td><td colspan=\"3\">PubMed</td><td colspan=\"3\">MSAcademic</td></tr><tr><td>#C |V</td><td colspan=\"3\"></td><td colspan=\"3\">6</td><td colspan=\"3\">3</td><td colspan=\"3\">15</td></tr><tr><td></td><td colspan=\"3\"></td><td colspan=\"3\">3312</td><td colspan=\"3\">19717</td><td colspan=\"3\">18333</td></tr><tr><td>|E</td><td colspan=\"3\">5429</td><td colspan=\"3\">4715</td><td colspan=\"3\">44338</td><td colspan=\"3\">81894</td></tr><tr><td>M</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td><td>3</td><td>5</td><td>10</td></tr><tr><td>Vil</td><td>903</td><td>542</td><td>271</td><td>1104</td><td>662</td><td>331</td><td>6572</td><td>3943</td><td>1972</td><td>6111</td><td>3667</td><td>1833</td></tr><tr><td>E</td><td>1675</td><td>968</td><td>450</td><td>1518</td><td>902</td><td>442</td><td>12932</td><td>7630</td><td>3789</td><td>23584</td><td>13949</td><td>5915</td></tr><tr><td>△E</td><td>403</td><td>589</td><td>929</td><td>161</td><td>206</td><td>300</td><td>5543</td><td>6189</td><td>6445</td><td>11141</td><td>12151</td><td>22743</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "We implement GraphSage with two layers using the mean aggregator [5]. The number of nodes sampled in each layer of GraphSage is 5. We use batch size 64 and set training epochs to 50. The training-validation-testing ratio is $6 0 \\% - 2 0 \\% - 2 0 \\%$ due to limited sizes of local subgraphs. Based on our observations in hyper-parameter studies for $\\alpha$ and the graph impairing ratio $h$ , we set $h \\% \\in [ 3 . 4 \\% , 2 7 . 8 \\% ]$ and $\\alpha { = } 1$ . All $\\lambda s$ are simply set to 1. Optimization is done with Adam with a learning rate of 0.001. We implement FedSage and FedSage $^ +$ in Python and execute all experiments on a server with 8 NVIDIA GeForce GTX 1080 Ti GPUs. ",
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+    {
+        "type": "text",
+        "text": "Since we are the first to study the novel yet important setting of subgraph federated learning, there are no existing baselines. We conduct comprehensive ablation evaluation by comparing FedSage and FedSage+ with three models, i.e., 1) GlobSage: the GraphSage model trained on the original global graph without missing links (as an upper bound for FL framework with GraphSage model alone), 2) LocSage: one GraphSage model trained solely on each subgraph, 3) LocSage+: the GraphSage plus NeighGen model jointly trained solely on each subgraph. ",
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+    },
+    {
+        "type": "text",
+        "text": "The metric used in our experiments is the node classification accuracy on the queries sampled from the testing nodes on the global graph. For globally shared models of GlobSage, FedSage, and FedSage+, we report the average accuracy over five random repetitions, while for locally possessed models of LocSage and LocSage+, the scores are further averaged across local models. ",
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+    {
+        "type": "text",
+        "text": "5.2 Experimental results ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Overall performance. We conduct comprehensive ablation experiments to verify the significant promotion brought by FedSage and FedSage $^ +$ for local owners in global node classification, as ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5b19bfedcb0a06bf44140d1411833d4c4b736cf99487367f89f09ba5ce727742.jpg",
+        "table_caption": [
+            "Table 2: Node classification results on four datasets with $M = 3 , 5$ , and 10. Besides averaged accuracy, we also provide the corresponding std. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Cora</td><td colspan=\"3\">Citesser</td></tr><tr><td>M=3</td><td>M=5</td><td>M=10</td><td>M=3</td><td>M=5</td><td>M=10</td></tr><tr><td>LocSage</td><td>0.5762 (±0.0302)</td><td>0.4431 (±0.0847)</td><td>0.2798 (±0.0080)</td><td>0.6789 (±0.054)</td><td>0.5612 (±0.086)</td><td>0.4240 (±0.0859)</td></tr><tr><td>LocSage+</td><td>0.5644 (±0.0219)</td><td>0.4533 (±0.047)</td><td>0.2851 (±0.0080)</td><td>0.6848 (±0.0517)</td><td>0.5676 (±0.0714)</td><td>0.4323 (±0.0715)</td></tr><tr><td>FedSage</td><td>0.8656 (±0.0043)</td><td>0.8645 (±0.0050)</td><td>0.8626 (±0.0103)</td><td>0.7241 (±0.0022)</td><td>0.7226 ±0.0066)</td><td>0.7158 (±0.0053)</td></tr><tr><td>FedSage+</td><td>0.8686 (±0.0054)</td><td>0.8648 (±0.0051)</td><td>0.8632 (±0.0034)</td><td>0.7454 (±0.0038)</td><td>0.7440 (±0.0025)</td><td>0.7392 (±0.0041)</td></tr><tr><td>GlobSage</td><td colspan=\"3\">0.8701 (±0.0042)</td><td colspan=\"3\">0.7561 (±0.0031)</td></tr><tr><td></td><td colspan=\"3\">PubMed</td><td colspan=\"3\">MSAcademic</td></tr><tr><td>Model LocSage</td><td>M=3 0.8447</td><td>M=5 0.8039</td><td>M=10 0.7148</td><td>M=3 0.8188</td><td>M=5 0.7426</td><td>M=10 0.5918</td></tr><tr><td>LocSage+</td><td>(±0.0047) 0.8481</td><td>(±0.0337) 0.8046</td><td>(±0.0951) 0.7039</td><td>(±0.0331) 0.8393</td><td>(±0.0790) 0.7480</td><td>(±0.1005) 0.5927</td></tr><tr><td>FedSage</td><td>(±0.0041) 0.8708</td><td>(±0.0318) 0.8696</td><td>(±0.0925) 0.8692</td><td>(±0.0330) 0.9327</td><td>(±0.0810) 0.9391</td><td>(±0.1094) 0.9262</td></tr><tr><td>FedSage+</td><td>(±0.0014) 0.8775</td><td>(±0.0035) 0.8755</td><td>(±0.0010) 0.8749 (±0.0013)</td><td>(±0.0005) 0.9359</td><td>(±0.0007) 0.9414</td><td>(±0.0009) 0.9314</td></tr><tr><td>GlobSage</td><td colspan=\"3\">(±0.0012) (±0.0047) 0.8776(±0.0011)</td><td colspan=\"3\">(±0.0005) (±0.0006) (±0.0009) 0.9681(±0.0006)</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f5d09c56497904b9874f53707008c0a9fc33ff3d97d4bd643722125b8b83b440.jpg",
+        "image_caption": [
+            "Figure 3: Node classification results on four datasets under different $\\alpha$ and $h$ values with $M { = } 3$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/d8edc2a8c89aa1b7af1e5c37f6bdd3d4ca1a825535041dd7cb01087d1f167ea4.jpg",
+        "image_caption": [
+            "(b) Hyper-parameter study for $h$ with $\\alpha = 1$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(a) Hyper-parameter study for $\\alpha$ with $h = 1 5 \\%$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "shown in Table 2. The most important observation emerging from the results is that FedSage+ not only clearly outperforms LocSage by an average of $2 3 . 1 8 \\%$ , but also distinctly overcomes the cross-subgraph missing neighbor problem by reducing the average accuracy drop from the $2 . 1 1 \\%$ of FedSage to $1 . 2 8 \\%$ , when compared with GlobSage (absolute accuracy difference). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The significant gaps between a locally obtained classifier, i.e., LocSage or LocSage+, and a federated trained classifier, i.e., FedSage or FedSage+, assay the benefits brought by the collaboration across data owners in our distributed subgraph system. Compared to FedSage, the further elevation brought by FedSage+ corroborates the assumed degeneration brought by missing cross-subgraph links and the effectiveness of our innovatively designed NeighGen module. Notably, when the graph is relatively sparse (e.g., see Citeseer in Table 1), FedSage $^ +$ significantly exhibits its robustness in resisting the cross-subgraph information loss compared to FedSage. Note that the gaps between LocSage and LocSage $^ +$ are comparatively smaller, indicating that our NeighGen serves more than a robust GNN trainer, but is rather uniquely crucial in the subgraph FL setting. ",
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+    {
+        "type": "image",
+        "img_path": "images/340fed2f9eb7820c32f1356b372f58b89eaf0278e38ddb1d7e0e43f7fd227aa5.jpg",
+        "image_caption": [
+            "Figure 4: Label distributions on the PubMed dataset with $M { = } 5$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9a0dba0d4f8b0360ca2fc6ffa8f34e11572c41664b2723573d2450a8cc02308.jpg",
+        "image_caption": [
+            "Figure 5: Training curves of different frameworks (GlobSage provides an upper bound). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Hyper-parameter studies. We compare the downstream task performance under different $\\alpha$ and $h$ values with three data owners. Results are shown in Fig. 3, where Fig. 3 (a) shows results when $h$ is fixed as $15 \\%$ , and Fig. 3 (b) shows results under $\\alpha { = } 1$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fig. 3 (a) indicates that choosing a proper $\\alpha$ , which brings the information from other subgraphs in the system, can constantly elevate the final testing accuracy. Across different datasets, the optimal $\\alpha$ is constantly around 1, and the performance is not influenced much unless $\\alpha$ is set to extreme values like 0.1 or 10. Referring to Fig. 3 (b), we can observe that either a too-small $( 1 \\% )$ or a too-large $( 3 0 \\% )$ hiding portion can degrade the learning process. A too-small $h$ can not provide sufficient data for training NeighGen, while a too-large $h$ can result in sparse local subgraphs that harm the effective training of GraphSage. Referring back to the graph statistics in Table 1 in the paper, the portion of actual missing edges compared to the global graph is within the range of $[ 3 . 4 \\%$ , $2 7 . 8 \\% ]$ , which explains why a value like $15 \\%$ can mostly boost the performance of FedSage+. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Case studies. To further understand how FedSage and ${ \\mathrm { F e d S a g e } } +$ improve the global classifier over LocSage, we provide case study results on PubMed with five data owners in Fig. 4. For the studied scenario, each data owner only possesses about $20 \\%$ of the nodes with rather biased label distributions, as shown in Fig. 4 (a). Such bias is due to the way we synthesize the distributed subgraph system with Louvain clustering, which is also realistic in real scenarios. Local bias essentially makes it hard for any local data owner with limited training samples to obtain a generalized classifier that is globally useful. Although with $1 3 . 9 \\%$ of the links missing among the system, both FedSage and FedSage+ empower local data owners in predicting labels that closely follow the ground-true global label distribution as shown in Fig. 4 (b). The figure clearly evidences that our FL models exhibit their advantages in learning a more realistic label distribution as our goal in Section 3.1, which is consistent with the observed performances in Table 2 and our theoretical implications in Section 6. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For Cora dataset with five data owners, we visualize testing accuracy, loss convergence, and runtime along 100 epochs in obtaining $F$ with FedSage, FedSage+, GlobSage, LocSage and LocSage+. The results are presented in Fig. 5. Both FedSage and FedSage+ can consistently achieve convergence with rapidly improved testing accuracy. Regarding runtime, even though the classifier from FedSage+ learns from distributed mended subgraphs, FedSage+ does not consume observable more training time compared to FedSage. Due to the additional communications and computations in subgraph FL, both FedSage and FedSage $^ +$ consume slightly more training time compared to GlobSage. ",
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+    {
+        "type": "text",
+        "text": "6 Implications on Generalization Bound ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we provide a theoretical implication for the generalization error associated with number of training samples, i.e., nodes in the distributed subgraph system, following Graph Neural Tangent Kernel (GNTK) [7] on universal graph neural networks. Thus, we are motivated to promote the FedSage and FedSage+ algorithms that include more nodes in the global graph through collaborative training with FL. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Setting. Our explanation builds on a generalized setting, where we assume a GNN $F$ with layerwise aggregation operations and fully-connected layers with ReLU activation functions, which includes GraphSage as a special case. The weights of $F$ , $\\phi$ , is i.i.d. sampled from a multivariate Gaussian distribution $\\mathbf { N } ( 0 , I )$ . For Graph $G = \\{ \\bar { V } , E , X \\}$ , we define the kernel matrix of two nodes $u , v \\in V$ as follows. Here we consider $F$ is in the GNTK format. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Definition 6.1 (Informal version of GNTK on node classification (Definition B.2)) Considering in the overparameterized regime for an GNN $F$ , $F$ is trained using gradient descent with infinite small learning rate. Given n nodes with corresponding labels as training samples, we denote $\\boldsymbol { \\Theta } \\in \\mathbb { R } ^ { n \\times n }$ as the the kernel matrix of GNTK. $\\mathbf { \\Theta } _ { \\mathbf { \\Theta } } \\Theta _ { u v }$ is defined as ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/18416646faaf1174abb3ac90b2b23d14591b62732d9c03c75243521bef625a64.jpg",
+        "text": "$$\n\\Theta _ { u v } = \\mathbb { E } _ { \\phi \\sim { \\bf N } ( 0 , I ) } \\left[ \\left. \\frac { \\partial F ( \\phi , G , u ) } { \\partial \\phi } , \\frac { F ( \\phi , G , v ) } { \\partial \\phi } \\right. \\right] \\in \\mathbb { R } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Full expression of $\\Theta$ is shown in the Appendix B. The generalization ability in the GNTK regime depends on the kernel matrix $\\Theta$ . We present the generalization bound associated with the number of training samples $n$ in Theorem 6.2. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Theorem 6.2 (Generalization bound) Given n training samples of nodes $\\left( u _ { i } , y _ { i } \\right) _ { i = 1 } ^ { n }$ drawn i.i.d. from the global graph $G$ , consider any loss function $l : \\mathbb { R } \\times \\mathbb { R } \\mapsto [ 0 , 1 ]$ that is $^ { l }$ -Lipschitz in the first argument such that $l ( y , y ) = 0$ . With probability at least $1 - \\sigma$ and constant $c \\in ( 0 , 1 )$ , the generalization error of GNTK for node classification can be upper-bounded by ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/65d065220f1e80b8760b6520b0378618b7ece2a39e7c73bb7466bad032b75ef3.jpg",
+        "text": "$$\nL _ { { \\mathcal { D } } ( F ) } = \\mathbb { E } _ { ( u ^ { \\prime } , y ) \\sim G } [ l ( F ( G , u ^ { \\prime } ) , y ) ] \\lesssim O ( 1 / n ^ { c } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Following the generalization bound analysis in [7], we use a standard generalization bound of kernel methods of [1], which shows the upper bound of our GNTK formation error depends on that of $\\mathbf { y } ^ { \\top } \\Theta ^ { ( - 1 ) } \\mathbf { y }$ and $\\operatorname { t r } ( \\Theta )$ , where $\\mathbf { y }$ is the label vector. Appendix C shows the full version of the proofs. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Implications. We show the error bound of GNTK on node classification corresponding to the number of training samples. Under the assumptions in Definition 6.1, our theoretical result indicates that more training samples bring down the generalization error , which provides plausible support for our goal of building a globally useful classifier through FL in Eq. (3.1). Such implications are also consistent with our experimental findings in Fig. 4 where our FedSage and FedSage+ models can learn more generalizable classifiers that follow the label distributions of the global graph through involving more training nodes across different subgraphs. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "7 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This work aims at obtaining a generalized node classification model in a distributed subgraph system without direct data sharing. To tackle the realistic yet unexplored issue of missing cross-subgraph links, we design a novel missing neighbor generator NeighGen with the corresponding local and federated training processes. Experimental results evidence the distinguished elevation brought by our FedSage and FedSage $^ +$ frameworks , which is consistent with our theoretical implications. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Though FedSage manifests advantageous performance, it confronts additional communication cost and potential privacy concerns. As communications are vital for federated learning, properly reducing communication and rigorously guaranteeing privacy protection in the distributed subgraph system can both be promising future directions. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            838,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This work is partially supported by the internal funding and GPU servers provided by the Computer Science Department of Emory University. We thank Dr. Pan Li from Purdue University for the suggestions on the design of our NeighGen mechanism. ",
+        "bbox": [
+            176,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References   \n[1] Peter L Bartlett and Shahar Mendelson. Rademacher and gaussian complexities: Risk bounds and structural results. JMLR, 3:463–482, 2002.   \n[2] Vincent D Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. Fast unfolding of communities in large networks. JSTAT, 2008(10):P10008, 2008.   \n[3] Liang Chen, Jintang Li, Qibiao Peng, Yang Liu, Zibin Zheng, and Carl Yang. Understanding structural vulnerability in graph convolutional networks. In IJCAI, 2021.   \n[4] Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. Adversarial attack on graph structured data. In ICML, 2018.   \n[5] CSIRO’s Data61. Stellargraph machine learning library. https://github.com/ stellargraph/stellargraph, 2018.   \n[6] Qi Dou, Tiffany Y So, Meirui Jiang, Quande Liu, Varut Vardhanabhuti, Georgios Kaissis, Zeju Li, Weixin Si, Heather HC Lee, Kevin Yu, et al. Federated deep learning for detecting covid-19 lung abnormalities in ct: a privacy-preserving multinational validation study. NPJ digital medicine, 4:1–11, 2021.   \n[7] Simon S. Du, Kangcheng Hou, Ruslan Salakhutdinov, Barnabás Póczos, Ruosong Wang, and Keyulu Xu. Graph neural tangent kernel: Fusing graph neural networks with graph kernels. In NeurIPS, 2019.   \n[8] Alireza Fallah, Aryan Mokhtari, and Asuman Ozdaglar. Personalized federated learning: A meta-learning approach. NeurIPS, 2020.   \n[9] Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. In ICML, 2017.   \n[10] Ross Girshick. Fast r-cnn. In ICCV, 2015.   \n[11] William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NeurIPS, 2017.   \n[12] Chaoyang He, Keshav Balasubramanian, Emir Ceyani, Carl Yang, Han Xie, Lichao Sun, Lifang He, Liangwei Yang, Philip S Yu, Yu Rong, Peilin Zhao, Junzhou Huang, Murali Annavaram, and Salman Avestimehr. Fedgraphnn: A federated learning system and benchmark for graph neural networks. arXiv preprint arXiv:2104.07145, 2021.   \n[13] Chaoyang He, Shen Li, Mahdi Soltanolkotabi, and Salman Avestimehr. Pipetransformer: Automated elastic pipelining for distributed training of transformers. arXiv preprint arXiv:2102.03161, 2021.   \n[14] Timothy M Hospedales, Antreas Antoniou, Paul Micaelli, and Amos J Storkey. Meta-learning in neural networks: A survey. TPAMI, 2021.   \n[15] Wei Jin, Yao Ma, Xiaorui Liu, Xianfeng Tang, Suhang Wang, and Jiliang Tang. Graph structure learning for robust graph neural networks. In SIGKDD, 2020.   \n[16] Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.   \n[17] Tian Li, Anit Kumar Sahu, Ameet Talwalkar, and Virginia Smith. Federated learning: Challenges, methods, and future directions. IEEE SPM, 37:50–60, 2020.   \n[18] Xinle Liang, Yang Liu, Tianjian Chen, Ming Liu, and Qiang Yang. Federated transfer reinforcement learning for autonomous driving. arXiv preprint arXiv:1910.06001, 2019.   \n[19] Quande Liu, Cheng Chen, Jing Qin, Qi Dou, and Pheng-Ann Heng. Feddg: Federated domain generalization on medical image segmentation via episodic learning in continuous frequency space. arXiv preprint arXiv:2103.06030, 2021.   \n[20] Gongxu Luo, Jianxin Li, Hao Peng, Carl Yang, Lichao Sun, Philip Yu, and Lifang He. Graph entropy guided node embedding dimension selection for graph neural networks. In IJCAI, 2021.   \n[21] Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. In AISTATS, 2017.   \n[22] Galileo Namata, Ben London, Lise Getoor, and Bert Huang. Query-driven active surveying for collective classification. In MLG workshop, 2012.   \n[23] Alex Nichol, Joshua Achiam, and John Schulman. On first-order meta-learning algorithms. arXiv preprint arXiv:1803.02999, 2018.   \n[24] Saif Ur Rehman, Asmat Ullah Khan, and Simon Fong. Graph mining: A survey of graph mining techniques. In ICDIM, 2012.   \n[25] Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Galligher, and Tina EliassiRad. Collective classification in network data. AI magazine, 29(3):93–93, 2008.   \n[26] Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Günnemann. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018.   \n[27] Chuhan Wu, Fangzhao Wu, Yang Cao, Yongfeng Huang, and Xing Xie. Fedgnn: Federated graph neural network for privacy-preserving recommendation. arXiv preprint arXiv:2102.04925, 2021.   \n[28] Man Wu, Shirui Pan, Chuan Zhou, Xiaojun Chang, and Xingquan Zhu. Unsupervised domain adaptive graph convolutional networks. In WWW, 2020.   \n[29] Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and S Yu Philip. A comprehensive survey on graph neural networks. TNNLS, 2020.   \n[30] Han Xie, Jing Ma, Li Xiong, and Carl Yang. Federated graph classification over non-iid graphs. In NeurIPS, 2021.   \n[31] Carl Yang, Haonan Wang, Ke Zhang, Liang Chen, and Lichao Sun. Secure deep graph generation with link differential privacy. In IJCAI, 2021.   \n[32] Carl Yang, Yuxin Xiao, Yu Zhang, Yizhou Sun, and Jiawei Han. Heterogeneous network representation learning: A unified framework with survey and benchmark. In TKDE, 2020.   \n[33] Carl Yang, Jieyu Zhang, and Jiawei Han. Co-embedding network nodes and hierarchical labels with taxonomy based generative adversarial nets. In ICDM, 2020.   \n[34] Carl Yang, Peiye Zhuang, Wenhan Shi, Alan Luu, and Pan Li. Conditional structure generation through graph variational generative adversarial nets. In NeurIPS, 2019.   \n[35] Qiang Yang, Yang Liu, Tianjian Chen, and Yongxin Tong. Federated machine learning: Concept and applications. TIST, 10(2):1–19, 2019.   \n[36] Yizhou Zhang, Guojie Song, Lun Du, Shuwen Yang, and Yilun Jin. DANE: domain adaptive network embedding. In IJCAI, 2019.   \n[37] Dingyuan Zhu, Ziwei Zhang, Peng Cui, and Wenwu Zhu. Robust graph convolutional networks against adversarial attacks. In SIGKDD, 2019.   \n[38] Qi Zhu, Yidan Xu, Haonan Wang, Chao Zhang, Jiawei Han, and Carl Yang. Transfer learning of graph neural networks with ego-graph information maximization. In NeurIPS, 2021.   \n[39] Xinghua Zhu, Jianzong Wang, Zhenhou Hong, and Jing Xiao. Empirical studies of institutional federated learning for natural language processing. In EMNLP, 2020.   \n[40] Daniel Zügner, Amir Akbarnejad, and Stephan Günnemann. Adversarial attacks on neural networks for graph data. In SIGKDD, 2018.   \n[41] Daniel Zügner and Stephan Günnemann. Adversarial attacks on graph neural networks via meta learning. In ICLR, 2019.   \n[42] Daniel Zügner and Stephan Günnemann. Certifiable robustness and robust training for graph convolutional networks. In SIGKDD, 2019. ",
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parse/train/SylKikSYDH/SylKikSYDH.md

@@ -0,0 +1,358 @@
+# COMPRESSIVE TRANSFORMERS FOR LONG-RANGE SEQUENCE MODELLING
+
+Jack W. Rae∗∗ † ‡ Anna Potapenko\*† Siddhant M. Jayakumar† Chloe Hillier†
+
+Timothy P. Lillicrap†‡
+
+# ABSTRACT
+
+We present the Compressive Transformer, an attentive sequence model which compresses past memories for long-range sequence learning. We find the Compressive Transformer obtains state-of-the-art language modelling results in the WikiText-103 and Enwik8 benchmarks, achieving $1 7 . 1 \ \mathrm { p p l }$ and 0.97 bpc respectively. We also find it can model high-frequency speech effectively and can be used as a memory mechanism for RL, demonstrated on an object matching task. To promote the domain of long-range sequence learning, we propose a new openvocabulary language modelling benchmark derived from books, PG-19.
+
+# 1 INTRODUCTION
+
+Humans have a remarkable ability to remember information over long time horizons. When reading a book, we build up a compressed representation of the past narrative, such as the characters and events that have built up the story so far. We can do this even if they are separated by thousands of words from the current text, or long stretches of time between readings. During daily life, we make use of memories at varying time-scales: from locating the car keys, placed in the morning, to recalling the name of an old friend from decades ago. These feats of memorisation are not achieved by storing every sensory glimpse throughout one’s lifetime, but via lossy compression. We aggressively select, filter, or integrate input stimuli based on factors of surprise, perceived danger, or repetition — amongst other signals (Richards and Frankland, 2017).
+
+Memory systems in artificial neural networks began with very compact representations of the past. Recurrent neural networks (RNNs, Rumelhart et al. (1986)) learn to represent the history of observations in a compressed state vector. The state is compressed because it uses far less space than the history of observations — the model only preserving information that is pertinent to the optimization of the loss. The LSTM (Hochreiter and Schmidhuber, 1997) is perhaps the most ubiquitous RNN variant; it uses learned gates on its state vector to determine what information is stored or forgotten from memory.
+
+However since the LSTM, there has been great benefit discovered in not bottlenecking all historical information in the state, but instead in keeping past activations around in an external memory and attending to them. The Transformer (Vaswani et al., 2017) is a sequence model which stores the hidden activation of every time-step, and integrates this information using an attention operator (Bahdanau et al., 2014). The Transformer will thus represent the past with a tensor (depth $\times$ memory size $\times$ dimension) of past observations that is, in practice, an order of magnitude larger than an LSTM’s hidden state. With this granular memory, the Transformer has brought about a step-change in state-of-the-art performance, within machine translation (Vaswani et al., 2017), language modelling (Dai et al., 2019; Shoeybi et al., 2019), video captioning (Zhou et al., 2018), and a multitude of language understanding benchmarks (Devlin et al., 2018; Yang et al., 2019) amongst others.
+
+One drawback in storing everything is the computational cost of attending to every time-step and the storage cost of preserving this large memory. Several works have focused on reducing the computational cost of attention with sparse access mechanisms (Rae et al., 2016; Child et al., 2019;
+
+Sukhbaatar et al., 2019; Lample et al., 2019). However sparse attention does not solve the storage problem, and often requires custom sparse kernels for efficient implementation. Instead we look back to the notion of compactly representing the past. We show this can be built with simple dense linear-algebra components, such as convolutions, and can reduce both the space and compute cost of our models.
+
+We propose the Compressive Transformer, a simple extension to the Transformer which maps past hidden activations (memories) to a smaller set of compressed representations (compressed memories). The Compressive Transformer uses the same attention mechanism over its set of memories and compressed memories, learning to query both its short-term granular memory and longer-term coarse memory. We observe this improves the modelling of text, achieving state-of-the-art results in character-based language modelling — 0.97 bpc on Enwik8 from the Hutter Prize (Hutter, 2012) — and word-level language modelling — 17.1 perplexity on WikiText-103 (Merity et al., 2016). Specifically, we see the Compressive Transformer improves the modelling of rare words.
+
+We show the Compressive Transformer works not only for language, but can also model the waveform of high-frequency speech with a trend of lower likelihood than the TransformerXL and Wavenet (Oord et al., 2016) when trained over 400,000 steps. We also show the Compressive Transformer can be used as a memory component within an RL agent, IMPALA (Espeholt et al., 2018), and can successfully compress and make use of past observations.
+
+Furthermore we present a new book-level language-modelling benchmark PG-19, extracted from texts in Project Gutenberg1, to further promote the direction of long-context sequence modelling. This is over double the size of existing LM benchmarks and contains text with much longer contexts.
+
+# 2 RELATED WORK
+
+There have been a variety of recent attempts to extend the range of attention, particularly in the Transformer, or to replace the attention operation with something less expensive. Wu et al. (2019) show that a convolution-like operator that runs in linear time can actually exceed the performance of the quadratic-time self-attention layer in the Transformer at sentence-to-sentence translation and sentence-level language modelling. However such a mechanism inhibits the flow of information across a large number of time-steps for a given layer, and has not shown to be beneficial for longrange sequence modelling.
+
+Dai et al. (2019) propose the TransformerXL, which keeps past activations around in memory. They also propose a novel relative positional embedding scheme which they see outperforms the Transformer’s original absolute positional system. Our model incorporates both of these ideas, the use of a memory to preserve prior activations and their relative positional embedding scheme.
+
+The Sparse Transformer (Child et al., 2019) uses fixed sparse attention masks to attend to roughly√ $\sqrt { n }$ locations in memory. This approach still requires keeping all memories around during training, however with careful re-materialization of activations and custom kernels, the authors are able to train the model with a reasonable budget of memory and compute. When run on Enwik8, the much larger attention window of 8, 000 improves model performance, but overall it does not significantly outperform a simpler TransformerXL with a much smaller attention window.
+
+The use of dynamic attention spans is explored in Sukhbaatar et al. (2019). Different attention heads can learn to have shorter or longer spans of attention — and they observe this achieves state-ofthe-art in character-based language modelling. This idea could easily be combined with our contribution — a compressive memory. However an efficient implementation is not possible on current dense-linear-algebra accelerators, such as Google’s TPUs, due to the need for dynamic and sparse computation. Our approach builds on simple dense linear algebra components, such as convolutions.
+
+# 3 MODEL
+
+We present the Compressive Transformer, a long-range sequence model which compacts past activations into a compressed memory2. The Compressive Transformer is a variant of the Transformer (Vaswani et al., 2017), a deep residual network which only uses attention to propagate information over time (namely multi-head attention). We build on the ideas of the TransformerXL (Dai et al., 2019) which maintains a memory of past activations at each layer to preserve a longer history of context. The TransformerXL discards past activations when they become sufficiently old (controlled by the size of the memory). The key principle of the Compressive Transformer is to compress these old memories, instead of discarding them, and store them in an additional compressed memory.
+
+![](images/0acd7690aaac7bffb9eb11c081c43adc68daad2cbdc94c5997f547d73d2d83e7.jpg)  
+Figure 1: The Compressive Transformer keeps a fine-grained memory of past activations, which are then compressed into coarser compressed memories. The above model has three layers, a sequence length ${ n _ { s } = 3 }$ , memory size ${ n _ { m } } = 6$ , compressed memory size $n _ { c m } = 6$ . The highlighted memories are compacted, with a compression function $f _ { c }$ per layer, to a single compressed memory — instead of being discarded at the next sequence. In this example, the rate of compression $c = 3$ .
+
+# 3.1 DESCRIPTION
+
+We define $n _ { m }$ and $n _ { c m }$ to be the number of respective memory and compressive memory slots in the model per layer. The overall input sequence $\mathcal { S } = x _ { 1 } , x _ { 2 } , \dotsc , x _ { | s | }$ represents input observations (e.g. tokens from a book). These are split into fixed-size windows of size $n _ { s }$ for the model to process in parallel. The model observes $\mathbf { x } = x _ { t } , \ldots , x _ { t + n _ { s } }$ at time $t$ , which we refer to as the sequence (e.g. in Figure 1). As the model moves to the next sequence, its $n _ { s }$ hidden activations are pushed into a fixed-sized FIFO memory (like the TransformerXL) of size $n _ { m }$ . The oldest $n _ { s }$ activations in memory are evicted, but unlike the TransformerXL we do not discard them. Instead we apply a compression operation, $f _ { c } : \mathbf { R } ^ { n _ { s } \times d }  \mathbf { R } ^ { \lfloor \frac { n _ { s } } { c } \rfloor \times d }$ , mapping the $n _ { s }$ oldest memories to $\lfloor \frac { n _ { s } } { c } \rfloor$ compressed memories which we then store in a secondary FIFO compressed memory of size $n _ { c m }$ . $d$ denotes the hidden size of activations and $c$ refers to the compression rate, a higher value indicates more coarse-grained compressed memories. The overall temporal range of the model becomes $l \times \left( n _ { s } + n _ { m } + c * n _ { c m } \right)$ , where $l$ is the number of layers — as discussed in Supplementary Section A. The full architecture is described in Algorithm 1.
+
+# Algorithm 1 Compressive Transformer
+
+At time zero   
+1: $\mathbf { m _ { 0 } } \gets \mathbf { 0 }$ // Initialize memory to zeros $( l \times n _ { m } \times d )$   
+2: $\mathbf { c m _ { 0 } } \gets \mathbf { 0 }$ // Initialize compressed memory to zeros $( l \times n _ { c m } \times d )$   
+At time t   
+3: $\mathbf { h } ^ { ( 1 ) }  \mathbf { x W _ { e m b } }$ // Embed input sequence $( n _ { s } \times d )$   
+4: for layer $i = 1 , 2 , \ldots , l$ do   
+5: mem(i) ← concat(cm(i)t , m(i)t ) $I / \left( \left( n _ { c m } + n _ { m } \right) \times d \right)$   
+6: $\tilde { \mathbf { a } } ^ { ( \mathbf { i } ) } \gets$ multihead attention(i)(h(i), mem(i)t ) // MHA over both mem types $( n _ { s } \times d )$   
+7: a(i) ← layer norm(˜a(i) + h(i)) // Regular skip $^ +$ layernorm $( n _ { c m } \times d )$   
+8: $\mathbf { o l d . m e m ^ { ( i ) } \gets m _ { t } ^ { ( i ) } } [ : n _ { s } ]$ // Oldest memories to be forgotten $( n _ { s } \times d )$   
+9: new $\mathbf { c m } ^ { ( \mathbf { i } ) } \gets f _ { c } ^ { ( i ) } ( \mathbf { o l d . m e m ^ { ( \mathbf { i } ) } } )$ // Compress oldest memories by factor $c \left( \left\lfloor { \frac { n _ { s } } { c } } \right\rfloor \times d \right)$   
+10: $\mathbf { m _ { t + 1 } ^ { ( i ) } } \gets \mathrm { c o n c a t } ( \mathbf { m _ { t } ^ { ( i ) } } , \mathbf { h ^ { ( i ) } } ) [ - n _ { m } \cdot ]$ // Update memory $( n _ { m } \times d )$   
+11: $\mathbf { c m _ { t } ^ { ( i ) } } \gets \mathrm { c o n c a t } ( \mathbf { c m _ { t } ^ { ( i ) } } , \mathbf { n e w . c m ^ { ( i ) } } ) [ - n _ { c m } :$ :] // Update compressed memory $( n _ { c m } \times d )$   
+12: $\mathbf { h } ^ { ( \mathbf { i } + 1 ) } \gets \mathrm { l a y e r . n o r m } ( \mathrm { m l p } ^ { ( i ) } ( \mathbf { a } ^ { ( \mathbf { i } ) } ) + \mathbf { a } ^ { ( \mathbf { i } ) } )$ // Mixing MLP $( n _ { s } \times d )$
+
+# Algorithm 2 Attention-Reconstruction Loss
+
+<table><tr><td colspan="3">1: Lattn ←0</td></tr><tr><td>2:</td><td>for layeri=1,2,...,l do</td><td></td></tr><tr><td>3:</td><td>h(i) ← stop-gradient(h(i))</td><td>// Stop compression grads from passing...</td></tr><tr><td>4:</td><td>old_mem(i)← stop-gradient(old_mem(i))</td><td>//..into transformer network.</td></tr><tr><td>5:</td><td>Q,K,V ← stop-gradient(attention params at layer i)// Re-use attention weight matrices.</td><td></td></tr><tr><td>6:</td><td>def attn(h,m) ← σ((hQ) (mK))(mV)</td><td>// Use content-based attention (no relative).</td></tr><tr><td>7:</td><td>new_cm(i) ← f(𝑖)(old_mem(i))</td><td>// Compression network (to be optimized).</td></tr><tr><td>8:</td><td>Lattn ← Lattn + |lttn(h(i),old-mem(i)) -attn(h(i),new_cm(i)|l2</td><td></td></tr></table>
+
+# 3.2 COMPRESSION FUNCTIONS AND LOSSES
+
+For choices of compression functions $f _ { c }$ we consider (1) max/mean pooling, where the kernel and stride is set to the compression rate $c$ ; (2) 1D convolution also with kernel & stride set to $c$ ; (3) dilated convolutions; (4) most-used where the memories are sorted by their average attention (usage) and the most-used are preserved. The pooling is used as a fast and simple baseline. The mostused compression scheme is inspired from the garbage collection mechanism in the Differentiable Neural Computer (Graves et al., 2016) where low-usage memories are erased. The convolutional compression functions contain parameters which require training.
+
+One can train the compression network using gradients from the loss; however for very old memories this requires backpropagating-through-time (BPTT) over long unrolls. As such we also consider some local auxiliary compression losses. We consider an auto-encoding loss where we reconstruct the original memories from the compressed memories $\mathcal { L } ^ { a e } = | | \mathbf { o l d . m e m ^ { ( i ) } } - g ( \mathbf { n e w . c m ^ { ( i ) } } ) | | _ { 2 }$ , where $\overline { { g } } \ : \ \mathbb { R } ^ { \frac { n _ { s } } { c } \times d } \  \ \mathbb { R } ^ { n _ { s } \times d }$ is learned. This is a lossless compression objective — it attempts to retain all information in memory. We also consider an attention-reconstruction loss described in Algorithm 2 which reconstructs the content-based attention over memory, with content-based attention over the compressed memories. This is a lossy objective, as information that is no longer attended to can be discarded, and we found this worked best. We stop compression loss gradients from passing into the main network as this prevents learning. Instead the Transformer optimizes the task objective and the compression network optimizes the compression objective conditioned on task-relevant representations; there is no need to mix the losses with a tuning constant.
+
+# 4 PG-19 BENCHMARK
+
+As models begin to incorporate longer-range memories, it is important to train and benchmark them on data containing larger contexts. Natural language in the form of text provides us with a vast repository of data containing long-range dependencies, that is easily accessible. We propose a new language modelling benchmark, PG-19, using text from books extracted from Project Gutenberg 3. We select Project Gutenberg books which were published over 100 years old, i.e. before 1919 (hence the name PG-19) to avoid complications with international copyright, and remove short texts. The dataset contains 28, 752 books, or $1 1 G B$ of text — which makes it over double the size of BookCorpus and Billion Word Benchmark.
+
+# 4.1 RELATED DATASETS
+
+The two most benchmarked word-level language modelling datasets either stress the modelling of stand-alone sentences (Billion Word Benchmark from Chelba et al. (2013)) or the modelling of a small selection of short news articles (Penn Treebank processed by Mikolov et al. (2010)). Merity et al. (2016) proposed the WikiText-103 dataset, which contains text from a high quality subset of English-language wikipedia articles. These articles are on average 3, 600 words long. This dataset has been a popular recent LM benchmark due to the potential to exploit longer-range dependencies (Grave et al., 2016; Rae et al., 2018; Bai et al., 2018b). However recent Transformer models, such as the TransformerXL (Dai et al., 2019) appear to be able to exploit temporal dependencies on the order of several thousand words. This motivates a larger dataset with longer contexts.
+
+Table 1: Comparison to existing popular language modelling benchmarks.   
+
+<table><tr><td></td><td>Avg. length (words)</td><td>Train Size</td><td>Vocab</td><td>Type</td></tr><tr><td>1B Word</td><td>27</td><td>4.15GB</td><td>793K</td><td>News (sentences)</td></tr><tr><td>Penn Treebank</td><td>355</td><td>5.1MB</td><td>10K</td><td>News (articles)</td></tr><tr><td>WikiText-103</td><td>3.6K</td><td>515MB</td><td>267K</td><td>Wikipedia (articles)</td></tr><tr><td>PG-19</td><td>69K</td><td>10.9GB</td><td>(open)</td><td>Books</td></tr></table>
+
+Books are a natural choice of long-form text, and provide us with stylistically rich and varied natural language. Texts extracted from books have been used for prior NLP benchmarks; such as the Children’s Book Test (Hill et al., 2015) and LAMBADA (Paperno et al., 2016). These benchmarks use text from Project Gutenberg, an online repository of books with expired US copyright, and BookCorpus (Zhu et al., 2015), a prior dataset of $1 1 K$ unpublished (at time of authorship) books. CBT and LAMBADA contain extracts from books, with a specific task of predicting held-out words. In the case of LAMBADA the held-out word is specifically designed to be predictable for humans with access to the full textual context — but difficult to guess with only a local context.
+
+CBT and LAMBADA are useful for probing the linguistic intelligence of models, but are not ideal for training long-range language models from scratch as they truncate text extracts to at most a couple of paragraphs, and discard a lot of the books’ text. There has been prior work on training models on book data using BookCorpus directly (e.g. BERT from Devlin et al. (2018)) however BookCorpus is no longer distributed due to licensing issues, and the source of data is dynamically changing — which makes exact benchmarking difficult over time.
+
+The NarrativeQA Book Comprehension Task (Kocisk ˇ y et al., 2018) uses Project Gutenberg texts \` paired with Wikipedia articles, which can be used as summaries. Due to the requirement of needing a corresponding summary, NarrativeQA contains a smaller selection of books: 1,527 versus the 28,752 books in PG-19. However it is reasonable that PG-19 may be useful for pre-training book summarisation models.
+
+# 4.2 STATISTICS
+
+A brief comparison of PG-19 to other LM datasets can be found in Table 1. We intentionally do not limit the vocabulary by unk-ing rare words, and release the dataset as an open-vocabulary benchmark. To compare models we propose to continue measuring the word-level perplexity. This can still be computed for any chosen character-based, byte-based or subword-based scheme. To do this, one calculates the total cross-entropy loss $\begin{array} { r } { L = - \dot { \sum } _ { t } \log ( p _ { t } | p _ { < t } ) } \end{array}$ over the given validation or test subset using a chosen tokenization scheme, and then one normalizes this value by the number of words: $L / n _ { w o r d s }$ where $n _ { w o r d s }$ is the total number of words in the given subset, taken from Table 2. The word-level perplexity is thus $e ^ { L / n _ { w o r d s } }$ . For sake of model comparisons, it is important to use the exact number of words computed in Table 2 as the normalisation constant.
+
+Alongside quantitative analyses, we build an LDA topic model (Blei et al., 2003) for a qualitative inspection of the text. We present key words for several topics in the Supplementary Table 10. These topics include art, education, naval exploration, geographical description, war, ancient civilisations, and more poetic topics concerning the human condition — love, society, religion, virtue etc. This contrasts to the more objective domains of Wikipedia and news corpora.
+
+# 5 EXPERIMENTS
+
+We optimised all models with Adam (Kingma and Ba, 2014). We used a learning rate schedule with a linear warmup from 1e-6 to 3e-4 and a cosine decay back down to 1e- $\mathbf { \nabla \cdot } n \mathbf { 6 }$ . For characterbased LM we used 4, 000 warmup steps with 100, 000 decay steps, and for word-based LM we used 16, 000 warmup steps with 500, 000 decay steps. We found that decreasing the optimisation update frequency helped (see Section 5.5.1), namely we only applied parameter updates every 4 steps after $6 0 , 0 0 0$ iterations. However we found the models would optimise well for a range of warmup/warmdown values. We clipped the gradients to have a norm of at most 0.1, which was crucial to successful optimisation.
+
+Table 2: PG-19 statistics split by subsets.   
+
+<table><tr><td></td><td>Train</td><td>Valid.</td><td>Test</td></tr><tr><td>#books</td><td>28.602</td><td>50</td><td>100</td></tr><tr><td># words</td><td>1,973,136,207</td><td>3,007,061</td><td>6,966,499</td></tr></table>
+
+Table 3: Eval. perplexities on PG-19.   
+
+<table><tr><td></td><td>Valid.</td><td>Test</td></tr><tr><td>36L TransformerXL</td><td>45.5</td><td>36.3</td></tr><tr><td>36L Compressive Transf.</td><td>43.4</td><td>33.6</td></tr></table>
+
+Table 4: State-of-the-art results on Enwik8.   
+
+<table><tr><td>Model 7L LSTM(Graves,2013)</td><td>BPC 1.67</td></tr><tr><td>LN HyperNetworks Ha et al. (2016) LN HM-LSTM Chung et al. (2016) ByteNet (Kalchbrenner et al.,2016) RHN Zilly et al. (2017) mLSTM Krause et al. (2016) 64L Transf. Al-Rfou et al. (2019) 24L TXL (Dai et al.,2019) Sparse Transf.(Child et al.,2019) Adaptive Transf. (Sukhbaatar et al.,2019)</td><td>1.34 1.32 1.31 1.27 1.24 1.06 0.99 0.991 0.98</td></tr><tr><td>24L TXL (ours) 24L Compressive Transformer</td><td>0.98 0.97</td></tr></table>
+
+Table 5: Compression approaches on Enwik8.   
+
+<table><tr><td>Compression fn</td><td>Compression loss</td><td>BPC</td></tr><tr><td>Conv</td><td>BPTT</td><td>0.996</td></tr><tr><td>Max Pooling</td><td>N/A</td><td>0.986</td></tr><tr><td>Conv</td><td>Auto-encoding</td><td>0.984</td></tr><tr><td>Mean Pooling</td><td>N/A</td><td>0.982</td></tr><tr><td>Most-used</td><td>N/A</td><td>0.980</td></tr><tr><td>Dilated conv</td><td>Attention</td><td>0.977</td></tr><tr><td>Conv</td><td>Attention</td><td>0.973</td></tr></table>
+
+# 5.1 PG-19
+
+We benchmark the Compressive Transformer against the TransformerXL on the newly proposed PG19 books dataset. Because it is open-vocabulary, we train a subword vocabulary of size 32000 with SubwordTextEncoder from the tfds package in TensorFlow and use the dataset statistics to compute word-level perplexity, as described in Section 4.2. We train a 36 layer Compressive Transformer with a window size of 512, both memory and compressed memory size of 512, and compression rate $C =$ 2. We compare this to a 36 layer TransformerXL trained with window size 512 and attention window 1024. The model was trained on 256 TPUv3 cores with a total batch size of 512 and converged after processing around 100 billion subword tokens. We display the results in Table 3 where we see the Compressive Transformer obtains a test perplexity of 33.6 versus the TransformerXL’s 36.3. Despite the dataset size, it is clearly a challenging domain. This can suit as a first baseline on the proposed long-range language modelling benchmark. We show samples from this model in Supplementary Section F. The model is able to generate long-form narrative of varying styles: from character dialogue, first person diary entries, to descriptive third-person text.
+
+# 5.2 ENWIK8
+
+We compare the TransformerXL and the Compressive Transformer on the standard character-level language modelling benchmark Enwiki8 taken from the Hutter Prize (Hutter, 2012), which contains 100M bytes of unprocessed Wikipedia text. We select the first 90MB for training, 5MB for validation, and the latter 5MB for testing — as per convention. We train 24-layer models with a sequence window size of 768. During training, we set the TransformerXL’s memory size to 2304, and for the Compressive Transformer we use memory of size 768 and compressed memory of size 1152 with compression rate $C = 3$ . During evaluation, we increased the TransformerXL memory size to 4096 and the compressed memory in our model to 3072 (after sweeping over the validation set), obtaining the numbers reported in Table 4. We show the effect of scaling the compressed memory size and evaluation performance in Supplementary Section C. The proposed model achieves the new state-of-the-art on this dataset with 0.97 bits-per-character.
+
+We compare compression functions and the use of auxiliary losses in Table 5. We sweep over compression rates of 2, 3, and 4 and report results with the best performing value for each row. BPTT signifies that no auxiliary compression loss was used to train the network other than the overall training loss. To feed gradients into the compression function we unrolled the model over double the sequence length and halved the batch size to fit the larger unroll into memory.
+
+Table 6: Validation and test perplexities on WikiText-103.   
+
+<table><tr><td></td><td>Valid.</td><td>Test</td></tr><tr><td>LSTM (Graves et al., 2014)</td><td></td><td>48.7</td></tr><tr><td>Temporal CNN (Bai et al.,2018a)</td><td>=</td><td>45.2</td></tr><tr><td>GCNN-14 (Dauphin et al.,2016)</td><td>=</td><td>37.2</td></tr><tr><td>Quasi-RNN Bradbury et al. (2016)</td><td>32</td><td>33</td></tr><tr><td>RMC (Santoro et al., 2018)</td><td>30.8</td><td>31.9</td></tr><tr><td>LSTM+Hebb. (Rae et al., 2018)</td><td>29.0</td><td>29.2</td></tr><tr><td>Transformer (Baevski and Auli,2019)</td><td>-</td><td>18.7</td></tr><tr><td>18L TransformerXL,M=384 (Dai et al.,2019)</td><td>-</td><td>18.3</td></tr><tr><td>18L TransformerXL,M=1024(ours)</td><td>=</td><td>18.1</td></tr><tr><td>18L Compressive Transformer,M=1024</td><td>16.0</td><td>17.1</td></tr></table>
+
+# 5.3 WIKITEXT-103
+
+We train an eighteen-layered Compressive Transformer on the closed-vocabulary word-level language modelling benchmark WikiText-103, which contains articles from Wikipedia. We train the model with a compressed memory size, memory size, and a sequence window size all equal to 512. We trained the model over 64 Tensor Processing Units (TPU) v3 with a batch size of 2 per core — making for a total batch size of 128. The model converged in a little over 12 hours. We found the single-layer convolution worked best, with a compression rate of $c = 4$ . This model obtained 17.6 perplexity on the test set. By tuning the memory size over the validation set — setting the memory size to 500, and compressed memory size to 1, 500 — we obtain 17.1 perplexity. This is 1.2 perplexity points over prior state of the art, and means the model places a $\approx 5 \%$ higher probability on the correct word over the prior SotA TransformerXL.
+
+It is worth noting that in Table 6 we do not list methods that use additional training data, or that make use of test-time labels to continue training the model on the test set (known as dynamic evaluation (Graves, 2013)). If we incorporate a very naive dynamic evaluation approach of loading a model checkpoint and continuing training over one epoch of the test set, then we obtain a test perplexity of 16.1. This is slightly better than the published 16.4 from Krause et al. (2019) — which uses a more sophisticated dynamic evaluation approach on top of the TransformerXL. However in most settings, one does not have access to test-time labels — and thus we do not focus on this setting. Furthermore there has been great progress in showing that more data equates to much better language modelling; Shoeybi et al. (2019) find a large transformer 8B-parameter transformer trained on 170GB of text obtains 10.7 word-level perplexity on WikiText-103. However it is not clear to what extent the WikiText-103 test set may be leaked inside these larger training corpora. For clarity of model comparisons, we compare to published results trained on the WikiText-103 training set.
+
+We break perplexity down by word frequency in Table 7 and see the Compressive Transformer makes only a small modelling improvement for frequent words $( 2 . 6 \%$ over the TransformerXL baseline) but obtains a much larger improvement of $\approx 2 0 \%$ for infrequent words. Furthermore, we see $\mathbf { 1 0 X }$ improvement in modelling rare words over the prior state-of-the-art LSTM language model published in 2018 — which demonstrates the rate of progress in this area.
+
+# 5.4 COMPRESSIBILITY OF LAYERS
+
+We can use compression to better understand the model’s mode of operation. We inspect how compressible Transformer’s activations are as they progress through higher layers in the network. One may expect representations to become more difficult to compress at higher layers, if more semantic information is represented there. We monitor the compression loss at each layer of our best-performing Compressive Transformer models trained on Enwik8 and WikiText-103 and display these in Supplementary Section B Figure 6. We note that the compression loss is about one order of magnitude higher for word-level language modelling (WikiText-103) over character-level langauge modelling (Enwik8). Furthermore the first layer of the Transformer is highly compressible. However there is not a clear trend of compression cost increasing with layer depth.
+
+Table 7: WikiText-103 test perplexity broken down by word frequency buckets. The most frequent bucket is words which appear in the training set more than 10, 000 times, displayed on the left. For reference, a uniform model would have perplexity $| V | = 2 . 6 e 5$ for all frequency buckets. \*LSTM comparison from Rae et al. (2018)   
+
+<table><tr><td></td><td>&gt;10K</td><td>1K-10K</td><td>100－1K</td><td>&lt;100</td><td>All</td></tr><tr><td>LSTM*</td><td>12.1</td><td>219</td><td>1,197</td><td>9,725</td><td>36.4</td></tr><tr><td>TransformerXL(ours)</td><td>7.8</td><td>61.2</td><td>188</td><td>1,123</td><td>18.1</td></tr><tr><td>Compressive Transformer</td><td>7.6</td><td>55.9</td><td>158</td><td>937</td><td>17.1</td></tr><tr><td>Relative gain over TXL</td><td>2.6%</td><td>9.5%</td><td>21%</td><td>19.9%</td><td>5.8%</td></tr></table>
+
+![](images/91df5905b3cf9156b5c7b63213402e2aaf75a6c641a804dccf9a8f9fec4a3a8d.jpg)  
+Figure 2: Attention weight on Enwik8. Average attention weight from the sequence over the compressed memory (oldest), memory, and sequence (newest) respectively. The sequence self-attention is causally masked, so more attention is placed on earlier elements in the sequence. There is an increase in attention at the transition from memory to compressed memory.
+
+![](images/0c169d95a9819eba8789424d7e7a0246e84e7fc6301d76f70dcb4d65a634b4eb.jpg)  
+Figure 3: Learning rate analysis. Reducing the learning rate (e.g. to zero) during training (on Enwik8) harms training performance. Reducing the frequency of optimisation updates (effectively increasing the batch size) is preferable.
+
+# 5.5 ATTENTION
+
+We inspect where the network is attending to on average, to determine whether it is using its compressed memory. We average the attention weight over a sample of 20, 000 sequences from a trained model on Enwik8. We aggregate the attention into eighteen buckets, six for each of the compressed memory, memory, and sequence respectively. We set the size of the sequence, memory and compressed memory all to be 768. We plot this average attention weight per bucket in Figure 2 with a $1 \sigma$ standard error. We see most of the attention is placed on the current sequence; with a greater weight placed on earlier elements of the sequence due to the causal self-attention mechanism which masks future attention weights. We also observe there is an increase in attention from the oldest activations stored in the regular memory, to the activations stored in the compressed memory. This goes against the trend of older memories being accessed less frequently — and gives evidence that the network is learning to preserve salient information.
+
+# 5.5.1 OPTIMISATION SCHEDULE
+
+We make an observation about an interesting but undesirable meta-learning phenomenon during long-context training. When the learning rate is tuned to be much smaller (or set to zero) during training, performance degrades drastically both for the TransformerXL and the Compressive Transformer. This is displayed in Figure 3.
+
+Usually we consider distributional shift from the training data to the test data, but we can also observe a shift in the model when transferring from a training to evaluation mode (even when the model is evaluated on the training data). In this case, this is due to the online updating of parameters whilst processing long contiguous articles. We would like the model to generalise well to scenarios where it is not continuously optimised. Updating the parameters only at article boundaries (and then resetting the state) could be one solution for long-range memory models, but this would slow down learning significantly.
+
+Instead, we propose reducing the frequency of optimisation updates during training. We find this allows for the best of both worlds — fast initial learning with frequent updates, and better generalisation near the end of training with less frequent updates (e.g. every 4 steps). Reducing the optimisation frequency increases the effective batch size, which has also been shown to be preferable to learning rate decay in image modelling (Smith et al., 2018). We observed a final performance improvement in our TransformerXL baseline on Enwik8, from 0.995 — which approximately replicates the published result — to 0.984 — which matches the most recent SotA architecture. We note, the additional space and compute cost of accumulating gradients is negligible across iterations, so there was no performance regression in using this scheme.
+
+# 5.6 SPEECH
+
+We train the Compressive Transformer on the waveform of speech to assess its performance on different modalities. Speech is interesting because it is sampled at an incredibly high frequency, but we know it contains a lot of information on the level of phonemes and entire phrases.
+
+To encourage long-term reasoning, we refrain from conditioning the model on speaker identity or text features, but focus on unconditional speech modelling. We train the model on 24.6 hours of 24kHz North American speech data. We chunk the sequences into windows of size 3840, roughly 80ms of audio, and compare a 20-layer Compressive Transformer to a 20-layer TransformerXL and a 30-layer WaveNet model (Oord et al., 2016) — a state-of-the-art audio generative model used to serve production speech synthesis applications at Google (Oord et al., 2018). All networks have approximately 40M parameters, as WaveNet is more parameter-efficient per layer. We train each network with 32 V100 GPUs, and a batch size of 1 per core (total batch size of 32) using synchronous training.
+
+WaveNet processes an entire chunk in parallel, however the TransformerXL and Compressive Transformer are trained with a window size of 768 and a total memory size of 1, 568 (for the Compressive Transformer we use 768 memory $+ 7 6 8$ compressed). We thus unroll the model over the sequence. Despite this sequential unroll, the attention-based models train at only half the speed of WaveNet. We see the test-set negative-log-likelihood in Figure 4, and observe that a Compressive Transformer with a compression rate of 4 is able to outperform the TransformerXL and maintain a slim advantage over WaveNet. However we only trained models for at most one week (with 32GPUs) and it would be advantageous to continue training until full convergence — before definitive conclusions are made.
+
+# 5.7 REINFORCEMENT LEARNING
+
+Compression is a good fit for video input sequences because subsequent frames have high mutual information. Here we do not test out the Compressive Transformer on video, but progress straight to a reinforcement learning agent task that receives a video stream of visual observations — but must ultimately learn to use its memory to reason over a policy.
+
+We test the Compressive Transformer as a drop-in replacement to an LSTM in the IMPALA setup (Espeholt et al., 2018). Otherwise, we use the same training framework and agent architecture as described in the original work with a fixed learning rate of 1.5e-5 and entropy cost coefficient of 2e-3. We test the Compressive Transformer on a challenging memory task within the DMLab-30 (Beattie et al., 2016) domain, rooms select nonmatching object. This requires the agent to explore a room in a visually rich 3D environment and remember the object present. The agent can then advance to a second room where it must select the object not present in the original room. This necessitates that the agent both remember events far in the past, and also learn to efficiently reason about them.
+
+We fix both the memory and compressed memory sizes to 64. In Figure 5, we present results for a range of compression rates, averaged over 3 seeds. We see that the best performing agents endowed with the Compressive Transformer are able to solve the task to human-level. We note that the model with compression rate 1 is unable to learn the task to the same proficiency. The speed of learning and stability seem to increase proportionally with higher rates of compression (up to a limit) – i.e.
+
+![](images/42afd920bfbb3132ee3f0bccc130234e666d527c199fd0bd2f67885c2d8766e7.jpg)  
+Figure 4: Speech Modelling. We see the Compressive Transformer is able to obtain competitive results against the state-of-the-art WaveNet in the modelling of raw speech sampled at $2 4 \mathrm { k H z }$ .
+
+![](images/73b459f5476814831f88dbae381c01075c186cec825da44f6a778c19c5f94da1.jpg)  
+Figure 5: Vision and RL. We see the Compressive Transformer integrates visual information across time within an IMPALA RL agent, trained on an object matching task.
+
+the effective memory window of the agent – and we find compression rate 4 to once again be the best performing. We see this as a promising sign that the architecture is able to efficiently learn, and suitably use, compressed representations of its visual input and hope to test this more widely in future work.
+
+# 6 CONCLUSION
+
+In this paper we explore the notion of compression as a means of extending the temporal receptive field of Transformer-based sequence models. We see a benefit to this approach in the domain of text, with the Compressive Transformer outperforming existing architectures at long-range language modelling. To continue innovation in this area, we also propose a new book-level LM benchmark, PG-19. This may be used to compare long-range language models, or to pre-train on other longrange reasoning language tasks, such as NarrativeQA (Kocisk ˇ y et al., 2018). \`
+
+We see the idea of compressive memories is applicable not only to the modality of text, but also audio, in the form of modelling the waveform of speech, and vision, within a reinforcement-learning agent trained on a maze-like memory task. In both cases, we compare to very strong baselines (Wavenet (Oord et al., 2016) and IMPALA (Espeholt et al., 2018)).
+
+The main limitation of this work is additional complexity, if the task one wishes to solve does not contain long-range reasoning then the Compressive Transformer is unlikely to provide additional benefit. However as a means of scaling memory and attention, we do think compression is a simpler approach to dynamic or sparse attention — which often requires custom kernels to make efficient. One can build effective compression modules from simple neural network components, such as convolutions. The compression components are immediately efficient to run on GPUs and TPUs.
+
+Memory systems for neural networks began as compressed state representations within RNNs. The recent wave of progress using attention-based models with deep and granular memories shows us that it is beneficial to refrain from immediately compressing the past. However we hypothesise that more powerful models will contain a mixture of granular recent memories and coarser compressed memories. Future directions could include the investigation of adaptive compression rates by layer, the use of long-range shallow memory layers together with deep short-range memory, and even the use of RNNs as compressors. Compressive memories should not be forgotten about just yet.
+
+# ACKNOWLEDGEMENTS
+
+We thank Chris Dyer, Felix Gimeno, and Koray Kavukcuoglu for reviewing the manuscript. We thank Peter Dayan, Adam Santoro, Jacob Menick, Emilio Parisotto, Hyunjik Kim, Simon Osindero, Sergey Bartunov, David Raposo, and Daan Wierstra for ideas regarding model design. We thank Yazhe Li and Aaron Van de Oord for their help and advice in instrumenting speech modelling experiments. Finally, we thank our wider DeepMind colleagues for supporting this project with stimulating discussions, engineering infrastructure, and positive reinforcement signals.
+
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+Z. Yang, Z. Dai, Y. Yang, J. Carbonell, R. Salakhutdinov, and Q. V. Le. Xlnet: Generalized autoregressive pretraining for language understanding. arXiv preprint arXiv:1906.08237, 2019.   
+L. Zhou, Y. Zhou, J. J. Corso, R. Socher, and C. Xiong. End-to-end dense video captioning with masked transformer. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8739–8748, 2018.   
+Y. Zhu, R. Kiros, R. Zemel, R. Salakhutdinov, R. Urtasun, A. Torralba, and S. Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In Proceedings of the IEEE international conference on computer vision, pages 19–27, 2015. J. G. Zilly, R. K. Srivastava, J. Koutn´ık, and J. Schmidhuber. Recurrent highway networks. In Proceedings of the 34th International Conference on Machine Learning-Volume 70, pages 4189– 4198. JMLR. org, 2017.
+
+# A TEMPORAL RANGE OF THE COMPRESSIVE TRANSFORMER
+
+The TransformerXL with a memory of size $n$ has a maximum temporal range of $l \times n$ with an attention cost of $\mathcal { O } ( n _ { s } ^ { 2 } + n _ { s } n )$ (see Dai et al. (2019) for a detailed discussion). The Compressive Transformer now has a maximum temporal range of $l \times \left( n _ { s } + n _ { m } + c * n _ { c m } \right)$ with an attention cost of $\mathcal { O } ( n _ { s } ^ { 2 } + n _ { s } ( n _ { m } + n _ { c m } ) )$ . For example, setting $n _ { c m } = n _ { m } = n / 2$ and $c = 3$ we obtain a maximum temporal range that is two times greater than the TransformerXL with an identical attention cost. Thus if we can learn in the $c > 1$ compressed setting, the temporal range of the model can be significantly increased.
+
+# B COMPRESSION ACROSS LAYERS
+
+We inspect the compression loss broken down by the layer index, to investigate whether there is a trend in network depth with how compressible the representations are. The compression loss here refers to the attention-reconstruction attention loss. We plot this for a 24 layer trained model on Enwik8, and an 18 layer model trained on WikiText-103. The compression loss for characterbased language modelling is about one order of magnitude lower than that of word-level language modelling. The first layer’s representations are highly compressible, however from then on there is no fixed trend. Some non-contiguous layers have a very similar compression loss (e.g. 4 & 6, 5 & 7) which suggests information is being routed from these layer pairs via the skip connection.
+
+![](images/ac86293c4cd4f466d587bbab8a7c5a4cb730e28f0ff5a8d8b0ff0bd03f5b3baf.jpg)  
+Figure 6: Model analysis. Compression loss broken down by layer.
+
+# C COMPARISON OF COMPRESSED MEMORY SIZES
+
+We compare the best test perplexity obtained for the Compressive Transformer trained on WikiText103 and Enwik8 across a range of compressed memory sizes. For both models, the best model used a 1D convolution compression network with a compression rate of 3. The Enwik8 model was trained with an embedding size of 1024, 8 attention heads, 24 layers, an mlp hidden size of 3072, a sequence window size of 768, and a memory size of 768. We see the best compressed memory size is 3, 072 in this sweep, facilitating a total attention window of 3840. The WikiText-103 model was trained with an embedding size of 1024, adaptive inputs using the same parameters as (Sukhbaatar et al., 2019), 16 attention heads, 18 layers, an mlp hidden size of 4096, a sequence window of size 512 and a memory of size 512. The best compressed memory size is 1536 resulting in a total attention window of c. 2048.
+
+<table><tr><td>Compressed Memory Size Enwik8 BPC</td><td>512 1.01</td><td>1024 0.99</td><td>2048 0.98</td><td>3072 0.97</td><td>4096 1.00</td></tr></table>
+
+Table 8: Compressed memory size vs test performance for Enwik8
+
+Table 9: Compressed memory size vs test performance for WikiText-103   
+
+<table><tr><td>Compressed Memory Size</td><td>256</td><td>512</td><td>1024</td><td>1536</td><td>2048</td></tr><tr><td>WikiText-103 Perplexity</td><td>18.2</td><td>17.9</td><td>17.6</td><td>17.1</td><td>17.7</td></tr></table>
+
+# D PG-19 PREPROCESSING
+
+The raw texts from the Gutenberg project were minimally pre-processed by removing boilerplate license text. We then also replaced discriminatory words with a unique $\langle \mathrm { D W x } \rangle$ token using the Ofcom list of discriminatory words 4.
+
+# E PG-19 TOPICS
+
+We present top-words for some of the topics on the PG-19 corpus. These were generated with LDA topic model (Blei et al., 2003).
+
+Table 10: Examples of top topics on PG-19 corpus.   
+
+<table><tr><td>Geography</td><td>War</td><td>Civilisations</td><td>Human Condition</td><td>Naval</td><td>Education</td><td>Art</td></tr><tr><td>water</td><td>people</td><td>roman</td><td>love</td><td>island</td><td>work</td><td>poet</td></tr><tr><td>river</td><td>emperor</td><td>rome</td><td>religion</td><td>ship</td><td>school</td><td>music</td></tr><tr><td>feet</td><td>war</td><td>greek</td><td>religious</td><td>sea</td><td>life</td><td>one</td></tr><tr><td>miles</td><td> army</td><td>city</td><td>life</td><td>men</td><td>children</td><td>poetry</td></tr><tr><td>north</td><td>death</td><td>gods</td><td>moral</td><td>captain</td><td>may</td><td>work</td></tr><tr><td>south</td><td>battle</td><td>king</td><td>human</td><td>coast</td><td>social</td><td>literature</td></tr><tr><td>mountains</td><td>city</td><td>first</td><td>society</td><td>land</td><td>child</td><td>art</td></tr><tr><td>sea</td><td>soldiers</td><td>caesar</td><td>man</td><td>great</td><td>education</td><td>great</td></tr><tr><td>lake</td><td>power</td><td>great</td><td>virtue</td><td>found</td><td>conditions</td><td>poem</td></tr><tr><td>rock</td><td>thousand</td><td>romans</td><td> nature</td><td>islands</td><td>well</td><td>written</td></tr><tr><td>mountain</td><td>arms</td><td>athens</td><td>marriage</td><td>shore</td><td> study</td><td>english</td></tr><tr><td>country</td><td>empire</td><td>greece</td><td>women</td><td>voyage</td><td>best</td><td>author</td></tr><tr><td>valley</td><td>upon</td><td>temple</td><td>christian</td><td>vessels</td><td>years</td><td>play</td></tr><tr><td>ice</td><td>country</td><td>son</td><td>age</td><td>time</td><td>possible</td><td>genius</td></tr><tr><td>west</td><td>time</td><td>egypt</td><td>law</td><td>english</td><td>class</td><td>style</td></tr></table>
+
+# F PG-19 SAMPLES
+
+We show a few different samples from the Compressive Transformer trained on PG-19. We use Nucleus Sampling with $p = 0 . 9 8$ (Holtzman et al., 2019). We choose extracts of books from the test set as prefixes. We see the model is able to continue in the style of the text, creating artificial dialogue or descriptive text, and remembering the names of characters over hundreds of words.
+
+As the Compressive Transformer is trained without state resetting, it is actually slightly out of sample when provided with the (relatively) short contexts. This is because its memory and compressed memory may be still empty (whereas they are always full during training). However we see a trend of the samples usually improving towards the end.
+
+# Context from Baby Mine by Maragaret Mayo:
+
+CHAPTER I
+
+Even in college Alfred Hardy was a young man of fixed ideas and high ideals and proud of it.
+
+His friend, Jimmy Jinks, had few ideas and no ideals, and was glad of it, and before half of their first college term had passed, Jimmy had ridded himself of all such worries as making up his own mind or directing his own morals. Alfred did all these things so much better, argued Jimmy, furthermore, Alfred LIKED to do them–Jimmy owed it to his friend to give him that pleasure.
+
+# Compressive Transformer:
+
+He did not like doing them in the most elegant of all possible marble walks–where freshmen and sophomores stand and talk and laugh and chatter till evening falls and look cool and still and cool and beautifully white in spite of the hot sun, but had to go there for a month before going home. It happened one day that he and Jimmy were strolling together in the green shade of St. Martin’s, and Jimmy naturally asked why he was so silent. He was very talkative as most boys are who have once got the habit of it on shore, so the need for answering was soon supplied.
+
+”I am wondering,” he said, ”why my old friend and chum, Jimmy Jinks, is living a single life and so has no boys. Have you not noticed that many of his old friends had their own boys to follow in their footsteps and help, and often helped successfully too?”
+
+”Oh, yes,” said Alfred, ”it was plain enough then that he liked to live by himself and got none of his present pleasures or entertainments because of the other fellow’s giving it to him.”
+
+”Then it IS sad,” said Jimmy, ”that an old friend like the friend of Big Lights, Jimmy Reynolds, should be living the single life and having no boys.”
+
+”And it is pretty true, too,” said Alfred, ”yet I believe it is the best thing that could happen even now.”
+
+”And so do I,” said Jimmy, ”and I also believe that it is time someone did something to make the things worse for the other’s partner.”
+
+”And so do I,” said Alfred, ”and so do I, and so do I.”
+
+”What can we do?” asked Jimmy.
+
+”I don’t know,” said Alfred, ”but if someone will come down to the valley and go through a regular mill with the old forces at work, doing the work of the two, and doing it better than any other Miller he ever saw or ever hoped to see, I think there will be a good deal of change in the things and things to be cared for for and for driven and counter-driven.”
+
+”I will come and do that mill,” said Jimmy.
+
+# Context from The Diary of Samuel Pepys:
+
+June 1st. Having taken our leaves of Sir W. Batten and my Lady, who are gone this morning to keep their Whitsuntide, Sir W. Pen and I and Mr. Gauden by water to Woolwich, and there went from ship to ship to give order for and take notice of their forwardness to go forth, and then to Deptford and did the like, having dined at Woolwich with Captain Poole at the tavern there. From Deptford we walked to Redriffe, calling at the half-way house, and there come into a room where there was infinite of new cakes placed that are made against Whitsuntide, and there we were very merry. By water home, and there did businesses of the office. Among others got my Lord’s imprest of L1000 and Mr. Creed’s of L10,000 against this voyage their bills signed. Having wrote letters into the country and read some things I went to bed.
+
+# Compressive Transformer:
+
+So I rose and did some business at the office, and then to dinner, where great abundance of good things of the kitchen I only being partaker in the feast. After dinner I went to look at the yard and found it in a very bad condition, so I went home and there finding no delight in seeing things I should make shift to get in my way and so I will leave off.
+
+So I took leave of my great friend, and the next day being Sunday, my wife and I and a great number of friends went by water to Deptford, and there took the oaths of allegiance and supremacy and promised such obedience to the Lord as should hereafter turn to the advantage of our State. Being come back we found the shops and warehouses in a pitiable condition, so my wife and I and all the rest of the friends went home and there did the like and by Saturday day I being alone in my office I found myself in a very bad situation, for my Lord, and Mr. Creed, and Pett were all standing ready to receive and receive the oaths of allegiance and right to make use of the ten days’ licence I had allowed for this purpose by virtue of the law that was such a help to the servant. Having looked at the ships, I told my wife what I had seen and that I was greatly troubled at my situation and, I hope that will mend it.
+
+So that is the end of a long and patient seeking after those things which in my opinion I deserve and may get if I can only by fair means get them.
+
+# Context from The Patrol of the Sun Dance Trail by Ralph Connor:
+
+High up on the hillside in the midst of a rugged group of jack pines the Union Jack shook out its folds gallantly in the breeze that swept down the Kicking Horse Pass. That gallant flag marked the headquarters of Superintendent Strong, of the North West Mounted Police, whose special duty it was to preserve law and order along the construction line of the Canadian Pacific Railway Company, now pushed west some scores of miles.
+
+Along the tote-road, which ran parallel to the steel, a man, dark of skin, slight but wiry, came running, his hard panting, his streaming face, his open mouth proclaiming his exhaustion. At a little trail that led to the left he paused, noted its course toward the flaunting flag, turned into it, then struggled up the rocky hillside till he came to the wooden shack, with a deep porch running round it, and surrounded by a rustic fence which enclosed a garden whose neatness illustrated a characteristic of the British soldier. The runner passed in through the gate and up the little gravel walk and began to ascend the steps.
+
+# Compressive Transformer:
+
+As though by mutual consent, all the three members of the Superintendent Force were standing on the veranda watching his progress, a man came strolling slowly down the path, stopping often to gaze curiously about him, then stopping once more when he saw the four standing on the veranda. His face was dark, his eyes prominent, and the lines that furrowed his forehead showed marks of many woes, yet his step was alert and he began to mount the steps with steady strides.
+
+The man’s attention was diverted by the unexpected appearance of the two policemen; a third man came slipping up, grumbling under his breath, and stopped long enough to look doubtfully around him, then slipped away again. In the meantime, the four on the veranda continued to watch the approach of the new arrival. In spite of himself, the Superintendent Force became conscious of a curious feeling–uneasiness that was almost fear–in the presence of that strange man. He would not allow himself to admit the fact, yet he felt it in his bones. But to the watchers, the plain, everyday features of that stranger and his coming, seemed only just what the Seven White Shee owed him–their weight, their hurry, their blast.
+
+Had a chariot been made for the good of the three horses, and had the driver been given orders that he should speed them that he might win, they would have been heartening things in the sight of the veteran and the victor. To you they would have been unintelligible to the root of your understanding. When you gaze up in the faces of those four gray horses, you can see clearly through the clouds of dust that rise from their hoofs, and discern plainly where the banker is and where the hobo. Then you will understand why you shall not press the bitter grapes and why you shall not spurn the generous doctrines. You will understand why you shall not praise the lash or the spur, for you will know where the true would be and where the false would be. Then you will understand why you, a man with reason and heart, need not tear your hair over-bitter and why you need not laugh over the blunders of an ignorant man.
+
+About nine o’clock that morning, two buggies, drawn by powerful horses, crossed the Rubicon and turned the railroad from Sandhurst into the Hollow of the Mountains. And though the charioteers stood at their horses’ heads, and their drivers cried at their loudest, there was not a man in the four teams who did not feel that his day was worth all the toil and all the peril that he had undergone. And if there were a man in them who did not know that–who did not feel that the road through the Hollow of the Mountains is made easy by the arrival of travelers and by the coming of government, there was one who did not at that moment care whether his day’s work were worth all the toil and all the danger that he had had to endure or whether it were not worth more than all.
+
+# AUTHOR CONTRIBUTIONS
+
+Model and Experiment design: JR, TL, AP, SJ   
+Dataset creation: AP, JR, CH   
+Text experiments: JR, AP   
+RL experiments: SJ   
+Speech experiments: JR

parse/train/SylKikSYDH/SylKikSYDH_content_list.json

@@ -0,0 +1,1708 @@
+[
+    {
+        "type": "text",
+        "text": "COMPRESSIVE TRANSFORMERS FOR LONG-RANGE SEQUENCE MODELLING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jack W. Rae∗∗ † ‡ Anna Potapenko\\*† Siddhant M. Jayakumar† Chloe Hillier† ",
+        "bbox": [
+            183,
+            172,
+            813,
+            188
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Timothy P. Lillicrap†‡ ",
+        "bbox": [
+            184,
+            208,
+            339,
+            223
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            260,
+            544,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present the Compressive Transformer, an attentive sequence model which compresses past memories for long-range sequence learning. We find the Compressive Transformer obtains state-of-the-art language modelling results in the WikiText-103 and Enwik8 benchmarks, achieving $1 7 . 1 \\ \\mathrm { p p l }$ and 0.97 bpc respectively. We also find it can model high-frequency speech effectively and can be used as a memory mechanism for RL, demonstrated on an object matching task. To promote the domain of long-range sequence learning, we propose a new openvocabulary language modelling benchmark derived from books, PG-19. ",
+        "bbox": [
+            233,
+            291,
+            764,
+            404
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            431,
+            336,
+            446
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Humans have a remarkable ability to remember information over long time horizons. When reading a book, we build up a compressed representation of the past narrative, such as the characters and events that have built up the story so far. We can do this even if they are separated by thousands of words from the current text, or long stretches of time between readings. During daily life, we make use of memories at varying time-scales: from locating the car keys, placed in the morning, to recalling the name of an old friend from decades ago. These feats of memorisation are not achieved by storing every sensory glimpse throughout one’s lifetime, but via lossy compression. We aggressively select, filter, or integrate input stimuli based on factors of surprise, perceived danger, or repetition — amongst other signals (Richards and Frankland, 2017). ",
+        "bbox": [
+            174,
+            462,
+            825,
+            588
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Memory systems in artificial neural networks began with very compact representations of the past. Recurrent neural networks (RNNs, Rumelhart et al. (1986)) learn to represent the history of observations in a compressed state vector. The state is compressed because it uses far less space than the history of observations — the model only preserving information that is pertinent to the optimization of the loss. The LSTM (Hochreiter and Schmidhuber, 1997) is perhaps the most ubiquitous RNN variant; it uses learned gates on its state vector to determine what information is stored or forgotten from memory. ",
+        "bbox": [
+            174,
+            594,
+            825,
+            693
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However since the LSTM, there has been great benefit discovered in not bottlenecking all historical information in the state, but instead in keeping past activations around in an external memory and attending to them. The Transformer (Vaswani et al., 2017) is a sequence model which stores the hidden activation of every time-step, and integrates this information using an attention operator (Bahdanau et al., 2014). The Transformer will thus represent the past with a tensor (depth $\\times$ memory size $\\times$ dimension) of past observations that is, in practice, an order of magnitude larger than an LSTM’s hidden state. With this granular memory, the Transformer has brought about a step-change in state-of-the-art performance, within machine translation (Vaswani et al., 2017), language modelling (Dai et al., 2019; Shoeybi et al., 2019), video captioning (Zhou et al., 2018), and a multitude of language understanding benchmarks (Devlin et al., 2018; Yang et al., 2019) amongst others. ",
+        "bbox": [
+            174,
+            699,
+            823,
+            838
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "One drawback in storing everything is the computational cost of attending to every time-step and the storage cost of preserving this large memory. Several works have focused on reducing the computational cost of attention with sparse access mechanisms (Rae et al., 2016; Child et al., 2019; ",
+        "bbox": [
+            174,
+            845,
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+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Sukhbaatar et al., 2019; Lample et al., 2019). However sparse attention does not solve the storage problem, and often requires custom sparse kernels for efficient implementation. Instead we look back to the notion of compactly representing the past. We show this can be built with simple dense linear-algebra components, such as convolutions, and can reduce both the space and compute cost of our models. ",
+        "bbox": [
+            174,
+            103,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We propose the Compressive Transformer, a simple extension to the Transformer which maps past hidden activations (memories) to a smaller set of compressed representations (compressed memories). The Compressive Transformer uses the same attention mechanism over its set of memories and compressed memories, learning to query both its short-term granular memory and longer-term coarse memory. We observe this improves the modelling of text, achieving state-of-the-art results in character-based language modelling — 0.97 bpc on Enwik8 from the Hutter Prize (Hutter, 2012) — and word-level language modelling — 17.1 perplexity on WikiText-103 (Merity et al., 2016). Specifically, we see the Compressive Transformer improves the modelling of rare words. ",
+        "bbox": [
+            174,
+            180,
+            825,
+            291
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We show the Compressive Transformer works not only for language, but can also model the waveform of high-frequency speech with a trend of lower likelihood than the TransformerXL and Wavenet (Oord et al., 2016) when trained over 400,000 steps. We also show the Compressive Transformer can be used as a memory component within an RL agent, IMPALA (Espeholt et al., 2018), and can successfully compress and make use of past observations. ",
+        "bbox": [
+            174,
+            299,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Furthermore we present a new book-level language-modelling benchmark PG-19, extracted from texts in Project Gutenberg1, to further promote the direction of long-context sequence modelling. This is over double the size of existing LM benchmarks and contains text with much longer contexts. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            436,
+            344,
+            453
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There have been a variety of recent attempts to extend the range of attention, particularly in the Transformer, or to replace the attention operation with something less expensive. Wu et al. (2019) show that a convolution-like operator that runs in linear time can actually exceed the performance of the quadratic-time self-attention layer in the Transformer at sentence-to-sentence translation and sentence-level language modelling. However such a mechanism inhibits the flow of information across a large number of time-steps for a given layer, and has not shown to be beneficial for longrange sequence modelling. ",
+        "bbox": [
+            174,
+            468,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Dai et al. (2019) propose the TransformerXL, which keeps past activations around in memory. They also propose a novel relative positional embedding scheme which they see outperforms the Transformer’s original absolute positional system. Our model incorporates both of these ideas, the use of a memory to preserve prior activations and their relative positional embedding scheme. ",
+        "bbox": [
+            174,
+            571,
+            825,
+            627
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The Sparse Transformer (Child et al., 2019) uses fixed sparse attention masks to attend to roughly√ $\\sqrt { n }$ locations in memory. This approach still requires keeping all memories around during training, however with careful re-materialization of activations and custom kernels, the authors are able to train the model with a reasonable budget of memory and compute. When run on Enwik8, the much larger attention window of 8, 000 improves model performance, but overall it does not significantly outperform a simpler TransformerXL with a much smaller attention window. ",
+        "bbox": [
+            174,
+            635,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The use of dynamic attention spans is explored in Sukhbaatar et al. (2019). Different attention heads can learn to have shorter or longer spans of attention — and they observe this achieves state-ofthe-art in character-based language modelling. This idea could easily be combined with our contribution — a compressive memory. However an efficient implementation is not possible on current dense-linear-algebra accelerators, such as Google’s TPUs, due to the need for dynamic and sparse computation. Our approach builds on simple dense linear algebra components, such as convolutions. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3 MODEL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            829,
+            267,
+            844
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We present the Compressive Transformer, a long-range sequence model which compacts past activations into a compressed memory2. The Compressive Transformer is a variant of the Transformer (Vaswani et al., 2017), a deep residual network which only uses attention to propagate information over time (namely multi-head attention). We build on the ideas of the TransformerXL (Dai et al., 2019) which maintains a memory of past activations at each layer to preserve a longer history of context. The TransformerXL discards past activations when they become sufficiently old (controlled by the size of the memory). The key principle of the Compressive Transformer is to compress these old memories, instead of discarding them, and store them in an additional compressed memory. ",
+        "bbox": [
+            176,
+            859,
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/0acd7690aaac7bffb9eb11c081c43adc68daad2cbdc94c5997f547d73d2d83e7.jpg",
+        "image_caption": [
+            "Figure 1: The Compressive Transformer keeps a fine-grained memory of past activations, which are then compressed into coarser compressed memories. The above model has three layers, a sequence length ${ n _ { s } = 3 }$ , memory size ${ n _ { m } } = 6$ , compressed memory size $n _ { c m } = 6$ . The highlighted memories are compacted, with a compression function $f _ { c }$ per layer, to a single compressed memory — instead of being discarded at the next sequence. In this example, the rate of compression $c = 3$ . "
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+        "text": "3.1 DESCRIPTION ",
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+        "text": "We define $n _ { m }$ and $n _ { c m }$ to be the number of respective memory and compressive memory slots in the model per layer. The overall input sequence $\\mathcal { S } = x _ { 1 } , x _ { 2 } , \\dotsc , x _ { | s | }$ represents input observations (e.g. tokens from a book). These are split into fixed-size windows of size $n _ { s }$ for the model to process in parallel. The model observes $\\mathbf { x } = x _ { t } , \\ldots , x _ { t + n _ { s } }$ at time $t$ , which we refer to as the sequence (e.g. in Figure 1). As the model moves to the next sequence, its $n _ { s }$ hidden activations are pushed into a fixed-sized FIFO memory (like the TransformerXL) of size $n _ { m }$ . The oldest $n _ { s }$ activations in memory are evicted, but unlike the TransformerXL we do not discard them. Instead we apply a compression operation, $f _ { c } : \\mathbf { R } ^ { n _ { s } \\times d }  \\mathbf { R } ^ { \\lfloor \\frac { n _ { s } } { c } \\rfloor \\times d }$ , mapping the $n _ { s }$ oldest memories to $\\lfloor \\frac { n _ { s } } { c } \\rfloor$ compressed memories which we then store in a secondary FIFO compressed memory of size $n _ { c m }$ . $d$ denotes the hidden size of activations and $c$ refers to the compression rate, a higher value indicates more coarse-grained compressed memories. The overall temporal range of the model becomes $l \\times \\left( n _ { s } + n _ { m } + c * n _ { c m } \\right)$ , where $l$ is the number of layers — as discussed in Supplementary Section A. The full architecture is described in Algorithm 1. ",
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+        "type": "text",
+        "text": "Algorithm 1 Compressive Transformer ",
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+        "text": "At time zero   \n1: $\\mathbf { m _ { 0 } } \\gets \\mathbf { 0 }$ // Initialize memory to zeros $( l \\times n _ { m } \\times d )$   \n2: $\\mathbf { c m _ { 0 } } \\gets \\mathbf { 0 }$ // Initialize compressed memory to zeros $( l \\times n _ { c m } \\times d )$   \nAt time t   \n3: $\\mathbf { h } ^ { ( 1 ) }  \\mathbf { x W _ { e m b } }$ // Embed input sequence $( n _ { s } \\times d )$   \n4: for layer $i = 1 , 2 , \\ldots , l$ do   \n5: mem(i) ← concat(cm(i)t , m(i)t ) $I / \\left( \\left( n _ { c m } + n _ { m } \\right) \\times d \\right)$   \n6: $\\tilde { \\mathbf { a } } ^ { ( \\mathbf { i } ) } \\gets$ multihead attention(i)(h(i), mem(i)t ) // MHA over both mem types $( n _ { s } \\times d )$   \n7: a(i) ← layer norm(˜a(i) + h(i)) // Regular skip $^ +$ layernorm $( n _ { c m } \\times d )$   \n8: $\\mathbf { o l d . m e m ^ { ( i ) } \\gets m _ { t } ^ { ( i ) } } [ : n _ { s } ]$ // Oldest memories to be forgotten $( n _ { s } \\times d )$   \n9: new $\\mathbf { c m } ^ { ( \\mathbf { i } ) } \\gets f _ { c } ^ { ( i ) } ( \\mathbf { o l d . m e m ^ { ( \\mathbf { i } ) } } )$ // Compress oldest memories by factor $c \\left( \\left\\lfloor { \\frac { n _ { s } } { c } } \\right\\rfloor \\times d \\right)$   \n10: $\\mathbf { m _ { t + 1 } ^ { ( i ) } } \\gets \\mathrm { c o n c a t } ( \\mathbf { m _ { t } ^ { ( i ) } } , \\mathbf { h ^ { ( i ) } } ) [ - n _ { m } \\cdot ]$ // Update memory $( n _ { m } \\times d )$   \n11: $\\mathbf { c m _ { t } ^ { ( i ) } } \\gets \\mathrm { c o n c a t } ( \\mathbf { c m _ { t } ^ { ( i ) } } , \\mathbf { n e w . c m ^ { ( i ) } } ) [ - n _ { c m } :$ :] // Update compressed memory $( n _ { c m } \\times d )$   \n12: $\\mathbf { h } ^ { ( \\mathbf { i } + 1 ) } \\gets \\mathrm { l a y e r . n o r m } ( \\mathrm { m l p } ^ { ( i ) } ( \\mathbf { a } ^ { ( \\mathbf { i } ) } ) + \\mathbf { a } ^ { ( \\mathbf { i } ) } )$ // Mixing MLP $( n _ { s } \\times d )$ ",
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+        "type": "text",
+        "text": "Algorithm 2 Attention-Reconstruction Loss ",
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+        "table_caption": [],
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+        "table_body": "<table><tr><td colspan=\"3\">1: Lattn ←0</td></tr><tr><td>2:</td><td>for layeri=1,2,...,l do</td><td></td></tr><tr><td>3:</td><td>h(i) ← stop-gradient(h(i))</td><td>// Stop compression grads from passing...</td></tr><tr><td>4:</td><td>old_mem(i)← stop-gradient(old_mem(i))</td><td>//..into transformer network.</td></tr><tr><td>5:</td><td>Q,K,V ← stop-gradient(attention params at layer i)// Re-use attention weight matrices.</td><td></td></tr><tr><td>6:</td><td>def attn(h,m) ← σ((hQ) (mK))(mV)</td><td>// Use content-based attention (no relative).</td></tr><tr><td>7:</td><td>new_cm(i) ← f(𝑖)(old_mem(i))</td><td>// Compression network (to be optimized).</td></tr><tr><td>8:</td><td>Lattn ← Lattn + |lttn(h(i),old-mem(i)) -attn(h(i),new_cm(i)|l2</td><td></td></tr></table>",
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+        "type": "text",
+        "text": "3.2 COMPRESSION FUNCTIONS AND LOSSES ",
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+        "text": "For choices of compression functions $f _ { c }$ we consider (1) max/mean pooling, where the kernel and stride is set to the compression rate $c$ ; (2) 1D convolution also with kernel & stride set to $c$ ; (3) dilated convolutions; (4) most-used where the memories are sorted by their average attention (usage) and the most-used are preserved. The pooling is used as a fast and simple baseline. The mostused compression scheme is inspired from the garbage collection mechanism in the Differentiable Neural Computer (Graves et al., 2016) where low-usage memories are erased. The convolutional compression functions contain parameters which require training. ",
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+        "text": "One can train the compression network using gradients from the loss; however for very old memories this requires backpropagating-through-time (BPTT) over long unrolls. As such we also consider some local auxiliary compression losses. We consider an auto-encoding loss where we reconstruct the original memories from the compressed memories $\\mathcal { L } ^ { a e } = | | \\mathbf { o l d . m e m ^ { ( i ) } } - g ( \\mathbf { n e w . c m ^ { ( i ) } } ) | | _ { 2 }$ , where $\\overline { { g } } \\ : \\ \\mathbb { R } ^ { \\frac { n _ { s } } { c } \\times d } \\  \\ \\mathbb { R } ^ { n _ { s } \\times d }$ is learned. This is a lossless compression objective — it attempts to retain all information in memory. We also consider an attention-reconstruction loss described in Algorithm 2 which reconstructs the content-based attention over memory, with content-based attention over the compressed memories. This is a lossy objective, as information that is no longer attended to can be discarded, and we found this worked best. We stop compression loss gradients from passing into the main network as this prevents learning. Instead the Transformer optimizes the task objective and the compression network optimizes the compression objective conditioned on task-relevant representations; there is no need to mix the losses with a tuning constant. ",
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+        "text": "4 PG-19 BENCHMARK ",
+        "text_level": 1,
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+        "text": "As models begin to incorporate longer-range memories, it is important to train and benchmark them on data containing larger contexts. Natural language in the form of text provides us with a vast repository of data containing long-range dependencies, that is easily accessible. We propose a new language modelling benchmark, PG-19, using text from books extracted from Project Gutenberg 3. We select Project Gutenberg books which were published over 100 years old, i.e. before 1919 (hence the name PG-19) to avoid complications with international copyright, and remove short texts. The dataset contains 28, 752 books, or $1 1 G B$ of text — which makes it over double the size of BookCorpus and Billion Word Benchmark. ",
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+        "text": "4.1 RELATED DATASETS ",
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+        "text": "The two most benchmarked word-level language modelling datasets either stress the modelling of stand-alone sentences (Billion Word Benchmark from Chelba et al. (2013)) or the modelling of a small selection of short news articles (Penn Treebank processed by Mikolov et al. (2010)). Merity et al. (2016) proposed the WikiText-103 dataset, which contains text from a high quality subset of English-language wikipedia articles. These articles are on average 3, 600 words long. This dataset has been a popular recent LM benchmark due to the potential to exploit longer-range dependencies (Grave et al., 2016; Rae et al., 2018; Bai et al., 2018b). However recent Transformer models, such as the TransformerXL (Dai et al., 2019) appear to be able to exploit temporal dependencies on the order of several thousand words. This motivates a larger dataset with longer contexts. ",
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+        "table_caption": [
+            "Table 1: Comparison to existing popular language modelling benchmarks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Avg. length (words)</td><td>Train Size</td><td>Vocab</td><td>Type</td></tr><tr><td>1B Word</td><td>27</td><td>4.15GB</td><td>793K</td><td>News (sentences)</td></tr><tr><td>Penn Treebank</td><td>355</td><td>5.1MB</td><td>10K</td><td>News (articles)</td></tr><tr><td>WikiText-103</td><td>3.6K</td><td>515MB</td><td>267K</td><td>Wikipedia (articles)</td></tr><tr><td>PG-19</td><td>69K</td><td>10.9GB</td><td>(open)</td><td>Books</td></tr></table>",
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+        "text": "",
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+        "text": "Books are a natural choice of long-form text, and provide us with stylistically rich and varied natural language. Texts extracted from books have been used for prior NLP benchmarks; such as the Children’s Book Test (Hill et al., 2015) and LAMBADA (Paperno et al., 2016). These benchmarks use text from Project Gutenberg, an online repository of books with expired US copyright, and BookCorpus (Zhu et al., 2015), a prior dataset of $1 1 K$ unpublished (at time of authorship) books. CBT and LAMBADA contain extracts from books, with a specific task of predicting held-out words. In the case of LAMBADA the held-out word is specifically designed to be predictable for humans with access to the full textual context — but difficult to guess with only a local context. ",
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+        "type": "text",
+        "text": "CBT and LAMBADA are useful for probing the linguistic intelligence of models, but are not ideal for training long-range language models from scratch as they truncate text extracts to at most a couple of paragraphs, and discard a lot of the books’ text. There has been prior work on training models on book data using BookCorpus directly (e.g. BERT from Devlin et al. (2018)) however BookCorpus is no longer distributed due to licensing issues, and the source of data is dynamically changing — which makes exact benchmarking difficult over time. ",
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+        "type": "text",
+        "text": "The NarrativeQA Book Comprehension Task (Kocisk ˇ y et al., 2018) uses Project Gutenberg texts \\` paired with Wikipedia articles, which can be used as summaries. Due to the requirement of needing a corresponding summary, NarrativeQA contains a smaller selection of books: 1,527 versus the 28,752 books in PG-19. However it is reasonable that PG-19 may be useful for pre-training book summarisation models. ",
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+    {
+        "type": "text",
+        "text": "4.2 STATISTICS ",
+        "text_level": 1,
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+        "text": "A brief comparison of PG-19 to other LM datasets can be found in Table 1. We intentionally do not limit the vocabulary by unk-ing rare words, and release the dataset as an open-vocabulary benchmark. To compare models we propose to continue measuring the word-level perplexity. This can still be computed for any chosen character-based, byte-based or subword-based scheme. To do this, one calculates the total cross-entropy loss $\\begin{array} { r } { L = - \\dot { \\sum } _ { t } \\log ( p _ { t } | p _ { < t } ) } \\end{array}$ over the given validation or test subset using a chosen tokenization scheme, and then one normalizes this value by the number of words: $L / n _ { w o r d s }$ where $n _ { w o r d s }$ is the total number of words in the given subset, taken from Table 2. The word-level perplexity is thus $e ^ { L / n _ { w o r d s } }$ . For sake of model comparisons, it is important to use the exact number of words computed in Table 2 as the normalisation constant. ",
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+        "type": "text",
+        "text": "Alongside quantitative analyses, we build an LDA topic model (Blei et al., 2003) for a qualitative inspection of the text. We present key words for several topics in the Supplementary Table 10. These topics include art, education, naval exploration, geographical description, war, ancient civilisations, and more poetic topics concerning the human condition — love, society, religion, virtue etc. This contrasts to the more objective domains of Wikipedia and news corpora. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We optimised all models with Adam (Kingma and Ba, 2014). We used a learning rate schedule with a linear warmup from 1e-6 to 3e-4 and a cosine decay back down to 1e- $\\mathbf { \\nabla \\cdot } n \\mathbf { 6 }$ . For characterbased LM we used 4, 000 warmup steps with 100, 000 decay steps, and for word-based LM we used 16, 000 warmup steps with 500, 000 decay steps. We found that decreasing the optimisation update frequency helped (see Section 5.5.1), namely we only applied parameter updates every 4 steps after $6 0 , 0 0 0$ iterations. However we found the models would optimise well for a range of warmup/warmdown values. We clipped the gradients to have a norm of at most 0.1, which was crucial to successful optimisation. ",
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+    {
+        "type": "table",
+        "img_path": "images/efbda3f84d18e9ae291c165c70cc15bb5bcf84278767a912dcd73c8f313de459.jpg",
+        "table_caption": [
+            "Table 2: PG-19 statistics split by subsets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Train</td><td>Valid.</td><td>Test</td></tr><tr><td>#books</td><td>28.602</td><td>50</td><td>100</td></tr><tr><td># words</td><td>1,973,136,207</td><td>3,007,061</td><td>6,966,499</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 3: Eval. perplexities on PG-19. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Valid.</td><td>Test</td></tr><tr><td>36L TransformerXL</td><td>45.5</td><td>36.3</td></tr><tr><td>36L Compressive Transf.</td><td>43.4</td><td>33.6</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: State-of-the-art results on Enwik8. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model 7L LSTM(Graves,2013)</td><td>BPC 1.67</td></tr><tr><td>LN HyperNetworks Ha et al. (2016) LN HM-LSTM Chung et al. (2016) ByteNet (Kalchbrenner et al.,2016) RHN Zilly et al. (2017) mLSTM Krause et al. (2016) 64L Transf. Al-Rfou et al. (2019) 24L TXL (Dai et al.,2019) Sparse Transf.(Child et al.,2019) Adaptive Transf. (Sukhbaatar et al.,2019)</td><td>1.34 1.32 1.31 1.27 1.24 1.06 0.99 0.991 0.98</td></tr><tr><td>24L TXL (ours) 24L Compressive Transformer</td><td>0.98 0.97</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 5: Compression approaches on Enwik8. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Compression fn</td><td>Compression loss</td><td>BPC</td></tr><tr><td>Conv</td><td>BPTT</td><td>0.996</td></tr><tr><td>Max Pooling</td><td>N/A</td><td>0.986</td></tr><tr><td>Conv</td><td>Auto-encoding</td><td>0.984</td></tr><tr><td>Mean Pooling</td><td>N/A</td><td>0.982</td></tr><tr><td>Most-used</td><td>N/A</td><td>0.980</td></tr><tr><td>Dilated conv</td><td>Attention</td><td>0.977</td></tr><tr><td>Conv</td><td>Attention</td><td>0.973</td></tr></table>",
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+        "text": "5.1 PG-19 ",
+        "text_level": 1,
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+        "text": "We benchmark the Compressive Transformer against the TransformerXL on the newly proposed PG19 books dataset. Because it is open-vocabulary, we train a subword vocabulary of size 32000 with SubwordTextEncoder from the tfds package in TensorFlow and use the dataset statistics to compute word-level perplexity, as described in Section 4.2. We train a 36 layer Compressive Transformer with a window size of 512, both memory and compressed memory size of 512, and compression rate $C =$ 2. We compare this to a 36 layer TransformerXL trained with window size 512 and attention window 1024. The model was trained on 256 TPUv3 cores with a total batch size of 512 and converged after processing around 100 billion subword tokens. We display the results in Table 3 where we see the Compressive Transformer obtains a test perplexity of 33.6 versus the TransformerXL’s 36.3. Despite the dataset size, it is clearly a challenging domain. This can suit as a first baseline on the proposed long-range language modelling benchmark. We show samples from this model in Supplementary Section F. The model is able to generate long-form narrative of varying styles: from character dialogue, first person diary entries, to descriptive third-person text. ",
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+        "type": "text",
+        "text": "5.2 ENWIK8 ",
+        "text_level": 1,
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+        "text": "We compare the TransformerXL and the Compressive Transformer on the standard character-level language modelling benchmark Enwiki8 taken from the Hutter Prize (Hutter, 2012), which contains 100M bytes of unprocessed Wikipedia text. We select the first 90MB for training, 5MB for validation, and the latter 5MB for testing — as per convention. We train 24-layer models with a sequence window size of 768. During training, we set the TransformerXL’s memory size to 2304, and for the Compressive Transformer we use memory of size 768 and compressed memory of size 1152 with compression rate $C = 3$ . During evaluation, we increased the TransformerXL memory size to 4096 and the compressed memory in our model to 3072 (after sweeping over the validation set), obtaining the numbers reported in Table 4. We show the effect of scaling the compressed memory size and evaluation performance in Supplementary Section C. The proposed model achieves the new state-of-the-art on this dataset with 0.97 bits-per-character. ",
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+        "text": "We compare compression functions and the use of auxiliary losses in Table 5. We sweep over compression rates of 2, 3, and 4 and report results with the best performing value for each row. BPTT signifies that no auxiliary compression loss was used to train the network other than the overall training loss. To feed gradients into the compression function we unrolled the model over double the sequence length and halved the batch size to fit the larger unroll into memory. ",
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+        "table_caption": [
+            "Table 6: Validation and test perplexities on WikiText-103. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Valid.</td><td>Test</td></tr><tr><td>LSTM (Graves et al., 2014)</td><td></td><td>48.7</td></tr><tr><td>Temporal CNN (Bai et al.,2018a)</td><td>=</td><td>45.2</td></tr><tr><td>GCNN-14 (Dauphin et al.,2016)</td><td>=</td><td>37.2</td></tr><tr><td>Quasi-RNN Bradbury et al. (2016)</td><td>32</td><td>33</td></tr><tr><td>RMC (Santoro et al., 2018)</td><td>30.8</td><td>31.9</td></tr><tr><td>LSTM+Hebb. (Rae et al., 2018)</td><td>29.0</td><td>29.2</td></tr><tr><td>Transformer (Baevski and Auli,2019)</td><td>-</td><td>18.7</td></tr><tr><td>18L TransformerXL,M=384 (Dai et al.,2019)</td><td>-</td><td>18.3</td></tr><tr><td>18L TransformerXL,M=1024(ours)</td><td>=</td><td>18.1</td></tr><tr><td>18L Compressive Transformer,M=1024</td><td>16.0</td><td>17.1</td></tr></table>",
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "5.3 WIKITEXT-103 ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We train an eighteen-layered Compressive Transformer on the closed-vocabulary word-level language modelling benchmark WikiText-103, which contains articles from Wikipedia. We train the model with a compressed memory size, memory size, and a sequence window size all equal to 512. We trained the model over 64 Tensor Processing Units (TPU) v3 with a batch size of 2 per core — making for a total batch size of 128. The model converged in a little over 12 hours. We found the single-layer convolution worked best, with a compression rate of $c = 4$ . This model obtained 17.6 perplexity on the test set. By tuning the memory size over the validation set — setting the memory size to 500, and compressed memory size to 1, 500 — we obtain 17.1 perplexity. This is 1.2 perplexity points over prior state of the art, and means the model places a $\\approx 5 \\%$ higher probability on the correct word over the prior SotA TransformerXL. ",
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+    {
+        "type": "text",
+        "text": "It is worth noting that in Table 6 we do not list methods that use additional training data, or that make use of test-time labels to continue training the model on the test set (known as dynamic evaluation (Graves, 2013)). If we incorporate a very naive dynamic evaluation approach of loading a model checkpoint and continuing training over one epoch of the test set, then we obtain a test perplexity of 16.1. This is slightly better than the published 16.4 from Krause et al. (2019) — which uses a more sophisticated dynamic evaluation approach on top of the TransformerXL. However in most settings, one does not have access to test-time labels — and thus we do not focus on this setting. Furthermore there has been great progress in showing that more data equates to much better language modelling; Shoeybi et al. (2019) find a large transformer 8B-parameter transformer trained on 170GB of text obtains 10.7 word-level perplexity on WikiText-103. However it is not clear to what extent the WikiText-103 test set may be leaked inside these larger training corpora. For clarity of model comparisons, we compare to published results trained on the WikiText-103 training set. ",
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+        "type": "text",
+        "text": "We break perplexity down by word frequency in Table 7 and see the Compressive Transformer makes only a small modelling improvement for frequent words $( 2 . 6 \\%$ over the TransformerXL baseline) but obtains a much larger improvement of $\\approx 2 0 \\%$ for infrequent words. Furthermore, we see $\\mathbf { 1 0 X }$ improvement in modelling rare words over the prior state-of-the-art LSTM language model published in 2018 — which demonstrates the rate of progress in this area. ",
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+    {
+        "type": "text",
+        "text": "5.4 COMPRESSIBILITY OF LAYERS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We can use compression to better understand the model’s mode of operation. We inspect how compressible Transformer’s activations are as they progress through higher layers in the network. One may expect representations to become more difficult to compress at higher layers, if more semantic information is represented there. We monitor the compression loss at each layer of our best-performing Compressive Transformer models trained on Enwik8 and WikiText-103 and display these in Supplementary Section B Figure 6. We note that the compression loss is about one order of magnitude higher for word-level language modelling (WikiText-103) over character-level langauge modelling (Enwik8). Furthermore the first layer of the Transformer is highly compressible. However there is not a clear trend of compression cost increasing with layer depth. ",
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+        "table_caption": [
+            "Table 7: WikiText-103 test perplexity broken down by word frequency buckets. The most frequent bucket is words which appear in the training set more than 10, 000 times, displayed on the left. For reference, a uniform model would have perplexity $| V | = 2 . 6 e 5$ for all frequency buckets. \\*LSTM comparison from Rae et al. (2018) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>&gt;10K</td><td>1K-10K</td><td>100－1K</td><td>&lt;100</td><td>All</td></tr><tr><td>LSTM*</td><td>12.1</td><td>219</td><td>1,197</td><td>9,725</td><td>36.4</td></tr><tr><td>TransformerXL(ours)</td><td>7.8</td><td>61.2</td><td>188</td><td>1,123</td><td>18.1</td></tr><tr><td>Compressive Transformer</td><td>7.6</td><td>55.9</td><td>158</td><td>937</td><td>17.1</td></tr><tr><td>Relative gain over TXL</td><td>2.6%</td><td>9.5%</td><td>21%</td><td>19.9%</td><td>5.8%</td></tr></table>",
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+        "image_caption": [
+            "Figure 2: Attention weight on Enwik8. Average attention weight from the sequence over the compressed memory (oldest), memory, and sequence (newest) respectively. The sequence self-attention is causally masked, so more attention is placed on earlier elements in the sequence. There is an increase in attention at the transition from memory to compressed memory. "
+        ],
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+        "image_caption": [
+            "Figure 3: Learning rate analysis. Reducing the learning rate (e.g. to zero) during training (on Enwik8) harms training performance. Reducing the frequency of optimisation updates (effectively increasing the batch size) is preferable. "
+        ],
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+    {
+        "type": "text",
+        "text": "5.5 ATTENTION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We inspect where the network is attending to on average, to determine whether it is using its compressed memory. We average the attention weight over a sample of 20, 000 sequences from a trained model on Enwik8. We aggregate the attention into eighteen buckets, six for each of the compressed memory, memory, and sequence respectively. We set the size of the sequence, memory and compressed memory all to be 768. We plot this average attention weight per bucket in Figure 2 with a $1 \\sigma$ standard error. We see most of the attention is placed on the current sequence; with a greater weight placed on earlier elements of the sequence due to the causal self-attention mechanism which masks future attention weights. We also observe there is an increase in attention from the oldest activations stored in the regular memory, to the activations stored in the compressed memory. This goes against the trend of older memories being accessed less frequently — and gives evidence that the network is learning to preserve salient information. ",
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+    {
+        "type": "text",
+        "text": "5.5.1 OPTIMISATION SCHEDULE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We make an observation about an interesting but undesirable meta-learning phenomenon during long-context training. When the learning rate is tuned to be much smaller (or set to zero) during training, performance degrades drastically both for the TransformerXL and the Compressive Transformer. This is displayed in Figure 3. ",
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+    {
+        "type": "text",
+        "text": "Usually we consider distributional shift from the training data to the test data, but we can also observe a shift in the model when transferring from a training to evaluation mode (even when the model is evaluated on the training data). In this case, this is due to the online updating of parameters whilst processing long contiguous articles. We would like the model to generalise well to scenarios where it is not continuously optimised. Updating the parameters only at article boundaries (and then resetting the state) could be one solution for long-range memory models, but this would slow down learning significantly. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Instead, we propose reducing the frequency of optimisation updates during training. We find this allows for the best of both worlds — fast initial learning with frequent updates, and better generalisation near the end of training with less frequent updates (e.g. every 4 steps). Reducing the optimisation frequency increases the effective batch size, which has also been shown to be preferable to learning rate decay in image modelling (Smith et al., 2018). We observed a final performance improvement in our TransformerXL baseline on Enwik8, from 0.995 — which approximately replicates the published result — to 0.984 — which matches the most recent SotA architecture. We note, the additional space and compute cost of accumulating gradients is negligible across iterations, so there was no performance regression in using this scheme. ",
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+    {
+        "type": "text",
+        "text": "5.6 SPEECH ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We train the Compressive Transformer on the waveform of speech to assess its performance on different modalities. Speech is interesting because it is sampled at an incredibly high frequency, but we know it contains a lot of information on the level of phonemes and entire phrases. ",
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+    {
+        "type": "text",
+        "text": "To encourage long-term reasoning, we refrain from conditioning the model on speaker identity or text features, but focus on unconditional speech modelling. We train the model on 24.6 hours of 24kHz North American speech data. We chunk the sequences into windows of size 3840, roughly 80ms of audio, and compare a 20-layer Compressive Transformer to a 20-layer TransformerXL and a 30-layer WaveNet model (Oord et al., 2016) — a state-of-the-art audio generative model used to serve production speech synthesis applications at Google (Oord et al., 2018). All networks have approximately 40M parameters, as WaveNet is more parameter-efficient per layer. We train each network with 32 V100 GPUs, and a batch size of 1 per core (total batch size of 32) using synchronous training. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "WaveNet processes an entire chunk in parallel, however the TransformerXL and Compressive Transformer are trained with a window size of 768 and a total memory size of 1, 568 (for the Compressive Transformer we use 768 memory $+ 7 6 8$ compressed). We thus unroll the model over the sequence. Despite this sequential unroll, the attention-based models train at only half the speed of WaveNet. We see the test-set negative-log-likelihood in Figure 4, and observe that a Compressive Transformer with a compression rate of 4 is able to outperform the TransformerXL and maintain a slim advantage over WaveNet. However we only trained models for at most one week (with 32GPUs) and it would be advantageous to continue training until full convergence — before definitive conclusions are made. ",
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+    {
+        "type": "text",
+        "text": "5.7 REINFORCEMENT LEARNING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Compression is a good fit for video input sequences because subsequent frames have high mutual information. Here we do not test out the Compressive Transformer on video, but progress straight to a reinforcement learning agent task that receives a video stream of visual observations — but must ultimately learn to use its memory to reason over a policy. ",
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+    {
+        "type": "text",
+        "text": "We test the Compressive Transformer as a drop-in replacement to an LSTM in the IMPALA setup (Espeholt et al., 2018). Otherwise, we use the same training framework and agent architecture as described in the original work with a fixed learning rate of 1.5e-5 and entropy cost coefficient of 2e-3. We test the Compressive Transformer on a challenging memory task within the DMLab-30 (Beattie et al., 2016) domain, rooms select nonmatching object. This requires the agent to explore a room in a visually rich 3D environment and remember the object present. The agent can then advance to a second room where it must select the object not present in the original room. This necessitates that the agent both remember events far in the past, and also learn to efficiently reason about them. ",
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+    {
+        "type": "text",
+        "text": "We fix both the memory and compressed memory sizes to 64. In Figure 5, we present results for a range of compression rates, averaged over 3 seeds. We see that the best performing agents endowed with the Compressive Transformer are able to solve the task to human-level. We note that the model with compression rate 1 is unable to learn the task to the same proficiency. The speed of learning and stability seem to increase proportionally with higher rates of compression (up to a limit) – i.e. ",
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+        "img_path": "images/42afd920bfbb3132ee3f0bccc130234e666d527c199fd0bd2f67885c2d8766e7.jpg",
+        "image_caption": [
+            "Figure 4: Speech Modelling. We see the Compressive Transformer is able to obtain competitive results against the state-of-the-art WaveNet in the modelling of raw speech sampled at $2 4 \\mathrm { k H z }$ . "
+        ],
+        "image_footnote": [],
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+        "page_idx": 9
+    },
+    {
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+        "img_path": "images/73b459f5476814831f88dbae381c01075c186cec825da44f6a778c19c5f94da1.jpg",
+        "image_caption": [
+            "Figure 5: Vision and RL. We see the Compressive Transformer integrates visual information across time within an IMPALA RL agent, trained on an object matching task. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "the effective memory window of the agent – and we find compression rate 4 to once again be the best performing. We see this as a promising sign that the architecture is able to efficiently learn, and suitably use, compressed representations of its visual input and hope to test this more widely in future work. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper we explore the notion of compression as a means of extending the temporal receptive field of Transformer-based sequence models. We see a benefit to this approach in the domain of text, with the Compressive Transformer outperforming existing architectures at long-range language modelling. To continue innovation in this area, we also propose a new book-level LM benchmark, PG-19. This may be used to compare long-range language models, or to pre-train on other longrange reasoning language tasks, such as NarrativeQA (Kocisk ˇ y et al., 2018). \\` ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We see the idea of compressive memories is applicable not only to the modality of text, but also audio, in the form of modelling the waveform of speech, and vision, within a reinforcement-learning agent trained on a maze-like memory task. In both cases, we compare to very strong baselines (Wavenet (Oord et al., 2016) and IMPALA (Espeholt et al., 2018)). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The main limitation of this work is additional complexity, if the task one wishes to solve does not contain long-range reasoning then the Compressive Transformer is unlikely to provide additional benefit. However as a means of scaling memory and attention, we do think compression is a simpler approach to dynamic or sparse attention — which often requires custom kernels to make efficient. One can build effective compression modules from simple neural network components, such as convolutions. The compression components are immediately efficient to run on GPUs and TPUs. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Memory systems for neural networks began as compressed state representations within RNNs. The recent wave of progress using attention-based models with deep and granular memories shows us that it is beneficial to refrain from immediately compressing the past. However we hypothesise that more powerful models will contain a mixture of granular recent memories and coarser compressed memories. Future directions could include the investigation of adaptive compression rates by layer, the use of long-range shallow memory layers together with deep short-range memory, and even the use of RNNs as compressors. Compressive memories should not be forgotten about just yet. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We thank Chris Dyer, Felix Gimeno, and Koray Kavukcuoglu for reviewing the manuscript. We thank Peter Dayan, Adam Santoro, Jacob Menick, Emilio Parisotto, Hyunjik Kim, Simon Osindero, Sergey Bartunov, David Raposo, and Daan Wierstra for ideas regarding model design. We thank Yazhe Li and Aaron Van de Oord for their help and advice in instrumenting speech modelling experiments. Finally, we thank our wider DeepMind colleagues for supporting this project with stimulating discussions, engineering infrastructure, and positive reinforcement signals. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "REFERENCES   \nR. Al-Rfou, D. Choe, N. Constant, M. Guo, and L. Jones. Character-level language modeling with deeper self-attention. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 3159–3166, 2019.   \nA. Baevski and M. Auli. Adaptive input representations for neural language modeling. arXiv preprint arXiv:1809.10853, 2019.   \nD. Bahdanau, K. Cho, and Y. Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014.   \nS. Bai, J. Z. Kolter, and V. Koltun. Convolutional sequence modeling revisited, 2018a. URL https://openreview.net/forum?id $_ { \\cdot } =$ rk8wKk-R-.   \nS. Bai, J. Z. Kolter, and V. Koltun. Trellis networks for sequence modeling. arXiv preprint arXiv:1810.06682, 2018b.   \nC. Beattie, J. Z. Leibo, D. Teplyashin, T. Ward, M. Wainwright, H. Kuttler, A. Lefrancq, S. Green, ¨ V. Valdes, A. Sadik, J. Schrittwieser, K. Anderson, S. York, M. Cant, A. Cain, A. 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Transformerxl: Attentive language models beyond a fixed-length context. arXiv preprint arXiv:1901.02860, 2019.   \nY. N. Dauphin, A. Fan, M. Auli, and D. Grangier. Language modeling with gated convolutional networks. arXiv preprint arXiv:1612.08083, 2016.   \nJ. 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.   \nL. Espeholt, H. Soyer, R. Munos, K. Simonyan, V. Mnih, T. Ward, Y. Doron, V. Firoiu, T. Harley, I. Dunning, et al. Impala: Scalable distributed deep-rl with importance weighted actor-learner architectures. In International Conference on Machine Learning, pages 1406–1415, 2018.   \nE. Grave, A. Joulin, and N. Usunier. Improving neural language models with a continuous cache. arXiv preprint arXiv:1612.04426, 2016.   \nA. Graves. Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850, 2013.   \nA. Graves, G. Wayne, and I. Danihelka. Neural turing machines. arXiv preprint arXiv:1410.5401, 2014.   \nA. Graves, G. Wayne, M. Reynolds, T. Harley, I. Danihelka, A. Grabska-Barwinska, S. G. Col-´ menarejo, E. Grefenstette, T. Ramalho, J. Agapiou, et al. Hybrid computing using a neural network with dynamic external memory. Nature, 538(7626):471, 2016.   \nD. Ha, A. Dai, and Q. V. Le. Hypernetworks. arXiv preprint arXiv:1609.09106, 2016.   \nF. Hill, A. Bordes, S. Chopra, and J. Weston. The goldilocks principle: Reading children’s books with explicit memory representations. arXiv preprint arXiv:1511.02301, 2015. S. Hochreiter and J. Schmidhuber. Long short-term memory. Neural computation, 9(8):1735–1780, 1997.   \nA. Holtzman, J. Buys, M. Forbes, and Y. Choi. The curious case of neural text degeneration. arXiv preprint arXiv:1904.09751, 2019.   \nM. Hutter. The human knowledge compression contest. URL http://prize. hutter1. net, 6, 2012. N. Kalchbrenner, L. Espeholt, K. Simonyan, A. v. d. Oord, A. Graves, and K. Kavukcuoglu. Neural machine translation in linear time. arXiv preprint arXiv:1610.10099, 2016.   \nD. P. Kingma and J. Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.   \nT. Kocisk ˇ y, J. Schwarz, P. Blunsom, C. Dyer, K. M. Hermann, G. Melis, and E. Grefenstette. The \\` narrativeqa reading comprehension challenge. Transactions of the Association for Computational Linguistics, 6:317–328, 2018.   \nB. Krause, L. Lu, I. Murray, and S. Renals. Multiplicative lstm for sequence modelling. arXiv preprint arXiv:1609.07959, 2016.   \nB. Krause, E. Kahembwe, I. Murray, and S. Renals. Dynamic evaluation of transformer language models. CoRR, abs/1904.08378, 2019. URL http://arxiv.org/abs/1904.08378. G. Lample, A. Sablayrolles, M. Ranzato, L. Denoyer, and H. Jegou. Large memory layers with ´ product keys. arXiv preprint arXiv:1907.05242, 2019.   \nS. Merity, C. Xiong, J. Bradbury, and R. Socher. Pointer sentinel mixture models. arXiv preprint arXiv:1609.07843, 2016.   \nT. Mikolov, M. Karafiat, L. Burget, J. ´ Cernock ˇ y, and S. Khudanpur. Recurrent neural network \\` based language model. In Eleventh Annual Conference of the International Speech Communication Association, 2010.   \nA. Oord, Y. Li, I. Babuschkin, K. Simonyan, O. Vinyals, K. Kavukcuoglu, G. Driessche, E. Lockhart, L. Cobo, F. Stimberg, et al. Parallel wavenet: Fast high-fidelity speech synthesis. In International Conference on Machine Learning, pages 3915–3923, 2018.   \nA. v. d. Oord, S. Dieleman, H. Zen, K. Simonyan, O. Vinyals, A. Graves, N. Kalchbrenner, A. Senior, and K. Kavukcuoglu. Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03499, 2016.   \nD. Paperno, G. Kruszewski, A. Lazaridou, Q. Pham, R. Bernardi, S. Pezzelle, M. Baroni, G. Boleda, R. Fernandez, K. Erk, et al. The lambada dataset: Word prediction requiring a broad discourse ´ context. Association for Computational Linguistics, 2016.   \nJ. Rae, J. J. Hunt, I. Danihelka, T. Harley, A. W. Senior, G. Wayne, A. Graves, and T. Lillicrap. Scaling memory-augmented neural networks with sparse reads and writes. In Advances in Neural Information Processing Systems, pages 3621–3629, 2016.   \nJ. W. Rae, C. Dyer, P. Dayan, and T. P. Lillicrap. Fast parametric learning with activation memorization. arXiv preprint arXiv:1803.10049, 2018.   \nB. A. Richards and P. W. Frankland. The persistence and transience of memory. Neuron, 94(6): 1071–1084, 2017.   \nD. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning representations by back-propagating errors. Nature, 323(6088):533, 1986.   \nA. Santoro, R. Faulkner, D. Raposo, J. Rae, M. Chrzanowski, T. Weber, D. Wierstra, O. Vinyals, R. Pascanu, and T. Lillicrap. Relational recurrent neural networks. In Advances in Neural Information Processing Systems, pages 7299–7310, 2018.   \nM. Shoeybi, M. Patwary, R. Puri, P. LeGresley, J. Casper, and B. Catanzaro. Megatron-lm: Training multi-billion parameter language models using model parallelism, 2019.   \nS. Smith, P. jan Kindermans, C. Ying, and Q. V. Le. Don’t decay the learning rate, increase the batch size. 2018. URL https://openreview.net/pdf?id ${ . } = { }$ B1Yy1BxCZ. S. Sukhbaatar, E. Grave, P. Bojanowski, and A. Joulin. Adaptive attention span in transformers. arXiv preprint arXiv:1905.07799, 2019.   \nA. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin. Attention is all you need. In Advances in neural information processing systems, pages 5998–6008, 2017.   \nF. Wu, A. Fan, A. Baevski, Y. N. Dauphin, and M. Auli. Pay less attention with lightweight and dynamic convolutions. arXiv preprint arXiv:1901.10430, 2019.   \nZ. Yang, Z. Dai, Y. Yang, J. Carbonell, R. Salakhutdinov, and Q. V. Le. Xlnet: Generalized autoregressive pretraining for language understanding. arXiv preprint arXiv:1906.08237, 2019.   \nL. Zhou, Y. Zhou, J. J. Corso, R. Socher, and C. Xiong. End-to-end dense video captioning with masked transformer. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8739–8748, 2018.   \nY. Zhu, R. Kiros, R. Zemel, R. Salakhutdinov, R. Urtasun, A. Torralba, and S. Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In Proceedings of the IEEE international conference on computer vision, pages 19–27, 2015. J. G. Zilly, R. K. Srivastava, J. Koutn´ık, and J. Schmidhuber. Recurrent highway networks. In Proceedings of the 34th International Conference on Machine Learning-Volume 70, pages 4189– 4198. JMLR. org, 2017. ",
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A TEMPORAL RANGE OF THE COMPRESSIVE TRANSFORMER ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "The TransformerXL with a memory of size $n$ has a maximum temporal range of $l \\times n$ with an attention cost of $\\mathcal { O } ( n _ { s } ^ { 2 } + n _ { s } n )$ (see Dai et al. (2019) for a detailed discussion). The Compressive Transformer now has a maximum temporal range of $l \\times \\left( n _ { s } + n _ { m } + c * n _ { c m } \\right)$ with an attention cost of $\\mathcal { O } ( n _ { s } ^ { 2 } + n _ { s } ( n _ { m } + n _ { c m } ) )$ . For example, setting $n _ { c m } = n _ { m } = n / 2$ and $c = 3$ we obtain a maximum temporal range that is two times greater than the TransformerXL with an identical attention cost. Thus if we can learn in the $c > 1$ compressed setting, the temporal range of the model can be significantly increased. ",
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+    },
+    {
+        "type": "text",
+        "text": "B COMPRESSION ACROSS LAYERS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We inspect the compression loss broken down by the layer index, to investigate whether there is a trend in network depth with how compressible the representations are. The compression loss here refers to the attention-reconstruction attention loss. We plot this for a 24 layer trained model on Enwik8, and an 18 layer model trained on WikiText-103. The compression loss for characterbased language modelling is about one order of magnitude lower than that of word-level language modelling. The first layer’s representations are highly compressible, however from then on there is no fixed trend. Some non-contiguous layers have a very similar compression loss (e.g. 4 & 6, 5 & 7) which suggests information is being routed from these layer pairs via the skip connection. ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ac86293c4cd4f466d587bbab8a7c5a4cb730e28f0ff5a8d8b0ff0bd03f5b3baf.jpg",
+        "image_caption": [
+            "Figure 6: Model analysis. Compression loss broken down by layer. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "C COMPARISON OF COMPRESSED MEMORY SIZES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We compare the best test perplexity obtained for the Compressive Transformer trained on WikiText103 and Enwik8 across a range of compressed memory sizes. For both models, the best model used a 1D convolution compression network with a compression rate of 3. The Enwik8 model was trained with an embedding size of 1024, 8 attention heads, 24 layers, an mlp hidden size of 3072, a sequence window size of 768, and a memory size of 768. We see the best compressed memory size is 3, 072 in this sweep, facilitating a total attention window of 3840. The WikiText-103 model was trained with an embedding size of 1024, adaptive inputs using the same parameters as (Sukhbaatar et al., 2019), 16 attention heads, 18 layers, an mlp hidden size of 4096, a sequence window of size 512 and a memory of size 512. The best compressed memory size is 1536 resulting in a total attention window of c. 2048. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9b5717cc0e4ccb7b017505628b8bc32ac87de2acfe3159333379654379b92717.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Compressed Memory Size Enwik8 BPC</td><td>512 1.01</td><td>1024 0.99</td><td>2048 0.98</td><td>3072 0.97</td><td>4096 1.00</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 8: Compressed memory size vs test performance for Enwik8 ",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e4e35544ede3400da210215d541deab40edc86d4bb25bda1f66516931f6feb69.jpg",
+        "table_caption": [
+            "Table 9: Compressed memory size vs test performance for WikiText-103 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Compressed Memory Size</td><td>256</td><td>512</td><td>1024</td><td>1536</td><td>2048</td></tr><tr><td>WikiText-103 Perplexity</td><td>18.2</td><td>17.9</td><td>17.6</td><td>17.1</td><td>17.7</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "D PG-19 PREPROCESSING ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The raw texts from the Gutenberg project were minimally pre-processed by removing boilerplate license text. We then also replaced discriminatory words with a unique $\\langle \\mathrm { D W x } \\rangle$ token using the Ofcom list of discriminatory words 4. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "E PG-19 TOPICS ",
+        "text_level": 1,
+        "bbox": [
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+            297
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We present top-words for some of the topics on the PG-19 corpus. These were generated with LDA topic model (Blei et al., 2003). ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/66326489e1adda3643e1b564ccf51190c7865443b92a6b940f4def603f2bf2cc.jpg",
+        "table_caption": [
+            "Table 10: Examples of top topics on PG-19 corpus. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Geography</td><td>War</td><td>Civilisations</td><td>Human Condition</td><td>Naval</td><td>Education</td><td>Art</td></tr><tr><td>water</td><td>people</td><td>roman</td><td>love</td><td>island</td><td>work</td><td>poet</td></tr><tr><td>river</td><td>emperor</td><td>rome</td><td>religion</td><td>ship</td><td>school</td><td>music</td></tr><tr><td>feet</td><td>war</td><td>greek</td><td>religious</td><td>sea</td><td>life</td><td>one</td></tr><tr><td>miles</td><td> army</td><td>city</td><td>life</td><td>men</td><td>children</td><td>poetry</td></tr><tr><td>north</td><td>death</td><td>gods</td><td>moral</td><td>captain</td><td>may</td><td>work</td></tr><tr><td>south</td><td>battle</td><td>king</td><td>human</td><td>coast</td><td>social</td><td>literature</td></tr><tr><td>mountains</td><td>city</td><td>first</td><td>society</td><td>land</td><td>child</td><td>art</td></tr><tr><td>sea</td><td>soldiers</td><td>caesar</td><td>man</td><td>great</td><td>education</td><td>great</td></tr><tr><td>lake</td><td>power</td><td>great</td><td>virtue</td><td>found</td><td>conditions</td><td>poem</td></tr><tr><td>rock</td><td>thousand</td><td>romans</td><td> nature</td><td>islands</td><td>well</td><td>written</td></tr><tr><td>mountain</td><td>arms</td><td>athens</td><td>marriage</td><td>shore</td><td> study</td><td>english</td></tr><tr><td>country</td><td>empire</td><td>greece</td><td>women</td><td>voyage</td><td>best</td><td>author</td></tr><tr><td>valley</td><td>upon</td><td>temple</td><td>christian</td><td>vessels</td><td>years</td><td>play</td></tr><tr><td>ice</td><td>country</td><td>son</td><td>age</td><td>time</td><td>possible</td><td>genius</td></tr><tr><td>west</td><td>time</td><td>egypt</td><td>law</td><td>english</td><td>class</td><td>style</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "F PG-19 SAMPLES ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We show a few different samples from the Compressive Transformer trained on PG-19. We use Nucleus Sampling with $p = 0 . 9 8$ (Holtzman et al., 2019). We choose extracts of books from the test set as prefixes. We see the model is able to continue in the style of the text, creating artificial dialogue or descriptive text, and remembering the names of characters over hundreds of words. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As the Compressive Transformer is trained without state resetting, it is actually slightly out of sample when provided with the (relatively) short contexts. This is because its memory and compressed memory may be still empty (whereas they are always full during training). However we see a trend of the samples usually improving towards the end. ",
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+    },
+    {
+        "type": "text",
+        "text": "Context from Baby Mine by Maragaret Mayo: ",
+        "text_level": 1,
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+        "page_idx": 15
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+    {
+        "type": "text",
+        "text": "CHAPTER I ",
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Even in college Alfred Hardy was a young man of fixed ideas and high ideals and proud of it. ",
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+    {
+        "type": "text",
+        "text": "His friend, Jimmy Jinks, had few ideas and no ideals, and was glad of it, and before half of their first college term had passed, Jimmy had ridded himself of all such worries as making up his own mind or directing his own morals. Alfred did all these things so much better, argued Jimmy, furthermore, Alfred LIKED to do them–Jimmy owed it to his friend to give him that pleasure. ",
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+    },
+    {
+        "type": "text",
+        "text": "Compressive Transformer: ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "He did not like doing them in the most elegant of all possible marble walks–where freshmen and sophomores stand and talk and laugh and chatter till evening falls and look cool and still and cool and beautifully white in spite of the hot sun, but had to go there for a month before going home. It happened one day that he and Jimmy were strolling together in the green shade of St. Martin’s, and Jimmy naturally asked why he was so silent. He was very talkative as most boys are who have once got the habit of it on shore, so the need for answering was soon supplied. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "”I am wondering,” he said, ”why my old friend and chum, Jimmy Jinks, is living a single life and so has no boys. Have you not noticed that many of his old friends had their own boys to follow in their footsteps and help, and often helped successfully too?” ",
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "”Oh, yes,” said Alfred, ”it was plain enough then that he liked to live by himself and got none of his present pleasures or entertainments because of the other fellow’s giving it to him.” ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "”Then it IS sad,” said Jimmy, ”that an old friend like the friend of Big Lights, Jimmy Reynolds, should be living the single life and having no boys.” ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "”And it is pretty true, too,” said Alfred, ”yet I believe it is the best thing that could happen even now.” ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "”And so do I,” said Jimmy, ”and I also believe that it is time someone did something to make the things worse for the other’s partner.” ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "”And so do I,” said Alfred, ”and so do I, and so do I.” ",
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+        "text": "”I don’t know,” said Alfred, ”but if someone will come down to the valley and go through a regular mill with the old forces at work, doing the work of the two, and doing it better than any other Miller he ever saw or ever hoped to see, I think there will be a good deal of change in the things and things to be cared for for and for driven and counter-driven.” ",
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+        "text": "”I will come and do that mill,” said Jimmy. ",
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+    {
+        "type": "text",
+        "text": "Context from The Diary of Samuel Pepys: ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 16
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+        "type": "text",
+        "text": "June 1st. Having taken our leaves of Sir W. Batten and my Lady, who are gone this morning to keep their Whitsuntide, Sir W. Pen and I and Mr. Gauden by water to Woolwich, and there went from ship to ship to give order for and take notice of their forwardness to go forth, and then to Deptford and did the like, having dined at Woolwich with Captain Poole at the tavern there. From Deptford we walked to Redriffe, calling at the half-way house, and there come into a room where there was infinite of new cakes placed that are made against Whitsuntide, and there we were very merry. By water home, and there did businesses of the office. Among others got my Lord’s imprest of L1000 and Mr. Creed’s of L10,000 against this voyage their bills signed. Having wrote letters into the country and read some things I went to bed. ",
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+        "type": "text",
+        "text": "Compressive Transformer: ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "So I rose and did some business at the office, and then to dinner, where great abundance of good things of the kitchen I only being partaker in the feast. After dinner I went to look at the yard and found it in a very bad condition, so I went home and there finding no delight in seeing things I should make shift to get in my way and so I will leave off. ",
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+        "type": "text",
+        "text": "So I took leave of my great friend, and the next day being Sunday, my wife and I and a great number of friends went by water to Deptford, and there took the oaths of allegiance and supremacy and promised such obedience to the Lord as should hereafter turn to the advantage of our State. Being come back we found the shops and warehouses in a pitiable condition, so my wife and I and all the rest of the friends went home and there did the like and by Saturday day I being alone in my office I found myself in a very bad situation, for my Lord, and Mr. Creed, and Pett were all standing ready to receive and receive the oaths of allegiance and right to make use of the ten days’ licence I had allowed for this purpose by virtue of the law that was such a help to the servant. Having looked at the ships, I told my wife what I had seen and that I was greatly troubled at my situation and, I hope that will mend it. ",
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+        "type": "text",
+        "text": "So that is the end of a long and patient seeking after those things which in my opinion I deserve and may get if I can only by fair means get them. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Context from The Patrol of the Sun Dance Trail by Ralph Connor: ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "High up on the hillside in the midst of a rugged group of jack pines the Union Jack shook out its folds gallantly in the breeze that swept down the Kicking Horse Pass. That gallant flag marked the headquarters of Superintendent Strong, of the North West Mounted Police, whose special duty it was to preserve law and order along the construction line of the Canadian Pacific Railway Company, now pushed west some scores of miles. ",
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+        "text": "Along the tote-road, which ran parallel to the steel, a man, dark of skin, slight but wiry, came running, his hard panting, his streaming face, his open mouth proclaiming his exhaustion. At a little trail that led to the left he paused, noted its course toward the flaunting flag, turned into it, then struggled up the rocky hillside till he came to the wooden shack, with a deep porch running round it, and surrounded by a rustic fence which enclosed a garden whose neatness illustrated a characteristic of the British soldier. The runner passed in through the gate and up the little gravel walk and began to ascend the steps. ",
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+        "text": "Compressive Transformer: ",
+        "text_level": 1,
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+        "page_idx": 17
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+    {
+        "type": "text",
+        "text": "As though by mutual consent, all the three members of the Superintendent Force were standing on the veranda watching his progress, a man came strolling slowly down the path, stopping often to gaze curiously about him, then stopping once more when he saw the four standing on the veranda. His face was dark, his eyes prominent, and the lines that furrowed his forehead showed marks of many woes, yet his step was alert and he began to mount the steps with steady strides. ",
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+    {
+        "type": "text",
+        "text": "The man’s attention was diverted by the unexpected appearance of the two policemen; a third man came slipping up, grumbling under his breath, and stopped long enough to look doubtfully around him, then slipped away again. In the meantime, the four on the veranda continued to watch the approach of the new arrival. In spite of himself, the Superintendent Force became conscious of a curious feeling–uneasiness that was almost fear–in the presence of that strange man. He would not allow himself to admit the fact, yet he felt it in his bones. But to the watchers, the plain, everyday features of that stranger and his coming, seemed only just what the Seven White Shee owed him–their weight, their hurry, their blast. ",
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+    {
+        "type": "text",
+        "text": "Had a chariot been made for the good of the three horses, and had the driver been given orders that he should speed them that he might win, they would have been heartening things in the sight of the veteran and the victor. To you they would have been unintelligible to the root of your understanding. When you gaze up in the faces of those four gray horses, you can see clearly through the clouds of dust that rise from their hoofs, and discern plainly where the banker is and where the hobo. Then you will understand why you shall not press the bitter grapes and why you shall not spurn the generous doctrines. You will understand why you shall not praise the lash or the spur, for you will know where the true would be and where the false would be. Then you will understand why you, a man with reason and heart, need not tear your hair over-bitter and why you need not laugh over the blunders of an ignorant man. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "About nine o’clock that morning, two buggies, drawn by powerful horses, crossed the Rubicon and turned the railroad from Sandhurst into the Hollow of the Mountains. And though the charioteers stood at their horses’ heads, and their drivers cried at their loudest, there was not a man in the four teams who did not feel that his day was worth all the toil and all the peril that he had undergone. And if there were a man in them who did not know that–who did not feel that the road through the Hollow of the Mountains is made easy by the arrival of travelers and by the coming of government, there was one who did not at that moment care whether his day’s work were worth all the toil and all the danger that he had had to endure or whether it were not worth more than all. ",
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+    {
+        "type": "text",
+        "text": "AUTHOR CONTRIBUTIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            395,
+            118
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Model and Experiment design: JR, TL, AP, SJ   \nDataset creation: AP, JR, CH   \nText experiments: JR, AP   \nRL experiments: SJ   \nSpeech experiments: JR ",
+        "bbox": [
+            230,
+            127,
+            537,
+            219
+        ],
+        "page_idx": 18
+    }
+]

parse/train/kHSu4ebxFXY/kHSu4ebxFXY.md

@@ -0,0 +1,329 @@
+# MARS: MARKOV MOLECULAR SAMPLING FOR MULTI-OBJECTIVE DRUG DISCOVERY
+
+Yutong $\mathbf { X } \mathbf { i } \mathbf { e } ^ { \mathrm { { \dagger } } \circ }$ , Chence $\mathbf { S h i } ^ { \dagger \triangle }$ , Hao Zhou†∗, Yuwei Yang†, Weinan Zhang‡, Yong $\mathbf { V } \mathbf { u } ^ { \ddag }$ , Lei Li†∗   
+†ByteDance AI Lab, Shanghai, China   
+University of Michigan, Ann Arbor, MI, USA   
+4Montreal Institute of Learning Algorithms, Montreal, Canada ´   
+‡Department of Computer Science and Engineering, Shanghai Jiao Tong University, China
+
+# ABSTRACT
+
+Searching for novel molecules with desired chemical properties is crucial in drug discovery. Existing work focuses on developing neural models to generate either molecular sequences or chemical graphs. However, it remains a big challenge to find novel and diverse compounds satisfying several properties. In this paper, we propose MARS, a method for multi-objective drug molecule discovery. MARS is based on the idea of generating the chemical candidates by iteratively editing fragments of molecular graphs. To search for high-quality candidates, it employs Markov chain Monte Carlo sampling (MCMC) on molecules with an annealing scheme and an adaptive proposal. To further improve sample efficiency, MARS uses a graph neural network (GNN) to represent and select candidate edits, where the GNN is trained on-the-fly with samples from MCMC. Experiments show that MARS achieves state-of-the-art performance in various multi-objective settings where molecular bio-activity, drug-likeness, and synthesizability are considered. Remarkably, in the most challenging setting where all four objectives are simultaneously optimized, our approach outperforms previous methods significantly in comprehensive evaluations. The code is available at https://github.com/yutxie/mars.
+
+# 1 INTRODUCTION
+
+Drug discovery aims to find chemical compounds with desired target properties, such as high druglikeness (Bickerton et al., 2012, QED). The problem is also referred to as molecular design, molecular generation, or molecular search. The space of drug-like chemicals is enormous, approximate $1 0 ^ { 3 3 }$ for realistic drugs that could ever be synthesized (Polishchuk et al., 2013). Therefore it is very challenging to search for high-quality molecules from such a vast space — enumeration would take almost forever. For a particular disease, finding the right candidates targeting specific proteins further complicates the problem.
+
+Instead of enumerating or searching from the immense chemical space, recent work utilizes deep generative models to generate candidate molecules directly (Schwalbe-Koda & Gomez-Bombarelli, ´ 2020). However, most prior work focuses on generating molecules concerning a single property such as drug-likeness (QED) or octanol-water partition coefficient (logP) (Jin et al., 2018; You et al., 2018; Popova et al., 2019; Shi et al., 2020; Zang & Wang, 2020). While in practical settings, typical drug discovery requires consideration of multiple properties jointly (Nicolaou et al., 2012). For example, to find drug-like molecules that are easy to synthesize and exhibit high biological activity against the target protein. Naturally, multi-objective molecule design is much more challenging than the single-objective scenario (Jin et al., 2020).
+
+This paper studies the problem of multi-objective molecule design for drug discovery. An ideal solution should be efficient and meet the following criteria. $C I$ : It should satisfy multiple properties with high scores; C2: It should produce novel and diverse molecules; C3: Its generation process does not rely on either expert annotated or wet experimental data collected from a biochemistry lab (since it requires tremendous effort and hard to obtain). Existing molecule generation approaches are mainly designed for the single objective setting, and they could not meet all criteria in the setting of multiple objectives. These methods belong to four categories: a) generating candidates from a learned continuous latent space (Gomez-Bombarelli et al., 2018; Jin et al., 2018), b) through reinforcement ´ learning (You et al., 2018), c) using an encoder-decoder translation approach (Jin et al., 2019), or d) optimizing molecular properties through genetic algorithms (Nigam et al., 2020). Current stateof-the-art multi-objective molecular generation is a rationale-based method (Jin et al., 2020). In this approach, the authors propose to build molecules by composing multiple extracted rationales, and the model can generate compounds that are simultaneously active to multiple biological targets. However, such an approach will result in quite complex molecules when we have many objectives. This is because different objectives correspond to different rationales, and including all these rationales could lead to large molecules, which may be less drug-like and hard to be synthesized practically.
+
+In this paper, we propose MArkov moleculaR Sampling (MARS), a simple yet flexible method for drug discovery. The basic idea is to start from a seed molecule and keep generating candidate molecules by modifying fragments of molecular graphs from previous steps. It meets all the criteria C1-3. In MARS, the molecular design is formulated as an iterative editing procedure with its total objective consisting of multiple property scores (C1). MARS employs the annealed Markov chain Monte Carlo sampling method to search for optimal chemical compounds, which allows for the exploration of chemicals with novel and different fragments (C2). The proposal to modify molecular fragments is represented using graph neural networks (GNNs), whose parameters are adaptively learned. We used message passing neural networks (MPNNs) in practice (Gilmer et al., 2017), but other GNNs can fit the framework as well. Furthermore, MARS utilizes the sample paths generated on-the-fly to train the proposal network adaptively. Therefore, it does not rely on external annotated data (C3). With such an adaptive learnable proposal, it keeps improving the generation quality throughout the process.
+
+We evaluate MARS and four other baselines, one latest method for each of the four method categories. The benchmark includes a variety of multi-objective generation settings. Experiments show that our proposed MARS achieves state-of-the-art performance on five out of six tasks in terms of a comprehensive evaluation consisting of the success rate, novelty, and diversity of the generated molecules. Notably, in the most challenging setting where four objectives – bio-activities to two different targets, drug-likeness, and synthesizability – are simultaneously considered, our method achieves the state-of-the-art result and outperforms existing methods by $7 7 \%$ in the comprehensive evaluation.
+
+Our contributions are as follows:
+
+• We present MARS, a generic formulation of molecular design using Markov sampling, which can easily accommodate multiple objectives.   
+We develop an adaptive fragment-editing proposal based on GNN that is learnable on the fly with only samples self-generated and efficient in exploring the chemical space.   
+• Experiments verifies our proposed MARS framework can find novel and diverse bioactive molecules that are both drug-like and highly synthesizable.
+
+# 2 RELATED WORK
+
+Recent years have witnessed the success of applying deep generative models and molecular graph representation learning in drug discovery (Schwalbe-Koda & Gomez-Bombarelli, 2020; Guo & ´ Zhao, 2020). Existing approaches for molecular property optimization can be grouped into four categories, including generation with a) Bayesian inference, $^ b$ ) reinforcement learning, $c _ { . }$ ) encoderdecoder translation models, and d) evolutionary and genetic algorithms. The first category is learning continuous latent spaces for molecular sequences or graphs and generating from such spaces using Bayesian optimization (BO) (Gomez-Bombarelli et al., 2018; Jin et al., 2018; Winter et al., 2019). ´ These methods rely heavily on the quality of latent representations, which imposes huge challenges to the encoders when there are multiple properties to consider.
+
+Unlike the first class, other work uses reinforcement learning (RL) to optimize desired objectives directly in the explicit chemical space (De Cao & Kipf, 2018; Popova et al., 2018; You et al., 2018;
+
+Popova et al., 2019; Shi et al., 2020). However, the models are usually hard to train due to the high variance of RL.
+
+The third category directly trains a translation model that maps from an input molecule to a highquality output molecule (Jin et al., 2019; 2020). Although simple, such methods require many high-quality labeled data, making them impractical in scenarios where the data is limited.
+
+The last category of methods are evolutionary algorithms (EAs) and genetic algorithms (GAs) to explore large chemical space with certain property (Nicolaou et al., 2012; Devi et al., 2015; Jensen, 2019; Ahn et al., 2020). In Nigam et al. (2020), the authors propose to augment GA by adding an adversarial loss into the fitness evaluation to increase the diversity, and the augmented GA outperforms all other generative models in optimizing logP. Though flexible and straightforward, to make the search process efficient enough, most GA and EA methods require domain experts to design molecular mutation and crossover rules, which could be non-trivial to obtain.
+
+Besides single property optimization, there is recent work to address the multi-objective molecule generation problem. For example, Li et al. (2018) proposes to use a conditional generative model to incorporate several objectives flexibly, while Lim et al. (2020) leverages molecular scaffolds to control the properties of generated molecules better. Among them, the current state-of-the-art approach is a rationale-based method proposed by Jin et al. (2020). In this method, the authors propose to build molecules by assembling extracted rationales. Despite its great success in generating compounds simultaneously active to multiple biological targets, the combination of rationales might hinder the synthesizability and drug-likeness of produced molecules, as they tend to be large as the number of objectives grows. In contrast, our MARS framework turns the generation problem into a sampling procedure, which serves as an alternative way compared with deep generative models, and can efficiently discover bio-active molecules that are both drug-like and highly synthesizable.
+
+Remotely related is recent work to generate molecules through sampling. Seff et al. (2019) defines a Gibbs sampling procedure, in which the Markov chain alternates between randomly corrupting the molecules and recovering the corrupted ones with a learned reconstruction model. However, this method mainly focuses on generating molecules that follow the observed data distribution and cannot be directly tailored for property optimization. Different from this work, MARS is built upon the general MCMC sampling framework, which allows further enhancement with adaptive proposal learning to edit molecular graphs efficiently. Actually, generating instances from a discrete space with MCMC sampling methods is previously employed in various other applications, e.g., generating natural language sentences under various constraints (Miao et al., 2019; Zhang et al., 2019; Liu et al., 2020; Zhang et al., 2020).
+
+# 3 PROPOSED MARS APPROACH
+
+In this section, we present the MArkov moleculaR Sampling method (MARS) for multi-objective molecular design. We define a Markov chain over the explicit molecular graph space and design a kernel to navigate high probable candidates with acceptance and rejection.
+
+# 3.1 SAMPLING FROM THE MOLECULAR SPACE
+
+Our proposed MARS framework aims at sampling molecules with desired properties from the chemical space. Specifically, given $K$ properties of interest, the desired molecular distribution can be formulated as a combination of all objectives:
+
+$$
+\pi ( x ) = \underbrace { s _ { 1 } ( x ) \circ s _ { 2 } ( x ) \circ s _ { 3 } ( x ) \circ \dotsb \circ s _ { K } ( x ) } _ { \mathrm { d e s i r e d p r o p e r t i e s } }
+$$
+
+where $x$ is a molecule in the molecular space $\mathcal { X }$ . $\pi ( x )$ is an unnormalized distribution over molecules integrating the desired properties. $s _ { k } ( x )$ is a scoring function for the $k$ -th property and the “◦” operator stands for a combination of scores (e.g., summation or multiplication). In practical drug discovery, these terms could be related to the biological activity, drug-likeness, and synthesizability of molecules (Nicolaou et al., 2012). This framework allows flexible configuration according to various concrete applications. However, as the number of objectives grows, the joint distribution $\pi ( x )$ will become more complex and intractable, making the sampling non-trivial.
+
+In MARS, we propose to sample molecules from the desired distribution Eq. 1 using Markov chain Monte Carlo (MCMC) methods (Andrieu et al., 2003). Given a desired molecular distribution $\pi ( x )$ as the unnormalized target distribution, we define a Markov chain on the explicit chemical space $\mathcal { X }$ (i.e., each state of the Markov chain is a particular molecule) and introduce a proposal distribution $q ( x ^ { \prime } \mid x )$ to perform state transitions.
+
+![](images/c2ea58ad35cf4f220edb7e5b270574085a2edc3f8ad9160cf5909b708564cd7d.jpg)  
+Figure 1: The framework of MARS. During the sampling process: (a) starting from an arbitrary initial molecule $x ^ { ( 0 ) }$ in the molecular space $\mathcal { X }$ , (b) sampling a candidate molecule $x ^ { \prime } \in \mathcal { X }$ from the proposal distribution q(x0 | x(t−1)) at each step, and $\mathrm { ( c / d ) }$ the candidate $x ^ { \prime }$ is either accepted or rejected according to the acceptance rate $\mathcal { A } ( x ^ { ( t - 1 ) } , x ^ { \prime } ) \in [ 0 , 1 ]$ . By repeating this process, we can generate a sequence of molecules $\{ x ^ { ( t ) } \} _ { t = 0 } ^ { \infty }$ .
+
+Specifically, as shown in Figure 1, the sampling procedure of MARS starts from an initial molecule $x ^ { ( 0 ) } \in \mathcal { X }$ . At each time step $t$ , a molecule candidate $x ^ { \prime } \in \mathcal { X }$ will be sampled from the proposal distribution $q ( x ^ { \prime } \mid x ^ { ( t - 1 ) } )$ , where $x ^ { ( t - 1 ) }$ denotes the molecule at time step $t - 1$ . Then the proposed candidate $x ^ { \prime }$ could be either accepted $x ^ { ( t ) } = x ^ { \prime }$ or rejected $x ^ { ( t ) } = x ^ { ( t - 1 ) }$ according to the acceptance rate $\mathcal { A } ( x ^ { ( t - 1 ) } , x ^ { \prime } ) \in [ 0 , 1 ]$ controlled by the target distribution $\pi ( x )$ . By repeating this process, a sequence of molecules $\{ x ^ { ( t ) } \} _ { t = 0 } ^ { \infty }$ can be generated. Such sequence of molecules will converge to the target distribution $\pi ( x )$ if the proposal distribution and the acceptance mechanism are configured properly.
+
+The acceptance rate is calculated as follow:
+
+$$
+\mathcal { A } ( x , x ^ { \prime } ) = \operatorname* { m i n } \left\{ 1 , \frac { \pi ^ { \alpha } ( x ^ { \prime } ) q ( x | x ^ { \prime } ) } { \pi ^ { \alpha } ( x ) q ( x ^ { \prime } | x ) } \right\}
+$$
+
+where $\alpha$ is a coefficient that varies in different instantiations of MCMC algorithms. Here to find molecules that globally maximize the target distribution, we employ an annealing scheme (Laarhoven $\&$ Aarts, 1987) where $\alpha ~ = ~ 1 \bar { / } T$ and $T$ is a temperature controlled by a cooling schedule. In addition to this, other instantiations such as Metropolis-Hastings (MH) algorithm (Metropolis et al., 1953) where $\alpha = 1$ are also feasible under our general framework.
+
+As for the proposal distribution $q ( x ^ { \prime } \mid x )$ , it largely affects the sampling performance and should be designed elaborately. In general, it is crucial that the proposal distribution $q ( x ^ { \prime } \mid x )$ and the target distribution $\pi ( x ^ { \prime } )$ are as close as possible to ensure high sampling efficiency. So we propose using a proposal distribution $q _ { \theta } ( x ^ { \prime } \mid x )$ with learnable parameters to capture the desired molecular properties and develop a strategy to train the proposal throughout the sampling process adaptively. The details will be described in the next section.
+
+# 3.2 ADAPTIVE MOLECULAR GRAPH EDITING PROPOSAL
+
+In this section we will examine in detail our proposed adaptive proposal distribution $q _ { \theta } ( x ^ { \prime } \mid x )$ . A molecule is represented as a graph whose nodes are heavy atoms and edges are chemical bonds. The proposal distribution is defined over molecular graph editing actions. We use the message passing neural network (MPNN) to represent the proposal. Alternative parameterization schemes such as other graph neural networks are also possible. To sample molecules with desired properties effectively and efficiently, we also design a self-training strategy to learn the proposal MPNN during sampling in an adaptive manner.
+
+Molecular graph editing actions. To transform a molecule $x$ into another molecule $x ^ { \prime }$ , we consider two sets of graph editing actions, i.e., fragment adding and deleting. These actions are inspired by fragment-based drug design (FBDD) methodology, whose success in drug discovery has been proved in past decades (Kumar et al., 2012). In MARS, we define fragments as connected components in molecules separated by single bonds. To reduce the complexity of editing actions, we only consider fragments with a single attachment position. Moreover, we also define a fragment vocabulary that contains finitely many fragments, and only fragments in the vocabulary are allowed to be added onto a molecule. Examples for fragment adding and deleting actions are shown in Figure 2.
+
+![](images/e31475af681528898823031aaf3d98c029f3d27fcff92e7e5d1d40288d1451ce.jpg)  
+Figure 2: Left: Examples of molecular fragments and a fragment vocabulary. Red dashed lines represents cuttable bonds to extract fragments. Right: Examples of molecular graph editing actions.
+
+Specifically, given a molecule $x$ with $n$ atoms and $m$ bonds, we choose to add or delete a fragment onto or from this molecule randomly with probability $\begin{array} { l } { { \frac { 1 } { 2 } } } \end{array}$ for each set of actions. For the adding action, suppose we have a probability distribution over atoms $p _ { \mathrm { a d d } } ( x , u )$ and a probability distribution over fragments in the vocabulary $p _ { \mathrm { f r a g } } ( x , u , k )$ . Here $u \in [ n ]$ is an indicator of the atom in $x$ to which the fragment is adding to and $k \in [ V ]$ is an indicator of fragments in the vocabulary of size $V$ . We can compute the proposal distribution as follows:
+
+$$
+q ( x ^ { \prime } | x ) = { \frac { 1 } { 2 } } \cdot p _ { \mathrm { a d d } } ( x , u ) \cdot p _ { \mathrm { f r a g } } ( x , u , k )
+$$
+
+where $x ^ { \prime }$ is the molecule obtained by adding the $k$ -th fragment onto the atom $u$ in molecule $x$ .
+
+As for the deleting action, suppose we have a probability distribution over bonds1 $p _ { \mathrm { d e l } } ( x , b )$ where $b \in [ 2 m ]$ is an indicator of bonds in $x$ . We can compute the proposal distribution as follow:
+
+$$
+q ( x ^ { \prime } | x ) = \frac { 1 } { 2 } \cdot p _ { \mathrm { d e l } } ( x , b )
+$$
+
+where $x ^ { \prime }$ is the molecule obtained by removing bond $b$ and the attached fragment from molecule $x$
+
+Parameterizing with MPNNs. To better model the molecular graph editing actions, we propose to use MPNNs to suggest the probability distributions $( p _ { \mathrm { a d d } } , \bar { p _ { \mathrm { f r a g } } } , \bar { p _ { \mathrm { d e l } } } ) = \bar { \mathcal { M } } _ { \theta } ( x )$ where $\mathcal { M } _ { \theta }$ is a MPNN model specified by parameters $\theta$ , which has been proven powerful to predict chemical properties with molecular graphs (Gilmer et al., 2017). Given a molecule $x$ , we compute the probability distributions as follow:
+
+$$
+\begin{array} { r l } & { { \cal h } _ { u } ^ { \mathrm { n o d e } } = \mathrm { M P N N } ( x ) _ { u } \in \mathbb { R } ^ { d } } \\ & { \quad \quad \quad \quad \displaystyle { \boldsymbol h } _ { b } ^ { \mathrm { e q e } } = { \mathrm { C o n c a t } } ( { \boldsymbol h } _ { v } ^ { \mathrm { n o d e } } , { \boldsymbol h } _ { w } ^ { \mathrm { n o d e } } ) \in \mathbb { R } ^ { 2 d } } \\ & { \quad \quad \quad \quad p _ { \mathrm { a d d } } ( x ) = \mathrm { S o f t m a x } ( \{ \mathrm { M L P } _ { \mathrm { n o d e } } ( { \boldsymbol h } _ { u } ^ { \mathrm { n o d e } } ) ) \} _ { u = 1 } ^ { n } ) \in [ 0 , 1 ] ^ { n } } \\ & { \quad \quad \quad p _ { \mathrm { f r a g } } ( x , u ) = \mathrm { S o f t m a x } ( \mathrm { M L P } _ { \mathrm { n o d e } } ^ { \prime } ( { \boldsymbol h } _ { u } ^ { \mathrm { n o d e } } ) ) \in [ 0 , 1 ] ^ { | { \cal V } | } } \\ & { \quad \quad \quad p _ { \mathrm { d e l } } ( x ) = \mathrm { S o f t m a x } ( \{ \mathrm { M L P } _ { \mathrm { e d e } } ( { \boldsymbol h } _ { b } ^ { \mathrm { e q e } } ) ) \} _ { b = 1 } ^ { 2 m } ) \in [ 0 , 1 ] ^ { 2 m } } \end{array}
+$$
+
+where $u$ is an atom indicators, $\{ h _ { u } ^ { \mathrm { n o d e } } \} _ { u = 1 } ^ { n }$ e}nu=1 are node hidden representations, v, w are atoms connected with bond $b$ , $\{ h _ { b } ^ { \mathrm { e d g e } } \} _ { b = 1 } ^ { 2 m }$ u   are edge hidden representations, and ${ \bf M L P _ { n o d e } }$ , $\mathbf { M L P _ { n o d e } ^ { \prime } }$ , ${ \mathrm { \mathbf { M L P _ { e d g e } } } }$ are multilayer peceptrons (MLPs), similar to $\mathrm { H u }$ et al. (2020).
+
+Adaptive self-training. To capture the desired properties and improve the sampling effectiveness, we can train the editing model to increase the probability of suggesting high-quality candidate
+
+# Algorithm 1: MARS
+
+1 Set $N$ initial molecules $\{ x _ { i } ^ { ( 0 ) } \} _ { i = 1 } ^ { N }$ and initialize the molecular graph editing model $\mathcal { M } _ { \theta }$   
+2 Create an empty editing model training dataset $\mathcal { D } = \{ \}$   
+3 for $t = 1 , 2 , \ldots$ do   
+4 for $i = 1 , 2 , \dots , N$ do   
+5 Compute probability distributions $( p _ { \mathrm { a d d } } , p _ { \mathrm { f r a g } } , p _ { \mathrm { d e l } } ) = \mathcal { M } _ { \theta } ( x _ { i } ^ { ( t - 1 ) } )$ as Equations 7-9   
+6 Sample a candidate molecule $x ^ { \prime }$ from the proposal distribution $q ( x ^ { \prime } \mid x _ { i } ^ { ( t - 1 ) } )$ defined with   
+probability distributions $p _ { \mathrm { a d d } } , p _ { \mathrm { f r a g } } , p _ { \mathrm { d e l } }$ as Equations 3-4   
+7 if $u < \mathcal { A } ( x _ { i } ^ { ( t - 1 ) } , x ^ { \prime } )$ where $u \sim \mathcal { U } _ { [ 0 , 1 ] }$ then   
+8 Accept the candidate molecule $\boldsymbol { x } _ { i } ^ { ( \dot { t } ) } = \boldsymbol { x } ^ { \prime }$   
+9 else   
+10 Refuse the candidate molecule $x _ { i } ^ { ( t ) } = x _ { i } ^ { ( t - 1 ) }$   
+11 if The candidate improves the objectives, i.e. $\pi ( x ^ { \prime } ) > \pi ( x _ { i } ^ { ( t - 1 ) } )$ then   
+12 Adding the editing record $( x _ { i } ^ { ( t - 1 ) } , x ^ { \prime } )$ into the dataset $\mathcal { D }$   
+13 $\theta ^ { n e w } \longleftarrow \arg \operatorname* { m a x } \log M _ { \theta } ( \mathcal { D } )$
+
+molecules. Here we propose to train the model on-the-fly during the sampling process in an adaptive manner where the training data is collected from the sampling paths. By doing so, we can bypass the difficulty of lacking training instances that satisfy all property constraints. Mainly, we collect molecule candidates that improve our desired objectives and train the model $\mathcal { M } _ { \theta }$ in a maximum likelihood estimation (MLE) manner (i.e., to maximize the probability of producing the collected candidates). The overall MARS is described in Algorithm 1.
+
+Discussion on convergence. Compared with standard MCMC algorithms, MARS still falls in the Metropolis-Hastings algorithm but with an annealing scheme and an adaptive proposal, which results in inhomogeneous transition kernels. The convergence of adaptive MCMC is discussed in Rosenthal (2011). According to the diminishing adaptation condition, we can ensure convergence by making the difference of proposals in consecutive iterations diminish to zero. MARS can satisfy this condition by using an optimizer whose learning rate will shrink to zero eventually (e.g., Adam). Annealed MCMC is to find samples maximizing the target probability. The convergence of annealed MCMC is discussed in Andrieu et al. (2003).
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENT SETUP
+
+Biological objectives. Following Jin et al. (2020), we consider the following inhibition scores against two Alzheimer-related target proteins as the biological activity objectives. The score is given by a random forest model 2 that predicts based on Morgan fingerprint features of a molecule (Rogers & Hahn, 2010).
+
+• $\mathrm { G S K } 3 \beta$ : Inhibition against glycogen synthase kinase- $3 \beta$ .   
+• JNK3: Inhibition against c-Jun N-terminal kinase-3.
+
+Non-biological objectives. Following Jin et al. (2020), we adopt QED (Bickerton et al., 2012) and synthetic accessibility (SA) (Ertl & Schuffenhauer, 2009) to quantify the drug-likeness and synthesizability. We rescale the SA score (initially between 10 and 1) into [0, 1] such that molecules with higher scores are more synthesizable.
+
+Multi-objective generation setting. To evaluate the effectiveness of the proposed method for multiobjective drug design, we also consider the following more challenging objective combinations:
+
+• $\mathrm { G S K } 3 \beta { + } \mathrm { J N K } 3$ : Jointly inhibiting $\mathrm { G S K } 3 \beta$ and JNK3. The combination may provide potential benefits for the treatment of Alzheimer’s disease reported by Hu et al. (2009); Martin et al. (2013). $\mathrm { G S K } 3 \beta / \mathrm { J N K } 3 + \mathrm { Q E D } + \mathrm { S A } ;$ : Inhibiting $\mathrm { G S K } 3 \beta$ or JNK3 while being drug-like and synthetically accessible, which are quantified by QED and SA, respectively. $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \mathrm { + } \mathrm { Q E D } \mathrm { + } \mathrm { S A }$ : Jointly inhibiting $\mathrm { G S K } 3 \beta$ and JNK3 while being drug-like and synthetically accessible, which are quantified by QED and SA, respectively.
+
+Baselines. We compare MARS with the following methods – the latest ones from four categories mentioned in the related work (Sec. 2). GCPN (You et al., 2018) leverages RL to generate molecules atom by atom, and the adversarial loss is incorporated in the objective to generate more realistic molecules. JT-VAE (Jin et al., 2018) is a VAE-based approach that firstly generates junction trees and then assembles them into molecules. It performs Bayesian optimization (BO) to guide molecules towards desired properties. RationaleRL (Jin et al., 2020) is a state-of-the-art approach for multiproperty optimization, which generates molecules from combined rationales. $\mathbf { G A + D }$ (Nigam et al., 2020) is a heuristic search method that applies the genetic algorithm (GA) to find molecules with high property scores. An adversarial loss is incorporated in the fitness evaluation to increase the diversity of generated molecules.
+
+Evaluation metrics. Following Jin et al. (2020), we generate $N \ = \ 5 0 0 0$ molecules for each approach and compare the proposed method with the baselines on the following evaluation metrics: Success rate (SR) is the percentage of generated molecules that are evaluated as positive on all given objectives $\mathrm { ( Q E D \ge 0 . 6 }$ , $\mathbf { S A } \geq \ 0 . 6 7$ , the inhibition scores of $\mathrm { G S K } 3 \beta$ and JNK3 $\ge ~ 0 . 5 )$ ; Novelty $\mathbf { \Pi } ( \mathbf { N o v } )$ is the percentage of generated molecules with similarity less than 0.4 compared to the nearest neighbor $x _ { S \mathsf { N N } }$ in the training set (Olivecrona et al., 2017): $\begin{array} { r l } { \mathbf { N o v } } & { { } = } \end{array}$ $\textstyle { \frac { 1 } { n } } \sum _ { x \in { \mathcal { G } } } \mathbf { 1 } [ \sin ( x , x _ { \mathrm { S N N } } ) < { \bar { 0 . 4 } } ]$ ; Diversity (Div) measures the diversity of generated molecules, which can be calculated based on pairwise Tanimoto similarity over Morgan fingerprints $\sin ( x , x ^ { \prime } )$ as $\begin{array} { r } { \mathrm { D i v } = \frac { 2 } { n ( n - 1 ) } \sum _ { x \ne x ^ { \prime } \in \mathcal { G } } 1 - \dot { \sin ( x , x ^ { \prime } ) } } \end{array}$ ; PM is the product of the above three metrics, which is a more comprehensive evaluation of the proposed method. Intuitively, PM presents the percentage of generated molecules that are simultaneously bio-active, novel and diverse, which are essential criteria for molecules to be considered in building a suitable drug candidate library in early-stage drug discovery (Huggins et al., 2011).
+
+Implementation details. For the fragment vocabulary, we extract the top 1000 frequently appearing fragments that contain no more than 10 heavy atoms from the ChEMBL database (Gaulton et al., 2017) by enumerating single bonds to break. As for the sampling process, the unnormalized target distribution is set as $\begin{array} { r } { \bar { \pi } ( x ) = \sum _ { k } s _ { k } ( x ) } \end{array}$ where $s _ { k } ( x )$ is a scoring function for the above-mentioned properties of interests, the temperature is set as $T = 0 . 9 5 ^ { \lfloor t / 5 \rfloor }$ and we sample $N = 5 0 0 0$ molecules at one time. During sampling, the computation of $q ( x \mid x ^ { \prime } )$ is ignored and we approximate $\boldsymbol { \mathcal { A } } ( \boldsymbol { x } , \boldsymbol { x } ^ { \prime } )$ with $\mathrm { m i n } \{ 1 , \pi ^ { \alpha } ( x ^ { \bar { \prime } } ) / \pi ^ { \alpha } \bar { \alpha ( } x ) \bar { \} }$ to increase the computation efficiency. This is acceptable because in practice $q ( x \mid x ^ { \prime } )$ and $q ( x ^ { \prime } \mid x )$ is of order $O ( 1 )$ and $\boldsymbol { \mathcal { A } } ( \boldsymbol { x } , \boldsymbol { x } ^ { \prime } )$ will be gradually bounded by $\pi ^ { \alpha } \bar { ( } x ^ { \prime } ) / \pi ^ { \alpha } \bar { ( } x )$ as the temperature $T$ decrease to zero. The sampling paths are all starting with an identical molecule $\mathrm { ^ { 6 6 } C T ^ { - C } } ^ { \mathrm { 9 } }$ , which is also adopted by previous graph generation methods for organic molecules (You et al., 2018). The MPNN model has six layers, and the node embedding size is $d = 6 4$ . Moreover, for the model training, we use an Adam optimizer (Kingma & Ba, 2015) to update the model parameters with an initial learning rate set as $3 \times 1 0 ^ { - 4 }$ , the maximum dataset size is limited as $| \mathcal { D } | \overset { - } { \leq } 7 5 , 0 0 0$ , and at each step, we update the model for no more than 25 times.
+
+# 4.2 MAIN RESULTS AND ANALYSIS
+
+We perform ten independent runs for MARS. The quantitative results are summarized in Table 1 and Table 2. From these tables, we observe that MARS outperforms all the baselines on five out of six tasks in terms of PM. Furthermore, on the most challenging multi-objective optimization task, i.e., $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } \substack { + } \mathrm { S A }$ , it significantly surpasses the best baseline with a $7 7 \%$ improvement for the product of metrics PM. Additional results are shown in Appendix A.
+
+In comparing all these methods, the $\mathrm { G A + D }$ baseline is most similar to our MARS in terms of the high novelty and PM score, as both methods focus on molecular space exploration. However, the diversity score of $\mathrm { G A + D }$ drops a lot when optimizing multiple properties simultaneously, as GAs are likely to get trapped in regions of local optima (Paszkowicz, 2009). RationaleRL is a very strong baseline that performs better than MARS in the $\mathrm { G S K } 3 \beta { + } \mathrm { J N K } 3$ setting. Nevertheless, when taking the drug-likeness and synthetic accessibility into consideration, their performance falls short of ours and fails to generate novel molecules. The performance of GCPN and JT-VAE remains relatively low in most settings, as they are not tailored for multi-objective property optimization.
+
+Table 1: Comparison of different methods on molecular generation with only bio-activity objectives. Results of $\mathrm { G A + D }$ are obtained by running its open-source code. Results of other baselines are taken from Jin et al. (2020). For MARS, we report the mean and standard deviation of 10 independent experiments.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">GSK3β</td><td colspan="4">JNK3</td><td colspan="4">GSK3β+JNK3</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>GCPN</td><td>42.4%</td><td>11.6%</td><td>0.904</td><td>0.04</td><td>32.3%</td><td>4.4%</td><td>0.884</td><td>0.01</td><td>3.5%</td><td>8.0%</td><td>0.874</td><td>0.00</td></tr><tr><td>JT-VAE</td><td>32.2%</td><td>11.8%</td><td>0.901</td><td>0.03</td><td>23.5%</td><td>2.9%</td><td>0.882</td><td>0.01</td><td>3.3%</td><td>7.9%</td><td>0.883</td><td>0.00</td></tr><tr><td>RationaleRL</td><td>100.0%</td><td>53.4%</td><td>0.888</td><td>0.47</td><td>100.0%</td><td>46.2%</td><td>0.862</td><td>0.40</td><td>100.0%</td><td>97.3%</td><td>0.824</td><td>0.80</td></tr><tr><td>GA+D</td><td>84.6%</td><td>100.0%</td><td>0.714</td><td>0.60</td><td>52.8%</td><td>98.3%</td><td>0.726</td><td>0.38</td><td>84.7%</td><td>100.0%</td><td>0.424</td><td>0.36</td></tr><tr><td>MARS</td><td>100.0%</td><td>84.0%</td><td>0.718</td><td>0.60 ± 0.04</td><td>98.8%</td><td>88.9%</td><td>0.748</td><td>0.66 ±0.04</td><td>99.5%</td><td>75.3%</td><td>0.691</td><td>0.52 ±0.08</td></tr></table>
+
+Table 2: Comparison of different methods on molecular generation with bio-activity, QED, and SA objectives. Results of all baselines are obtained by running their open-source codes. For the results of MARS, we report the mean and standard deviation of 10 independent experiments.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">GSK3β+QED+SA</td><td colspan="4">JNK3+QED+SA</td><td colspan="4">GSK3β +JNK3+ QED +SA</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>GCPN</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td></tr><tr><td>JT-VAE</td><td>9.6%</td><td>95.8%</td><td>0.680</td><td>0.06</td><td>21.8%</td><td>100.0%</td><td>0.600</td><td>0.13</td><td>5.4%</td><td>100.0%</td><td>0.277</td><td>0.02</td></tr><tr><td>RationaleRL</td><td>69.9%</td><td>40.2%</td><td>0.893</td><td>0.25</td><td>62.3%</td><td>37.6%</td><td>0.865</td><td>0.20</td><td>75.0%</td><td>55.5%</td><td>0.706</td><td>0.29</td></tr><tr><td>GA+D</td><td>89.1%</td><td>100.0%</td><td>0.682</td><td>0.61</td><td>85.7%</td><td>99.8%</td><td>0.504</td><td>0.43</td><td>85.7%</td><td>100.0%</td><td>0.363</td><td>0.31</td></tr><tr><td>MARS</td><td>99.5%</td><td>95.0%</td><td>0.719</td><td>0.68 ±0.03</td><td>91.3%</td><td>94.8%</td><td>0.779</td><td>0.67 ± 0.02</td><td>92.3%</td><td>82.4%</td><td>0.719</td><td>0.55 ± 0.05</td></tr></table>
+
+Visualization. We use t-SNE (van der Maaten & Hinton, 2008) to visualize the distribution of generated positive molecules with the positive ones in the training set under the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } \substack { + } \mathrm { S A }$ setting. In the visualization, we use the ECFP6 fingerprints as suggested in Li et al. (2018). As shown by Figure 3, most molecules generated by $\mathrm { G A + D }$ fall into two massive clusters, which aligns their low diversity. Molecules generated by RationaleRL also tend to be clustered, with each cluster standing for a specific combination of rationales. By contrast, the molecules generated by MARS are evenly distributed in the space with a range of novel regions covered, which justifies our high novelty and diversity scores. We further visualize some molecules generated by MARS with high property scores in Figure 4, indicating its ability to generate highly synthesizable drug-like molecules that jointly inhibit $\mathrm { G S K } 3 \beta$ and JNK3. Additional examples of sampled molecules are shown in Appendix C.
+
+![](images/354e560c651a8808c3b974a4b0c14d32ebb2bdc639cd4e93f783461d0a67c543.jpg)  
+Figure 3: t-SNE visualization of generated molecules (gray) and positive molecules in the training set (blue).
+
+Running time. The computing server has two CPUs with 64 virtual cores $( 2 . 1 0 \mathrm { G H z } )$ , 231G memory (about 50G used), and one Tesla V100 GPU with 32G memory. In the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } + \mathrm { S A }$ setting, MARS takes roughly $T = 5 5 0$ sampling steps and 12 hours in total to converge (including the time used in proposing and evaluating molecules as well as MPNN model training). For other baselines, RationaleRL takes 5.7 hours to fine-tune the model, and $\mathrm { G A + D }$ takes 278 steps and $2 . 2 \mathrm { h }$ to achieve its best performance. Compared to the conventional drug discovery process, which usually takes months to years, the time we spent on molecular generation models is almost ignorable.
+
+![](images/5bcb89e0fc85613bdac8e49645a597468b528c3b82d188ba4ede2803bc68053d.jpg)  
+Figure 4: Sample molecules generated by MARS in the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 + \mathrm { Q E D } + \mathrm { S A }$ setting. The numbers in brackets are $\mathrm { G S K } 3 \beta$ , JNK3, QED, and SA scores of each molecule respectively.
+
+# 4.3 EFFECTS OF PROPOSAL AND ACCEPTANCE STRATEGY
+
+To justify the contributions of the designed proposal and acceptance strategy, we compare them with some naive ones and summarize the results of different combinations in Table 3. For acceptance strategies, Annealed stands for annealed MCMC where the acceptance rate is computed as Equation 2 given $\alpha = 1 / T$ , AlwaysAC stands for always accepting the candidate, i.e., $\bar { \mathcal { A } } ( \boldsymbol { x } , \boldsymbol { x } ^ { \prime } ) \equiv 1$ , and HillClimb stands for accepting the candidate only when the overall score is improved, i.e., ${ \mathcal A } ( x , x ^ { \prime } ) = \mathrm { s i g n } [ s ( x ^ { \prime } ) > s ( x ) ]$ . For proposal strategies, Random stands for random proposal where we randomly select atoms, bonds, and fragments to edit, and Adaptive stands for the adaptive fragment-based graph editing model trained during the sampling process as described in Section 3.2.
+
+Table 3: Results of different acceptance strategies and proposal strategies for molecular sampling.   
+
+<table><tr><td rowspan="2">AC Strategy</td><td rowspan="2">Proposal</td><td colspan="4">GSK3β + JNK3</td><td colspan="4">GSK3β + JNK3 + QED + SA</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>Annealed</td><td>Random</td><td>40.9%</td><td>94.9%</td><td>0.828</td><td>0.32</td><td>25.5%</td><td>80.4%</td><td>0.793</td><td>0.16</td></tr><tr><td>AlwaysAC</td><td>Adaptive</td><td>49.1%</td><td>88.4%</td><td>0.742</td><td>0.32</td><td>10.1%</td><td>94.6%</td><td>0.716</td><td>0.07</td></tr><tr><td>HillClimb</td><td>Adaptive</td><td>53.7%</td><td>96.1%</td><td>0.814</td><td>0.42</td><td>51.4%</td><td>86.6%</td><td>0.777</td><td>0.35</td></tr><tr><td>Annealed</td><td>Adaptive</td><td>99.5%</td><td>75.2%</td><td>0.688</td><td>0.52</td><td>92.3%</td><td>82.4%</td><td>0.719</td><td>0.55</td></tr></table>
+
+The results in Table 3 indicate that proposals will influence the performance of MARS dramatically (the first and the last row), especially when the number of objectives increases. The proposed adaptive proposal outperforms the random proposal and converges $4 . 6 \mathrm { x }$ faster in practice. By comparing the last three rows, we find the Annealed strategy outperforms the other two strategies by a large margin on both settings, as samples from such strategy are more likely to jump out of local optimums. Another interesting observation is that even with the naive AlwaysAC or heuristic HillClimb strategy, the MARS achieves comparable or even better performance than $\mathrm { G A + D }$ and RationaleRL in some settings, e.g., HillClimb on $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } \substack { + } \mathrm { S A }$ optimization, which again proves the effectiveness of the proposed proposal.
+
+# 5 CONCLUSION AND FUTURE WORK
+
+This paper proposes a simple yet flexible MArkov moleculaR Sampling framework (MARS) for multi-objective drug discovery. MARS includes a trainable proposal to modify chemical graph fragments, which is parameterized by an MPNN. Our experiments verify that MARS outperforms prior approaches on five out of six molecule generation tasks, and it is capable of finding novel and diverse bioactive molecules that are both drug-like and highly synthesizable. Future work can include further study of parameterization and training strategy of the molecular-editing proposal.
+
+# 6 ACKNOWLEDGEMENT
+
+We would like to thank Meihua Dang for refactoring much of the MARS code. Meihua also performed multiple experiments, which generates the results for the tables. We also thank Jiangjie Chen, Yuxuan Song, Jingjing Xu, Weiying Ma, Hang Li, and anonymous reviewers for their constructive comments and suggestions.
+
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+
+# Appendix
+
+# A PROPERTY SCORES OF SAMPLED MOLECULES
+
+The property score distributions of sampled $N = 5 0 0 0$ molecules of the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } + \mathrm { S A }$ setting are shown in Figure 5. The average of the metrics over the sampling path is shown in Figure 6.
+
+![](images/0bab267db78f46805300fd4872b6414180a7bb4eb7016542f504b51e5c1dbc4d.jpg)  
+Figure 5: Property score distributions of sampled $N = 5 0 0 0$ molecules. The red lines are success thresholds.
+
+![](images/beca3f6afb24e575ebdc42f47fe82e3b9ac74328c9f209f14eb9c32c698e18bc.jpg)  
+Figure 6: MARS sampling curves (average of 10 runs) for the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } \substack { + } \mathrm { S A }$ setting. SR: success rate. Nov: novelty. Div: diversity. PM: product of the three metrics. Shaded area shows the standard deviations over 10 independent runs.
+
+# B SINGLE OBJECTIVE GENERATION
+
+To study whether our proposed method is capable of single-objective molecular generation, we also investigate how MARS performs on the drug-likeness (QED) and the penalized octanol-water partition coefficient (penalized logP) optimization. The experiment results are shown in Table 4. In the experiments, our approach can obtain the best performance on both QED and logP optimization. And especially, MARS outperforms previous methods significantly in the logP generation task.
+
+Table 4: Comparison of different methods on single-objective molecular generation. Results of other baselines are taken from Shi et al. (2020) and Nigam et al. (2020).   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">1st</td><td colspan="2">QED</td><td colspan="3">Penalized logP</td></tr><tr><td>2nd</td><td>3rd</td><td>1st</td><td>2nd</td><td>3rd</td></tr><tr><td>GCPN (You et al., 2018)</td><td>0.948</td><td>0.947</td><td>0.946</td><td>7.98</td><td>7.85</td><td>7.80</td></tr><tr><td>JT-VAE (Jin et al., 2018)</td><td>0.925</td><td>0.911</td><td>0.91</td><td>5.30</td><td>4.93</td><td>4.49</td></tr><tr><td>GraphAF (Shi et al.,2020)</td><td>0.948</td><td>0.948</td><td>0.947</td><td>12.23</td><td>11.29</td><td>11.05</td></tr><tr><td>GB-GA (Jensen, 2019)</td><td>/</td><td>/</td><td>/</td><td>15.76± 5.71</td><td>/</td><td>/</td></tr><tr><td>GA+D (Nigam et al., 2020)</td><td>/</td><td>/</td><td>/</td><td>20.72 ± 3.14</td><td>/</td><td>1</td></tr><tr><td>MARS</td><td>0.948</td><td>0.948</td><td>0.948</td><td>44.99</td><td>44.32</td><td>43.81</td></tr></table>
+
+Moreover, from the results, we also can see how these two previously widely used metrics (Jin et al., 2018; You et al., 2018; Popova et al., 2019; Shi et al., 2020; Nigam et al., 2020) are questionable for both scientific study and practical use. Most of the generative methods (i.e., GCPN, JT-VAE, and GraphAF) can produce molecules with the highest possible QED score of 0.948, making the top QED score metric hard to distinguish different methods. As for logP optimization, heuristic search-based (i.e., GB-GA and $\mathrm { G A } { + } \mathrm { D }$ ) and sampling-based methods (i.e., MARS) can all easily beat generative models. This is because penalized logP score will prefer larger molecules that generative models can hardly produce. However, such large molecules are unrealistic for practical drug discovery, making the top penalized logP score metric problematic.
+
+# C EXAMPLES OF SAMPLED MOLECULES
+
+We also provide some examples of sampled molecules from the $\mathrm { G S K } 3 \beta + \mathrm { J N K } 3 \substack { + } \mathrm { Q E D } \substack { + } \mathrm { S A }$ setting.   
+The numbers under molecule graphs are $\mathrm { G S K } 3 \beta$ , JNK3, QED, and SA scores, respectively.
+
+![](images/e2ca1b502a5dc59d5526d2fa276b3cd5948939e14b67c341b48aa673a5e68f71.jpg)  
+Figure 7: 40 sampled molecules with highest average property scores.
+
+![](images/7f24c808c854564588e8e70bccbc39694c2afb8619644c6d8f6747313d4dc468.jpg)  
+Figure 8: 40 sampled molecules with highest $\mathrm { G S K } 3 \beta$ scores.
+
+![](images/7020507949ef8e7b21f6f22ead012f1062a5e37ddf166e51ed28bb6760af5cc2.jpg)  
+Figure 9: 40 sampled molecules with highest JNK3 scores.
+
+![](images/a51cc17dd310937444fd3757b6c5aee06bef2b107773be4e0dedb419e4abb89c.jpg)  
+Figure 10: 40 sampled molecules with highest QED scores.
+
+![](images/a0224a66ffeb2ef57e42d611c5756109dbabef25366aded3e6744d826cad9cf1.jpg)  
+Figure 11: 40 sampled molecules with highest SA scores.

parse/train/kHSu4ebxFXY/kHSu4ebxFXY_content_list.json

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+    {
+        "type": "text",
+        "text": "MARS: MARKOV MOLECULAR SAMPLING FOR MULTI-OBJECTIVE DRUG DISCOVERY ",
+        "text_level": 1,
+        "bbox": [
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+        "text": "Yutong $\\mathbf { X } \\mathbf { i } \\mathbf { e } ^ { \\mathrm { { \\dagger } } \\circ }$ , Chence $\\mathbf { S h i } ^ { \\dagger \\triangle }$ , Hao Zhou†∗, Yuwei Yang†, Weinan Zhang‡, Yong $\\mathbf { V } \\mathbf { u } ^ { \\ddag }$ , Lei Li†∗   \n†ByteDance AI Lab, Shanghai, China   \n\u0005University of Michigan, Ann Arbor, MI, USA   \n4Montreal Institute of Learning Algorithms, Montreal, Canada ´   \n‡Department of Computer Science and Engineering, Shanghai Jiao Tong University, China ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Searching for novel molecules with desired chemical properties is crucial in drug discovery. Existing work focuses on developing neural models to generate either molecular sequences or chemical graphs. However, it remains a big challenge to find novel and diverse compounds satisfying several properties. In this paper, we propose MARS, a method for multi-objective drug molecule discovery. MARS is based on the idea of generating the chemical candidates by iteratively editing fragments of molecular graphs. To search for high-quality candidates, it employs Markov chain Monte Carlo sampling (MCMC) on molecules with an annealing scheme and an adaptive proposal. To further improve sample efficiency, MARS uses a graph neural network (GNN) to represent and select candidate edits, where the GNN is trained on-the-fly with samples from MCMC. Experiments show that MARS achieves state-of-the-art performance in various multi-objective settings where molecular bio-activity, drug-likeness, and synthesizability are considered. Remarkably, in the most challenging setting where all four objectives are simultaneously optimized, our approach outperforms previous methods significantly in comprehensive evaluations. The code is available at https://github.com/yutxie/mars. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Drug discovery aims to find chemical compounds with desired target properties, such as high druglikeness (Bickerton et al., 2012, QED). The problem is also referred to as molecular design, molecular generation, or molecular search. The space of drug-like chemicals is enormous, approximate $1 0 ^ { 3 3 }$ for realistic drugs that could ever be synthesized (Polishchuk et al., 2013). Therefore it is very challenging to search for high-quality molecules from such a vast space — enumeration would take almost forever. For a particular disease, finding the right candidates targeting specific proteins further complicates the problem. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Instead of enumerating or searching from the immense chemical space, recent work utilizes deep generative models to generate candidate molecules directly (Schwalbe-Koda & Gomez-Bombarelli, ´ 2020). However, most prior work focuses on generating molecules concerning a single property such as drug-likeness (QED) or octanol-water partition coefficient (logP) (Jin et al., 2018; You et al., 2018; Popova et al., 2019; Shi et al., 2020; Zang & Wang, 2020). While in practical settings, typical drug discovery requires consideration of multiple properties jointly (Nicolaou et al., 2012). For example, to find drug-like molecules that are easy to synthesize and exhibit high biological activity against the target protein. Naturally, multi-objective molecule design is much more challenging than the single-objective scenario (Jin et al., 2020). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This paper studies the problem of multi-objective molecule design for drug discovery. An ideal solution should be efficient and meet the following criteria. $C I$ : It should satisfy multiple properties with high scores; C2: It should produce novel and diverse molecules; C3: Its generation process does not rely on either expert annotated or wet experimental data collected from a biochemistry lab (since it requires tremendous effort and hard to obtain). Existing molecule generation approaches are mainly designed for the single objective setting, and they could not meet all criteria in the setting of multiple objectives. These methods belong to four categories: a) generating candidates from a learned continuous latent space (Gomez-Bombarelli et al., 2018; Jin et al., 2018), b) through reinforcement ´ learning (You et al., 2018), c) using an encoder-decoder translation approach (Jin et al., 2019), or d) optimizing molecular properties through genetic algorithms (Nigam et al., 2020). Current stateof-the-art multi-objective molecular generation is a rationale-based method (Jin et al., 2020). In this approach, the authors propose to build molecules by composing multiple extracted rationales, and the model can generate compounds that are simultaneously active to multiple biological targets. However, such an approach will result in quite complex molecules when we have many objectives. This is because different objectives correspond to different rationales, and including all these rationales could lead to large molecules, which may be less drug-like and hard to be synthesized practically. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose MArkov moleculaR Sampling (MARS), a simple yet flexible method for drug discovery. The basic idea is to start from a seed molecule and keep generating candidate molecules by modifying fragments of molecular graphs from previous steps. It meets all the criteria C1-3. In MARS, the molecular design is formulated as an iterative editing procedure with its total objective consisting of multiple property scores (C1). MARS employs the annealed Markov chain Monte Carlo sampling method to search for optimal chemical compounds, which allows for the exploration of chemicals with novel and different fragments (C2). The proposal to modify molecular fragments is represented using graph neural networks (GNNs), whose parameters are adaptively learned. We used message passing neural networks (MPNNs) in practice (Gilmer et al., 2017), but other GNNs can fit the framework as well. Furthermore, MARS utilizes the sample paths generated on-the-fly to train the proposal network adaptively. Therefore, it does not rely on external annotated data (C3). With such an adaptive learnable proposal, it keeps improving the generation quality throughout the process. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate MARS and four other baselines, one latest method for each of the four method categories. The benchmark includes a variety of multi-objective generation settings. Experiments show that our proposed MARS achieves state-of-the-art performance on five out of six tasks in terms of a comprehensive evaluation consisting of the success rate, novelty, and diversity of the generated molecules. Notably, in the most challenging setting where four objectives – bio-activities to two different targets, drug-likeness, and synthesizability – are simultaneously considered, our method achieves the state-of-the-art result and outperforms existing methods by $7 7 \\%$ in the comprehensive evaluation. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Our contributions are as follows: ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• We present MARS, a generic formulation of molecular design using Markov sampling, which can easily accommodate multiple objectives.   \nWe develop an adaptive fragment-editing proposal based on GNN that is learnable on the fly with only samples self-generated and efficient in exploring the chemical space.   \n• Experiments verifies our proposed MARS framework can find novel and diverse bioactive molecules that are both drug-like and highly synthesizable. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Recent years have witnessed the success of applying deep generative models and molecular graph representation learning in drug discovery (Schwalbe-Koda & Gomez-Bombarelli, 2020; Guo & ´ Zhao, 2020). Existing approaches for molecular property optimization can be grouped into four categories, including generation with a) Bayesian inference, $^ b$ ) reinforcement learning, $c _ { . }$ ) encoderdecoder translation models, and d) evolutionary and genetic algorithms. The first category is learning continuous latent spaces for molecular sequences or graphs and generating from such spaces using Bayesian optimization (BO) (Gomez-Bombarelli et al., 2018; Jin et al., 2018; Winter et al., 2019). ´ These methods rely heavily on the quality of latent representations, which imposes huge challenges to the encoders when there are multiple properties to consider. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unlike the first class, other work uses reinforcement learning (RL) to optimize desired objectives directly in the explicit chemical space (De Cao & Kipf, 2018; Popova et al., 2018; You et al., 2018; ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Popova et al., 2019; Shi et al., 2020). However, the models are usually hard to train due to the high variance of RL. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The third category directly trains a translation model that maps from an input molecule to a highquality output molecule (Jin et al., 2019; 2020). Although simple, such methods require many high-quality labeled data, making them impractical in scenarios where the data is limited. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The last category of methods are evolutionary algorithms (EAs) and genetic algorithms (GAs) to explore large chemical space with certain property (Nicolaou et al., 2012; Devi et al., 2015; Jensen, 2019; Ahn et al., 2020). In Nigam et al. (2020), the authors propose to augment GA by adding an adversarial loss into the fitness evaluation to increase the diversity, and the augmented GA outperforms all other generative models in optimizing logP. Though flexible and straightforward, to make the search process efficient enough, most GA and EA methods require domain experts to design molecular mutation and crossover rules, which could be non-trivial to obtain. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Besides single property optimization, there is recent work to address the multi-objective molecule generation problem. For example, Li et al. (2018) proposes to use a conditional generative model to incorporate several objectives flexibly, while Lim et al. (2020) leverages molecular scaffolds to control the properties of generated molecules better. Among them, the current state-of-the-art approach is a rationale-based method proposed by Jin et al. (2020). In this method, the authors propose to build molecules by assembling extracted rationales. Despite its great success in generating compounds simultaneously active to multiple biological targets, the combination of rationales might hinder the synthesizability and drug-likeness of produced molecules, as they tend to be large as the number of objectives grows. In contrast, our MARS framework turns the generation problem into a sampling procedure, which serves as an alternative way compared with deep generative models, and can efficiently discover bio-active molecules that are both drug-like and highly synthesizable. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Remotely related is recent work to generate molecules through sampling. Seff et al. (2019) defines a Gibbs sampling procedure, in which the Markov chain alternates between randomly corrupting the molecules and recovering the corrupted ones with a learned reconstruction model. However, this method mainly focuses on generating molecules that follow the observed data distribution and cannot be directly tailored for property optimization. Different from this work, MARS is built upon the general MCMC sampling framework, which allows further enhancement with adaptive proposal learning to edit molecular graphs efficiently. Actually, generating instances from a discrete space with MCMC sampling methods is previously employed in various other applications, e.g., generating natural language sentences under various constraints (Miao et al., 2019; Zhang et al., 2019; Liu et al., 2020; Zhang et al., 2020). ",
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+    {
+        "type": "text",
+        "text": "3 PROPOSED MARS APPROACH",
+        "text_level": 1,
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+        "page_idx": 2
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+        "type": "text",
+        "text": "In this section, we present the MArkov moleculaR Sampling method (MARS) for multi-objective molecular design. We define a Markov chain over the explicit molecular graph space and design a kernel to navigate high probable candidates with acceptance and rejection. ",
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+    {
+        "type": "text",
+        "text": "3.1 SAMPLING FROM THE MOLECULAR SPACE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our proposed MARS framework aims at sampling molecules with desired properties from the chemical space. Specifically, given $K$ properties of interest, the desired molecular distribution can be formulated as a combination of all objectives: ",
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+        "type": "equation",
+        "img_path": "images/266b7eebf56c3f693309d8505978bc63f76b3f2c73c5932eed6079637ee44493.jpg",
+        "text": "$$\n\\pi ( x ) = \\underbrace { s _ { 1 } ( x ) \\circ s _ { 2 } ( x ) \\circ s _ { 3 } ( x ) \\circ \\dotsb \\circ s _ { K } ( x ) } _ { \\mathrm { d e s i r e d p r o p e r t i e s } }\n$$",
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+    {
+        "type": "text",
+        "text": "where $x$ is a molecule in the molecular space $\\mathcal { X }$ . $\\pi ( x )$ is an unnormalized distribution over molecules integrating the desired properties. $s _ { k } ( x )$ is a scoring function for the $k$ -th property and the “◦” operator stands for a combination of scores (e.g., summation or multiplication). In practical drug discovery, these terms could be related to the biological activity, drug-likeness, and synthesizability of molecules (Nicolaou et al., 2012). This framework allows flexible configuration according to various concrete applications. However, as the number of objectives grows, the joint distribution $\\pi ( x )$ will become more complex and intractable, making the sampling non-trivial. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In MARS, we propose to sample molecules from the desired distribution Eq. 1 using Markov chain Monte Carlo (MCMC) methods (Andrieu et al., 2003). Given a desired molecular distribution $\\pi ( x )$ as the unnormalized target distribution, we define a Markov chain on the explicit chemical space $\\mathcal { X }$ (i.e., each state of the Markov chain is a particular molecule) and introduce a proposal distribution $q ( x ^ { \\prime } \\mid x )$ to perform state transitions. ",
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+        "type": "image",
+        "img_path": "images/c2ea58ad35cf4f220edb7e5b270574085a2edc3f8ad9160cf5909b708564cd7d.jpg",
+        "image_caption": [
+            "Figure 1: The framework of MARS. During the sampling process: (a) starting from an arbitrary initial molecule $x ^ { ( 0 ) }$ in the molecular space $\\mathcal { X }$ , (b) sampling a candidate molecule $x ^ { \\prime } \\in \\mathcal { X }$ from the proposal distribution q(x0 | x(t−1)) at each step, and $\\mathrm { ( c / d ) }$ the candidate $x ^ { \\prime }$ is either accepted or rejected according to the acceptance rate $\\mathcal { A } ( x ^ { ( t - 1 ) } , x ^ { \\prime } ) \\in [ 0 , 1 ]$ . By repeating this process, we can generate a sequence of molecules $\\{ x ^ { ( t ) } \\} _ { t = 0 } ^ { \\infty }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, as shown in Figure 1, the sampling procedure of MARS starts from an initial molecule $x ^ { ( 0 ) } \\in \\mathcal { X }$ . At each time step $t$ , a molecule candidate $x ^ { \\prime } \\in \\mathcal { X }$ will be sampled from the proposal distribution $q ( x ^ { \\prime } \\mid x ^ { ( t - 1 ) } )$ , where $x ^ { ( t - 1 ) }$ denotes the molecule at time step $t - 1$ . Then the proposed candidate $x ^ { \\prime }$ could be either accepted $x ^ { ( t ) } = x ^ { \\prime }$ or rejected $x ^ { ( t ) } = x ^ { ( t - 1 ) }$ according to the acceptance rate $\\mathcal { A } ( x ^ { ( t - 1 ) } , x ^ { \\prime } ) \\in [ 0 , 1 ]$ controlled by the target distribution $\\pi ( x )$ . By repeating this process, a sequence of molecules $\\{ x ^ { ( t ) } \\} _ { t = 0 } ^ { \\infty }$ can be generated. Such sequence of molecules will converge to the target distribution $\\pi ( x )$ if the proposal distribution and the acceptance mechanism are configured properly. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The acceptance rate is calculated as follow: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b2c132e0541b3b7e0add7628be811357edd932241e4c7df5ceac2ea70f6526c3.jpg",
+        "text": "$$\n\\mathcal { A } ( x , x ^ { \\prime } ) = \\operatorname* { m i n } \\left\\{ 1 , \\frac { \\pi ^ { \\alpha } ( x ^ { \\prime } ) q ( x | x ^ { \\prime } ) } { \\pi ^ { \\alpha } ( x ) q ( x ^ { \\prime } | x ) } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\alpha$ is a coefficient that varies in different instantiations of MCMC algorithms. Here to find molecules that globally maximize the target distribution, we employ an annealing scheme (Laarhoven $\\&$ Aarts, 1987) where $\\alpha ~ = ~ 1 \\bar { / } T$ and $T$ is a temperature controlled by a cooling schedule. In addition to this, other instantiations such as Metropolis-Hastings (MH) algorithm (Metropolis et al., 1953) where $\\alpha = 1$ are also feasible under our general framework. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As for the proposal distribution $q ( x ^ { \\prime } \\mid x )$ , it largely affects the sampling performance and should be designed elaborately. In general, it is crucial that the proposal distribution $q ( x ^ { \\prime } \\mid x )$ and the target distribution $\\pi ( x ^ { \\prime } )$ are as close as possible to ensure high sampling efficiency. So we propose using a proposal distribution $q _ { \\theta } ( x ^ { \\prime } \\mid x )$ with learnable parameters to capture the desired molecular properties and develop a strategy to train the proposal throughout the sampling process adaptively. The details will be described in the next section. ",
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+    {
+        "type": "text",
+        "text": "3.2 ADAPTIVE MOLECULAR GRAPH EDITING PROPOSAL ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "In this section we will examine in detail our proposed adaptive proposal distribution $q _ { \\theta } ( x ^ { \\prime } \\mid x )$ . A molecule is represented as a graph whose nodes are heavy atoms and edges are chemical bonds. The proposal distribution is defined over molecular graph editing actions. We use the message passing neural network (MPNN) to represent the proposal. Alternative parameterization schemes such as other graph neural networks are also possible. To sample molecules with desired properties effectively and efficiently, we also design a self-training strategy to learn the proposal MPNN during sampling in an adaptive manner. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Molecular graph editing actions. To transform a molecule $x$ into another molecule $x ^ { \\prime }$ , we consider two sets of graph editing actions, i.e., fragment adding and deleting. These actions are inspired by fragment-based drug design (FBDD) methodology, whose success in drug discovery has been proved in past decades (Kumar et al., 2012). In MARS, we define fragments as connected components in molecules separated by single bonds. To reduce the complexity of editing actions, we only consider fragments with a single attachment position. Moreover, we also define a fragment vocabulary that contains finitely many fragments, and only fragments in the vocabulary are allowed to be added onto a molecule. Examples for fragment adding and deleting actions are shown in Figure 2. ",
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/e31475af681528898823031aaf3d98c029f3d27fcff92e7e5d1d40288d1451ce.jpg",
+        "image_caption": [
+            "Figure 2: Left: Examples of molecular fragments and a fragment vocabulary. Red dashed lines represents cuttable bonds to extract fragments. Right: Examples of molecular graph editing actions. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, given a molecule $x$ with $n$ atoms and $m$ bonds, we choose to add or delete a fragment onto or from this molecule randomly with probability $\\begin{array} { l } { { \\frac { 1 } { 2 } } } \\end{array}$ for each set of actions. For the adding action, suppose we have a probability distribution over atoms $p _ { \\mathrm { a d d } } ( x , u )$ and a probability distribution over fragments in the vocabulary $p _ { \\mathrm { f r a g } } ( x , u , k )$ . Here $u \\in [ n ]$ is an indicator of the atom in $x$ to which the fragment is adding to and $k \\in [ V ]$ is an indicator of fragments in the vocabulary of size $V$ . We can compute the proposal distribution as follows: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/fab572f4a4801e0781771fd54451a53cf0b34027be1349cc921571fb356b60ee.jpg",
+        "text": "$$\nq ( x ^ { \\prime } | x ) = { \\frac { 1 } { 2 } } \\cdot p _ { \\mathrm { a d d } } ( x , u ) \\cdot p _ { \\mathrm { f r a g } } ( x , u , k )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where $x ^ { \\prime }$ is the molecule obtained by adding the $k$ -th fragment onto the atom $u$ in molecule $x$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As for the deleting action, suppose we have a probability distribution over bonds1 $p _ { \\mathrm { d e l } } ( x , b )$ where $b \\in [ 2 m ]$ is an indicator of bonds in $x$ . We can compute the proposal distribution as follow: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/776b161deb4e389da2297463a50b3ddf9b2e28ee1b79e5ff8c9c655680657994.jpg",
+        "text": "$$\nq ( x ^ { \\prime } | x ) = \\frac { 1 } { 2 } \\cdot p _ { \\mathrm { d e l } } ( x , b )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $x ^ { \\prime }$ is the molecule obtained by removing bond $b$ and the attached fragment from molecule $x$ ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Parameterizing with MPNNs. To better model the molecular graph editing actions, we propose to use MPNNs to suggest the probability distributions $( p _ { \\mathrm { a d d } } , \\bar { p _ { \\mathrm { f r a g } } } , \\bar { p _ { \\mathrm { d e l } } } ) = \\bar { \\mathcal { M } } _ { \\theta } ( x )$ where $\\mathcal { M } _ { \\theta }$ is a MPNN model specified by parameters $\\theta$ , which has been proven powerful to predict chemical properties with molecular graphs (Gilmer et al., 2017). Given a molecule $x$ , we compute the probability distributions as follow: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fdd8d49ca4dd77cf5b3101fa0221d0733958bda138b015557124fdf4384ce5ff.jpg",
+        "text": "$$\n\\begin{array} { r l } & { { \\cal h } _ { u } ^ { \\mathrm { n o d e } } = \\mathrm { M P N N } ( x ) _ { u } \\in \\mathbb { R } ^ { d } } \\\\ & { \\quad \\quad \\quad \\quad \\displaystyle { \\boldsymbol h } _ { b } ^ { \\mathrm { e q e } } = { \\mathrm { C o n c a t } } ( { \\boldsymbol h } _ { v } ^ { \\mathrm { n o d e } } , { \\boldsymbol h } _ { w } ^ { \\mathrm { n o d e } } ) \\in \\mathbb { R } ^ { 2 d } } \\\\ & { \\quad \\quad \\quad \\quad p _ { \\mathrm { a d d } } ( x ) = \\mathrm { S o f t m a x } ( \\{ \\mathrm { M L P } _ { \\mathrm { n o d e } } ( { \\boldsymbol h } _ { u } ^ { \\mathrm { n o d e } } ) ) \\} _ { u = 1 } ^ { n } ) \\in [ 0 , 1 ] ^ { n } } \\\\ & { \\quad \\quad \\quad p _ { \\mathrm { f r a g } } ( x , u ) = \\mathrm { S o f t m a x } ( \\mathrm { M L P } _ { \\mathrm { n o d e } } ^ { \\prime } ( { \\boldsymbol h } _ { u } ^ { \\mathrm { n o d e } } ) ) \\in [ 0 , 1 ] ^ { | { \\cal V } | } } \\\\ & { \\quad \\quad \\quad p _ { \\mathrm { d e l } } ( x ) = \\mathrm { S o f t m a x } ( \\{ \\mathrm { M L P } _ { \\mathrm { e d e } } ( { \\boldsymbol h } _ { b } ^ { \\mathrm { e q e } } ) ) \\} _ { b = 1 } ^ { 2 m } ) \\in [ 0 , 1 ] ^ { 2 m } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $u$ is an atom indicators, $\\{ h _ { u } ^ { \\mathrm { n o d e } } \\} _ { u = 1 } ^ { n }$ e}nu=1 are node hidden representations, v, w are atoms connected with bond $b$ , $\\{ h _ { b } ^ { \\mathrm { e d g e } } \\} _ { b = 1 } ^ { 2 m }$ u   are edge hidden representations, and ${ \\bf M L P _ { n o d e } }$ , $\\mathbf { M L P _ { n o d e } ^ { \\prime } }$ , ${ \\mathrm { \\mathbf { M L P _ { e d g e } } } }$ are multilayer peceptrons (MLPs), similar to $\\mathrm { H u }$ et al. (2020). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adaptive self-training. To capture the desired properties and improve the sampling effectiveness, we can train the editing model to increase the probability of suggesting high-quality candidate ",
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+    {
+        "type": "text",
+        "text": "Algorithm 1: MARS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "1 Set $N$ initial molecules $\\{ x _ { i } ^ { ( 0 ) } \\} _ { i = 1 } ^ { N }$ and initialize the molecular graph editing model $\\mathcal { M } _ { \\theta }$   \n2 Create an empty editing model training dataset $\\mathcal { D } = \\{ \\}$   \n3 for $t = 1 , 2 , \\ldots$ do   \n4 for $i = 1 , 2 , \\dots , N$ do   \n5 Compute probability distributions $( p _ { \\mathrm { a d d } } , p _ { \\mathrm { f r a g } } , p _ { \\mathrm { d e l } } ) = \\mathcal { M } _ { \\theta } ( x _ { i } ^ { ( t - 1 ) } )$ as Equations 7-9   \n6 Sample a candidate molecule $x ^ { \\prime }$ from the proposal distribution $q ( x ^ { \\prime } \\mid x _ { i } ^ { ( t - 1 ) } )$ defined with   \nprobability distributions $p _ { \\mathrm { a d d } } , p _ { \\mathrm { f r a g } } , p _ { \\mathrm { d e l } }$ as Equations 3-4   \n7 if $u < \\mathcal { A } ( x _ { i } ^ { ( t - 1 ) } , x ^ { \\prime } )$ where $u \\sim \\mathcal { U } _ { [ 0 , 1 ] }$ then   \n8 Accept the candidate molecule $\\boldsymbol { x } _ { i } ^ { ( \\dot { t } ) } = \\boldsymbol { x } ^ { \\prime }$   \n9 else   \n10 Refuse the candidate molecule $x _ { i } ^ { ( t ) } = x _ { i } ^ { ( t - 1 ) }$   \n11 if The candidate improves the objectives, i.e. $\\pi ( x ^ { \\prime } ) > \\pi ( x _ { i } ^ { ( t - 1 ) } )$ then   \n12 Adding the editing record $( x _ { i } ^ { ( t - 1 ) } , x ^ { \\prime } )$ into the dataset $\\mathcal { D }$   \n13 $\\theta ^ { n e w } \\longleftarrow \\arg \\operatorname* { m a x } \\log M _ { \\theta } ( \\mathcal { D } )$ ",
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+    {
+        "type": "text",
+        "text": "molecules. Here we propose to train the model on-the-fly during the sampling process in an adaptive manner where the training data is collected from the sampling paths. By doing so, we can bypass the difficulty of lacking training instances that satisfy all property constraints. Mainly, we collect molecule candidates that improve our desired objectives and train the model $\\mathcal { M } _ { \\theta }$ in a maximum likelihood estimation (MLE) manner (i.e., to maximize the probability of producing the collected candidates). The overall MARS is described in Algorithm 1. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Discussion on convergence. Compared with standard MCMC algorithms, MARS still falls in the Metropolis-Hastings algorithm but with an annealing scheme and an adaptive proposal, which results in inhomogeneous transition kernels. The convergence of adaptive MCMC is discussed in Rosenthal (2011). According to the diminishing adaptation condition, we can ensure convergence by making the difference of proposals in consecutive iterations diminish to zero. MARS can satisfy this condition by using an optimizer whose learning rate will shrink to zero eventually (e.g., Adam). Annealed MCMC is to find samples maximizing the target probability. The convergence of annealed MCMC is discussed in Andrieu et al. (2003). ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENT SETUP ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Biological objectives. Following Jin et al. (2020), we consider the following inhibition scores against two Alzheimer-related target proteins as the biological activity objectives. The score is given by a random forest model 2 that predicts based on Morgan fingerprint features of a molecule (Rogers & Hahn, 2010). ",
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+    {
+        "type": "text",
+        "text": "• $\\mathrm { G S K } 3 \\beta$ : Inhibition against glycogen synthase kinase- $3 \\beta$ .   \n• JNK3: Inhibition against c-Jun N-terminal kinase-3. ",
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+        "type": "text",
+        "text": "Non-biological objectives. Following Jin et al. (2020), we adopt QED (Bickerton et al., 2012) and synthetic accessibility (SA) (Ertl & Schuffenhauer, 2009) to quantify the drug-likeness and synthesizability. We rescale the SA score (initially between 10 and 1) into [0, 1] such that molecules with higher scores are more synthesizable. ",
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+    {
+        "type": "text",
+        "text": "Multi-objective generation setting. To evaluate the effectiveness of the proposed method for multiobjective drug design, we also consider the following more challenging objective combinations: ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• $\\mathrm { G S K } 3 \\beta { + } \\mathrm { J N K } 3$ : Jointly inhibiting $\\mathrm { G S K } 3 \\beta$ and JNK3. The combination may provide potential benefits for the treatment of Alzheimer’s disease reported by Hu et al. (2009); Martin et al. (2013). $\\mathrm { G S K } 3 \\beta / \\mathrm { J N K } 3 + \\mathrm { Q E D } + \\mathrm { S A } ;$ : Inhibiting $\\mathrm { G S K } 3 \\beta$ or JNK3 while being drug-like and synthetically accessible, which are quantified by QED and SA, respectively. $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\mathrm { + } \\mathrm { Q E D } \\mathrm { + } \\mathrm { S A }$ : Jointly inhibiting $\\mathrm { G S K } 3 \\beta$ and JNK3 while being drug-like and synthetically accessible, which are quantified by QED and SA, respectively. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Baselines. We compare MARS with the following methods – the latest ones from four categories mentioned in the related work (Sec. 2). GCPN (You et al., 2018) leverages RL to generate molecules atom by atom, and the adversarial loss is incorporated in the objective to generate more realistic molecules. JT-VAE (Jin et al., 2018) is a VAE-based approach that firstly generates junction trees and then assembles them into molecules. It performs Bayesian optimization (BO) to guide molecules towards desired properties. RationaleRL (Jin et al., 2020) is a state-of-the-art approach for multiproperty optimization, which generates molecules from combined rationales. $\\mathbf { G A + D }$ (Nigam et al., 2020) is a heuristic search method that applies the genetic algorithm (GA) to find molecules with high property scores. An adversarial loss is incorporated in the fitness evaluation to increase the diversity of generated molecules. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. Following Jin et al. (2020), we generate $N \\ = \\ 5 0 0 0$ molecules for each approach and compare the proposed method with the baselines on the following evaluation metrics: Success rate (SR) is the percentage of generated molecules that are evaluated as positive on all given objectives $\\mathrm { ( Q E D \\ge 0 . 6 }$ , $\\mathbf { S A } \\geq \\ 0 . 6 7$ , the inhibition scores of $\\mathrm { G S K } 3 \\beta$ and JNK3 $\\ge ~ 0 . 5 )$ ; Novelty $\\mathbf { \\Pi } ( \\mathbf { N o v } )$ is the percentage of generated molecules with similarity less than 0.4 compared to the nearest neighbor $x _ { S \\mathsf { N N } }$ in the training set (Olivecrona et al., 2017): $\\begin{array} { r l } { \\mathbf { N o v } } & { { } = } \\end{array}$ $\\textstyle { \\frac { 1 } { n } } \\sum _ { x \\in { \\mathcal { G } } } \\mathbf { 1 } [ \\sin ( x , x _ { \\mathrm { S N N } } ) < { \\bar { 0 . 4 } } ]$ ; Diversity (Div) measures the diversity of generated molecules, which can be calculated based on pairwise Tanimoto similarity over Morgan fingerprints $\\sin ( x , x ^ { \\prime } )$ as $\\begin{array} { r } { \\mathrm { D i v } = \\frac { 2 } { n ( n - 1 ) } \\sum _ { x \\ne x ^ { \\prime } \\in \\mathcal { G } } 1 - \\dot { \\sin ( x , x ^ { \\prime } ) } } \\end{array}$ ; PM is the product of the above three metrics, which is a more comprehensive evaluation of the proposed method. Intuitively, PM presents the percentage of generated molecules that are simultaneously bio-active, novel and diverse, which are essential criteria for molecules to be considered in building a suitable drug candidate library in early-stage drug discovery (Huggins et al., 2011). ",
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+    {
+        "type": "text",
+        "text": "Implementation details. For the fragment vocabulary, we extract the top 1000 frequently appearing fragments that contain no more than 10 heavy atoms from the ChEMBL database (Gaulton et al., 2017) by enumerating single bonds to break. As for the sampling process, the unnormalized target distribution is set as $\\begin{array} { r } { \\bar { \\pi } ( x ) = \\sum _ { k } s _ { k } ( x ) } \\end{array}$ where $s _ { k } ( x )$ is a scoring function for the above-mentioned properties of interests, the temperature is set as $T = 0 . 9 5 ^ { \\lfloor t / 5 \\rfloor }$ and we sample $N = 5 0 0 0$ molecules at one time. During sampling, the computation of $q ( x \\mid x ^ { \\prime } )$ is ignored and we approximate $\\boldsymbol { \\mathcal { A } } ( \\boldsymbol { x } , \\boldsymbol { x } ^ { \\prime } )$ with $\\mathrm { m i n } \\{ 1 , \\pi ^ { \\alpha } ( x ^ { \\bar { \\prime } } ) / \\pi ^ { \\alpha } \\bar { \\alpha ( } x ) \\bar { \\} }$ to increase the computation efficiency. This is acceptable because in practice $q ( x \\mid x ^ { \\prime } )$ and $q ( x ^ { \\prime } \\mid x )$ is of order $O ( 1 )$ and $\\boldsymbol { \\mathcal { A } } ( \\boldsymbol { x } , \\boldsymbol { x } ^ { \\prime } )$ will be gradually bounded by $\\pi ^ { \\alpha } \\bar { ( } x ^ { \\prime } ) / \\pi ^ { \\alpha } \\bar { ( } x )$ as the temperature $T$ decrease to zero. The sampling paths are all starting with an identical molecule $\\mathrm { ^ { 6 6 } C T ^ { - C } } ^ { \\mathrm { 9 } }$ , which is also adopted by previous graph generation methods for organic molecules (You et al., 2018). The MPNN model has six layers, and the node embedding size is $d = 6 4$ . Moreover, for the model training, we use an Adam optimizer (Kingma & Ba, 2015) to update the model parameters with an initial learning rate set as $3 \\times 1 0 ^ { - 4 }$ , the maximum dataset size is limited as $| \\mathcal { D } | \\overset { - } { \\leq } 7 5 , 0 0 0$ , and at each step, we update the model for no more than 25 times. ",
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+    {
+        "type": "text",
+        "text": "4.2 MAIN RESULTS AND ANALYSIS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We perform ten independent runs for MARS. The quantitative results are summarized in Table 1 and Table 2. From these tables, we observe that MARS outperforms all the baselines on five out of six tasks in terms of PM. Furthermore, on the most challenging multi-objective optimization task, i.e., $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } \\substack { + } \\mathrm { S A }$ , it significantly surpasses the best baseline with a $7 7 \\%$ improvement for the product of metrics PM. Additional results are shown in Appendix A. ",
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+    {
+        "type": "text",
+        "text": "In comparing all these methods, the $\\mathrm { G A + D }$ baseline is most similar to our MARS in terms of the high novelty and PM score, as both methods focus on molecular space exploration. However, the diversity score of $\\mathrm { G A + D }$ drops a lot when optimizing multiple properties simultaneously, as GAs are likely to get trapped in regions of local optima (Paszkowicz, 2009). RationaleRL is a very strong baseline that performs better than MARS in the $\\mathrm { G S K } 3 \\beta { + } \\mathrm { J N K } 3$ setting. Nevertheless, when taking the drug-likeness and synthetic accessibility into consideration, their performance falls short of ours and fails to generate novel molecules. The performance of GCPN and JT-VAE remains relatively low in most settings, as they are not tailored for multi-objective property optimization. ",
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+        "type": "table",
+        "img_path": "images/042a5ad692f83f30418736d0eb747b1d4859ffc4915527c74b96bc7a5eb07f1f.jpg",
+        "table_caption": [
+            "Table 1: Comparison of different methods on molecular generation with only bio-activity objectives. Results of $\\mathrm { G A + D }$ are obtained by running its open-source code. Results of other baselines are taken from Jin et al. (2020). For MARS, we report the mean and standard deviation of 10 independent experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">GSK3β</td><td colspan=\"4\">JNK3</td><td colspan=\"4\">GSK3β+JNK3</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>GCPN</td><td>42.4%</td><td>11.6%</td><td>0.904</td><td>0.04</td><td>32.3%</td><td>4.4%</td><td>0.884</td><td>0.01</td><td>3.5%</td><td>8.0%</td><td>0.874</td><td>0.00</td></tr><tr><td>JT-VAE</td><td>32.2%</td><td>11.8%</td><td>0.901</td><td>0.03</td><td>23.5%</td><td>2.9%</td><td>0.882</td><td>0.01</td><td>3.3%</td><td>7.9%</td><td>0.883</td><td>0.00</td></tr><tr><td>RationaleRL</td><td>100.0%</td><td>53.4%</td><td>0.888</td><td>0.47</td><td>100.0%</td><td>46.2%</td><td>0.862</td><td>0.40</td><td>100.0%</td><td>97.3%</td><td>0.824</td><td>0.80</td></tr><tr><td>GA+D</td><td>84.6%</td><td>100.0%</td><td>0.714</td><td>0.60</td><td>52.8%</td><td>98.3%</td><td>0.726</td><td>0.38</td><td>84.7%</td><td>100.0%</td><td>0.424</td><td>0.36</td></tr><tr><td>MARS</td><td>100.0%</td><td>84.0%</td><td>0.718</td><td>0.60 ± 0.04</td><td>98.8%</td><td>88.9%</td><td>0.748</td><td>0.66 ±0.04</td><td>99.5%</td><td>75.3%</td><td>0.691</td><td>0.52 ±0.08</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e4cd757e3b49dc028432824428c0415c20702b7ba59819741712e17dd9c6e687.jpg",
+        "table_caption": [
+            "Table 2: Comparison of different methods on molecular generation with bio-activity, QED, and SA objectives. Results of all baselines are obtained by running their open-source codes. For the results of MARS, we report the mean and standard deviation of 10 independent experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">GSK3β+QED+SA</td><td colspan=\"4\">JNK3+QED+SA</td><td colspan=\"4\">GSK3β +JNK3+ QED +SA</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>GCPN</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td><td>0.0%</td><td>0.0%</td><td>0.000</td><td>0.00</td></tr><tr><td>JT-VAE</td><td>9.6%</td><td>95.8%</td><td>0.680</td><td>0.06</td><td>21.8%</td><td>100.0%</td><td>0.600</td><td>0.13</td><td>5.4%</td><td>100.0%</td><td>0.277</td><td>0.02</td></tr><tr><td>RationaleRL</td><td>69.9%</td><td>40.2%</td><td>0.893</td><td>0.25</td><td>62.3%</td><td>37.6%</td><td>0.865</td><td>0.20</td><td>75.0%</td><td>55.5%</td><td>0.706</td><td>0.29</td></tr><tr><td>GA+D</td><td>89.1%</td><td>100.0%</td><td>0.682</td><td>0.61</td><td>85.7%</td><td>99.8%</td><td>0.504</td><td>0.43</td><td>85.7%</td><td>100.0%</td><td>0.363</td><td>0.31</td></tr><tr><td>MARS</td><td>99.5%</td><td>95.0%</td><td>0.719</td><td>0.68 ±0.03</td><td>91.3%</td><td>94.8%</td><td>0.779</td><td>0.67 ± 0.02</td><td>92.3%</td><td>82.4%</td><td>0.719</td><td>0.55 ± 0.05</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Visualization. We use t-SNE (van der Maaten & Hinton, 2008) to visualize the distribution of generated positive molecules with the positive ones in the training set under the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } \\substack { + } \\mathrm { S A }$ setting. In the visualization, we use the ECFP6 fingerprints as suggested in Li et al. (2018). As shown by Figure 3, most molecules generated by $\\mathrm { G A + D }$ fall into two massive clusters, which aligns their low diversity. Molecules generated by RationaleRL also tend to be clustered, with each cluster standing for a specific combination of rationales. By contrast, the molecules generated by MARS are evenly distributed in the space with a range of novel regions covered, which justifies our high novelty and diversity scores. We further visualize some molecules generated by MARS with high property scores in Figure 4, indicating its ability to generate highly synthesizable drug-like molecules that jointly inhibit $\\mathrm { G S K } 3 \\beta$ and JNK3. Additional examples of sampled molecules are shown in Appendix C. ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/354e560c651a8808c3b974a4b0c14d32ebb2bdc639cd4e93f783461d0a67c543.jpg",
+        "image_caption": [
+            "Figure 3: t-SNE visualization of generated molecules (gray) and positive molecules in the training set (blue). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Running time. The computing server has two CPUs with 64 virtual cores $( 2 . 1 0 \\mathrm { G H z } )$ , 231G memory (about 50G used), and one Tesla V100 GPU with 32G memory. In the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } + \\mathrm { S A }$ setting, MARS takes roughly $T = 5 5 0$ sampling steps and 12 hours in total to converge (including the time used in proposing and evaluating molecules as well as MPNN model training). For other baselines, RationaleRL takes 5.7 hours to fine-tune the model, and $\\mathrm { G A + D }$ takes 278 steps and $2 . 2 \\mathrm { h }$ to achieve its best performance. Compared to the conventional drug discovery process, which usually takes months to years, the time we spent on molecular generation models is almost ignorable. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/5bcb89e0fc85613bdac8e49645a597468b528c3b82d188ba4ede2803bc68053d.jpg",
+        "image_caption": [
+            "Figure 4: Sample molecules generated by MARS in the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 + \\mathrm { Q E D } + \\mathrm { S A }$ setting. The numbers in brackets are $\\mathrm { G S K } 3 \\beta$ , JNK3, QED, and SA scores of each molecule respectively. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3 EFFECTS OF PROPOSAL AND ACCEPTANCE STRATEGY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            272,
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+    },
+    {
+        "type": "text",
+        "text": "To justify the contributions of the designed proposal and acceptance strategy, we compare them with some naive ones and summarize the results of different combinations in Table 3. For acceptance strategies, Annealed stands for annealed MCMC where the acceptance rate is computed as Equation 2 given $\\alpha = 1 / T$ , AlwaysAC stands for always accepting the candidate, i.e., $\\bar { \\mathcal { A } } ( \\boldsymbol { x } , \\boldsymbol { x } ^ { \\prime } ) \\equiv 1$ , and HillClimb stands for accepting the candidate only when the overall score is improved, i.e., ${ \\mathcal A } ( x , x ^ { \\prime } ) = \\mathrm { s i g n } [ s ( x ^ { \\prime } ) > s ( x ) ]$ . For proposal strategies, Random stands for random proposal where we randomly select atoms, bonds, and fragments to edit, and Adaptive stands for the adaptive fragment-based graph editing model trained during the sampling process as described in Section 3.2. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/039c0f89809c54c916d9e3afa81cceaf901444bf811371fb0860a99666c1d9dd.jpg",
+        "table_caption": [
+            "Table 3: Results of different acceptance strategies and proposal strategies for molecular sampling. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">AC Strategy</td><td rowspan=\"2\">Proposal</td><td colspan=\"4\">GSK3β + JNK3</td><td colspan=\"4\">GSK3β + JNK3 + QED + SA</td></tr><tr><td>SR</td><td>Nov</td><td>Div</td><td>PM</td><td>SR</td><td>Nov</td><td>Div</td><td>PM</td></tr><tr><td>Annealed</td><td>Random</td><td>40.9%</td><td>94.9%</td><td>0.828</td><td>0.32</td><td>25.5%</td><td>80.4%</td><td>0.793</td><td>0.16</td></tr><tr><td>AlwaysAC</td><td>Adaptive</td><td>49.1%</td><td>88.4%</td><td>0.742</td><td>0.32</td><td>10.1%</td><td>94.6%</td><td>0.716</td><td>0.07</td></tr><tr><td>HillClimb</td><td>Adaptive</td><td>53.7%</td><td>96.1%</td><td>0.814</td><td>0.42</td><td>51.4%</td><td>86.6%</td><td>0.777</td><td>0.35</td></tr><tr><td>Annealed</td><td>Adaptive</td><td>99.5%</td><td>75.2%</td><td>0.688</td><td>0.52</td><td>92.3%</td><td>82.4%</td><td>0.719</td><td>0.55</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The results in Table 3 indicate that proposals will influence the performance of MARS dramatically (the first and the last row), especially when the number of objectives increases. The proposed adaptive proposal outperforms the random proposal and converges $4 . 6 \\mathrm { x }$ faster in practice. By comparing the last three rows, we find the Annealed strategy outperforms the other two strategies by a large margin on both settings, as samples from such strategy are more likely to jump out of local optimums. Another interesting observation is that even with the naive AlwaysAC or heuristic HillClimb strategy, the MARS achieves comparable or even better performance than $\\mathrm { G A + D }$ and RationaleRL in some settings, e.g., HillClimb on $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } \\substack { + } \\mathrm { S A }$ optimization, which again proves the effectiveness of the proposed proposal. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This paper proposes a simple yet flexible MArkov moleculaR Sampling framework (MARS) for multi-objective drug discovery. MARS includes a trainable proposal to modify chemical graph fragments, which is parameterized by an MPNN. Our experiments verify that MARS outperforms prior approaches on five out of six molecule generation tasks, and it is capable of finding novel and diverse bioactive molecules that are both drug-like and highly synthesizable. Future work can include further study of parameterization and training strategy of the molecular-editing proposal. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGEMENT ",
+        "text_level": 1,
+        "bbox": [
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+            835,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Meihua Dang for refactoring much of the MARS code. Meihua also performed multiple experiments, which generates the results for the tables. We also thank Jiangjie Chen, Yuxuan Song, Jingjing Xu, Weiying Ma, Hang Li, and anonymous reviewers for their constructive comments and suggestions. ",
+        "bbox": [
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+    },
+    {
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+    {
+        "type": "text",
+        "text": "Appendix ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            316,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A PROPERTY SCORES OF SAMPLED MOLECULES",
+        "text_level": 1,
+        "bbox": [
+            174,
+            148,
+            596,
+            166
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The property score distributions of sampled $N = 5 0 0 0$ molecules of the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } + \\mathrm { S A }$ setting are shown in Figure 5. The average of the metrics over the sampling path is shown in Figure 6. ",
+        "bbox": [
+            173,
+            189,
+            823,
+            218
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/0bab267db78f46805300fd4872b6414180a7bb4eb7016542f504b51e5c1dbc4d.jpg",
+        "image_caption": [
+            "Figure 5: Property score distributions of sampled $N = 5 0 0 0$ molecules. The red lines are success thresholds. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            218,
+            258,
+            766,
+            587
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/beca3f6afb24e575ebdc42f47fe82e3b9ac74328c9f209f14eb9c32c698e18bc.jpg",
+        "image_caption": [
+            "Figure 6: MARS sampling curves (average of 10 runs) for the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } \\substack { + } \\mathrm { S A }$ setting. SR: success rate. Nov: novelty. Div: diversity. PM: product of the three metrics. Shaded area shows the standard deviations over 10 independent runs. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            307,
+            652,
+            684,
+            854
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B SINGLE OBJECTIVE GENERATION",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            488,
+            118
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "To study whether our proposed method is capable of single-objective molecular generation, we also investigate how MARS performs on the drug-likeness (QED) and the penalized octanol-water partition coefficient (penalized logP) optimization. The experiment results are shown in Table 4. In the experiments, our approach can obtain the best performance on both QED and logP optimization. And especially, MARS outperforms previous methods significantly in the logP generation task. ",
+        "bbox": [
+            174,
+            133,
+            825,
+            204
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/38869c19b2b9442606ff92cbf3fcb87f59c031d4e5ee4f26402f210a0f6c747c.jpg",
+        "table_caption": [
+            "Table 4: Comparison of different methods on single-objective molecular generation. Results of other baselines are taken from Shi et al. (2020) and Nigam et al. (2020). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">1st</td><td colspan=\"2\">QED</td><td colspan=\"3\">Penalized logP</td></tr><tr><td>2nd</td><td>3rd</td><td>1st</td><td>2nd</td><td>3rd</td></tr><tr><td>GCPN (You et al., 2018)</td><td>0.948</td><td>0.947</td><td>0.946</td><td>7.98</td><td>7.85</td><td>7.80</td></tr><tr><td>JT-VAE (Jin et al., 2018)</td><td>0.925</td><td>0.911</td><td>0.91</td><td>5.30</td><td>4.93</td><td>4.49</td></tr><tr><td>GraphAF (Shi et al.,2020)</td><td>0.948</td><td>0.948</td><td>0.947</td><td>12.23</td><td>11.29</td><td>11.05</td></tr><tr><td>GB-GA (Jensen, 2019)</td><td>/</td><td>/</td><td>/</td><td>15.76± 5.71</td><td>/</td><td>/</td></tr><tr><td>GA+D (Nigam et al., 2020)</td><td>/</td><td>/</td><td>/</td><td>20.72 ± 3.14</td><td>/</td><td>1</td></tr><tr><td>MARS</td><td>0.948</td><td>0.948</td><td>0.948</td><td>44.99</td><td>44.32</td><td>43.81</td></tr></table>",
+        "bbox": [
+            200,
+            244,
+            795,
+            383
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Moreover, from the results, we also can see how these two previously widely used metrics (Jin et al., 2018; You et al., 2018; Popova et al., 2019; Shi et al., 2020; Nigam et al., 2020) are questionable for both scientific study and practical use. Most of the generative methods (i.e., GCPN, JT-VAE, and GraphAF) can produce molecules with the highest possible QED score of 0.948, making the top QED score metric hard to distinguish different methods. As for logP optimization, heuristic search-based (i.e., GB-GA and $\\mathrm { G A } { + } \\mathrm { D }$ ) and sampling-based methods (i.e., MARS) can all easily beat generative models. This is because penalized logP score will prefer larger molecules that generative models can hardly produce. However, such large molecules are unrealistic for practical drug discovery, making the top penalized logP score metric problematic. ",
+        "bbox": [
+            173,
+            396,
+            825,
+            522
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C EXAMPLES OF SAMPLED MOLECULES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            542,
+            526,
+            558
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We also provide some examples of sampled molecules from the $\\mathrm { G S K } 3 \\beta + \\mathrm { J N K } 3 \\substack { + } \\mathrm { Q E D } \\substack { + } \\mathrm { S A }$ setting.   \nThe numbers under molecule graphs are $\\mathrm { G S K } 3 \\beta$ , JNK3, QED, and SA scores, respectively. ",
+        "bbox": [
+            174,
+            574,
+            823,
+            602
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/e2ca1b502a5dc59d5526d2fa276b3cd5948939e14b67c341b48aa673a5e68f71.jpg",
+        "image_caption": [
+            "Figure 7: 40 sampled molecules with highest average property scores. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            97,
+            818,
+            914
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/7f24c808c854564588e8e70bccbc39694c2afb8619644c6d8f6747313d4dc468.jpg",
+        "image_caption": [
+            "Figure 8: 40 sampled molecules with highest $\\mathrm { G S K } 3 \\beta$ scores. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            80,
+            816,
+            917
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/7020507949ef8e7b21f6f22ead012f1062a5e37ddf166e51ed28bb6760af5cc2.jpg",
+        "image_caption": [
+            "Figure 9: 40 sampled molecules with highest JNK3 scores. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            187,
+            103,
+            808,
+            911
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/a51cc17dd310937444fd3757b6c5aee06bef2b107773be4e0dedb419e4abb89c.jpg",
+        "image_caption": [
+            "Figure 10: 40 sampled molecules with highest QED scores. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            82,
+            805,
+            917
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "image",
+        "img_path": "images/a0224a66ffeb2ef57e42d611c5756109dbabef25366aded3e6744d826cad9cf1.jpg",
+        "image_caption": [
+            "Figure 11: 40 sampled molecules with highest SA scores. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            80,
+            816,
+            919
+        ],
+        "page_idx": 18
+    }
+]

parse/train/qDrpme0FAi/qDrpme0FAi.md

@@ -0,0 +1,244 @@
+# Mining the Benefits of Two-stage and One-stage HOI Detection
+
+Aixi Zhang1∗ Yue Liao2\* Si Liu2† Miao Lu1 Yongliang Wang1 Chen Gao2 Xiaobo Li1 1Alibaba Group 2Beihang University
+
+# Abstract
+
+Two-stage methods have dominated Human-Object Interaction (HOI) detection for several years. Recently, one-stage HOI detection methods have become popular. In this paper, we aim to explore the essential pros and cons of two-stage and one-stage methods. With this as the goal, we find that conventional two-stage methods mainly suffer from positioning positive interactive human-object pairs, while one-stage methods are challenging to make an appropriate trade-off on multi-task learning, i.e., object detection, and interaction classification. Therefore, a core problem is how to take the essence and discard the dregs from the conventional two types of methods. To this end, we propose a novel one-stage framework with disentangling human-object detection and interaction classification in a cascade manner. In detail, we first design a human-object pair generator based on a state-of-the-art one-stage HOI detector by removing the interaction classification module or head and then design a relatively isolated interaction classifier to classify each human-object pair. Two cascade decoders in our proposed framework can focus on one specific task, detection or interaction classification. In terms of the specific implementation, we adopt a transformer-based HOI detector as our base model. The newly introduced disentangling paradigm outperforms existing methods by a large margin, with a significant relative mAP gain of $9 . 3 2 \%$ on HICO-Det. The source codes are available at https://github.com/YueLiao/CDN.
+
+# 1 Introduction
+
+The goal of Human-Object Interaction (HOI) detection [2, 20, 6, 18, 7, 8, 17, 3] is to make a machine detailedly understand human activities from a static image. Human activities in this task are abstracted as a set of <human, object, action $\mid >$ HOI triplets. Thus, an HOI detector is required to locate humanobject pairs and classify their corresponding action simultaneously. Based on this definition, we can summarize conventional HOI detection methods into two paradigms, i.e., two-stage methods, and one-stage methods. These two paradigms have made significant progress with the development of deep learning, but both paradigms still have their shortcomings due to their structural design. This paper aims to present a detailed analysis of methods under these two paradigms and propose a solution to mine the benefits of two-stage and one-stage methods.
+
+We first take a closer look at the conventional two-stage and one-stage HOI detectors. Conventional two-stage methods [6, 2, 18, 5] are mostly with a serial architecture. As shown in Figure 1 (a), two-stage methods detect humans and objects first and then feeds the human-object pairs, which are generated by matching humans and objects one by one, into an interaction classifier. The serial architecture suffers from locating the interactive human-object pairs under the interference of a large number of negative pairs only based on local region features. Otherwise, the efficiency of two-stage methods is also limited by the serial architecture. To alleviate these problems, one-stage methods [20, 13, 39, 3, 28, 14] are proposed to detect the HOI triplets directly and break HOI detection as multi-task learning, i.e., human-object detection and interaction classification, which is shown in Figure 1(b). Therefore, one-stage methods can easily focus on the interactive human-object pairs and effectively extract corresponding features in an end-to-end manner. However, it is difficult for a single model to make a good trade-off on multi-task learning since human-object detection and interaction classification are two very different tasks, which requires the model to focus on different visual features. As shown in Figure 1(c), though some previous methods [20, 3] design two parallel branches to detect instances and predict interaction respectively, the interaction classification branch still needs to regress additional offsets to associate humans and objects. Thus the interaction branch is also required to make a trade-off between interaction classification and human and object positioning.
+
+![](images/ac35478e213beafd7a15fa28c4e7cd0444a1562cc847359b60b9274bd73b91d5.jpg)  
+Figure 1: (a) Two-stage framework, (b) one-stage end-to-end framework, (c) one-stage framework with parallel architecture, and (d) our one-stage framework with a cascade disentangling head.
+
+Therefore, the intuitive idea is to take the essence and discard the dregs from the two paradigms. To attain this, we propose a novel end-to-end one-stage framework with disentangling human-object detection and interaction classification in a cascade manner, namely Cascade Disentangling Network (CDN). The original intention of our framework is to keep the advantages of conventional onestage methods, directly and accurately locating the interactive human-object pairs, and bring the advantages of two-stage methods into our one-stage framework, disentangling human-object detection and interaction classification. As shown in Figure 1(d), in our proposed framework, we design a human-object pair decoder based on the one-stage paradigm by removing the interaction classification function, namely HO-PD, and following an isolated interaction classifier. To instantiate our idea with an end-to-end manner, we design the HO-PD based on the previous state-of-the-art one-stage transformer-based HOI detector, HOI-Trans [39] and QPIC [28], where we remove the interaction classification head for each query and make it focus on human-object pairs detection. Otherwise, we design an independent HOI decoder for interaction classification to make the interaction classification unaffected by human-object detection. Therefore, there exists a core problem, i.e., how to link the human-object pair and the corresponding action class. To address this problem, we initialize the query embedding of the HOI decoder with the output of the last layer of the HO-PD. In this case, the HOI decoder is able to learn the corresponding action category under the guidance of the query embedding and free out from the human-object detection task. Moreover, we design a decoupling dynamic re-weighting manner to handle the long-tailed problems in HOI detection.
+
+Our contributions can be summarized threefold: (1) We conduct a detailed analysis of two conventional HOI detection paradigms, i.e., two-stage and one-stage. (2) We propose a novel one-stage framework with a cascade disentangling decoder to combine the advantages of two-stage and onestage methods. (3) Our method outperforms previous state-of-the-art methods by a large margin on the HOI detection task, especially achieves a $2 5 . 3 5 \%$ performance gain on rare classes of HICO-Det.
+
+# 2 Analysis of Two-stage and One-stage HOI detectors
+
+We first introduce a unified formulation for the HOI detection problem. Given a human-centric image $\pmb { I }$ , the model $T ( \cdot )$ is required to predict a set of HOI triplets $\mathbf { \bar {  { S } } } = \{ ( b _ { i } ^ { h } , b _ { i } ^ { o } , a _ { i } ) , i \in \{ 1 , 2 , \cdot \cdot \cdot , K \} \}$ , where $b _ { i } ^ { h }$ , $b _ { i } ^ { o }$ and $a _ { i }$ denotes a human bounding-box, an object bounding-box and their corresponding action category, respectively.
+
+Two-stage HOI detector. Two-stage detectors can be regarded as an instance-driven manner, detecting instances first and predicting interaction based on the detected instances. The two-stage detector divides $T ( \cdot )$ into two stages, i.e., detection $T _ { d } ( \cdot )$ and interaction classification $T _ { c } ( \cdot )$ . In the first stage, we suppose that $T _ { d } ( \cdot )$ produces $M$ human bounding-boxes and $N$ object bounding-boxes. Here the ‘object’ is a universal object which includes human as one class. Therefore, $T _ { d } ( \cdot )$ generates $M \times N$ human-object pairs. In general, the number of true-positive interactive human-object pairs, denoted as $K ^ { \prime }$ , is much smaller than $M \times N$ . However, in the second stage, $T _ { c } ( \cdot )$ needs to scan all $M \times N$ pairs one by one and predict an action category with its corresponding confidence score. In this case, $T _ { c } ( \cdot )$ is required to inference $M \times N$ times to find $K ^ { \prime }$ interactive pairs from $M \times N$ pairs. We argue that this manner causes three problems. Firstly, these models produce a more additional computational cost, whose time complexity is $\mathcal { O } ( M \times N ) \gg \mathcal { O } ( K ^ { \prime } )$ . Secondly, the imbalance between positive and negative samples makes the model easily overfit to negative samples. Thus the model tends to assign a ‘no-interaction’ class for human-object pairs with very high confidence, suppressing the true-positive samples. Thirdly, the accuracy of interaction classification is influenced by the non-end-to-end pipeline. Because the interaction classification is mostly based on the region features extracted by $T _ { d } ( \cdot )$ , while the core of $T _ { d } ( \cdot )$ is to regress bounding-boxes and its extracted features pay more attention to the edge of regions, thereby such features are not good options for interaction classification, which needs more context. However, it is an excellent property for two-stage methods that disentangling detection and interaction classification makes each stage focus on its task and produce good results in each stage.
+
+One-stage HOI detector. As for one-stage methods, they detect all HOI triplets $S$ directly and simultaneously with an end-to-end framework. Such paradigm has greatly relieved the three problems of two-stage methods, especially for efficiency, where the time complexity is reduced to $\mathcal { O } ( K ^ { \prime } )$ . Most one-stage methods are interaction-driven, which directly locate the interaction point [20] or interactive human-object pairs [39], thereby reducing negative sample interference. However, coupling human-object detection and interaction classification limit their performance because it is hard to generate a unified feature representation for two very different tasks. Though the parallel one-stage methods break HOI detection into two parallel branches, their interaction branch still suffers from multi-task learning. Specifically, the optimization target of interaction branch is $\mathcal { P } ( e _ { h } , e _ { o } , a | V )$ , where $e _ { h }$ and $e _ { o }$ are associative embeddings, e.g., offset, to match interaction with human and object respectively. Therefore, even if detection is organized as an independent branch, the interaction branch must position humans and objects for the association. The set-based detectors couple detection and interaction completely, whose optimization function is $\mathcal { P } ( b ^ { h } , b ^ { o } , a | V )$ .
+
+Next, we introduce a simple one-stage framework with disentangling human-object detection and interaction classification, namely CDN, to mine the benefits of two-stage and one-stage HOI detectors. Our CDN disentangles the original set-based one-stage optimization function into two cascade decoders. Firstly, we predict human-object pair by ${ \mathcal { P } } ( b ^ { h } , \dot { b } ^ { o } | V )$ . Secondly, we apply an isolated decoder to predict the action category by $\mathcal { P } ( a | V , b ^ { h } , b ^ { o } )$ . More details are in the following.
+
+# 3 Method
+
+In this section, we will present a detailed introduction to the pipeline of our proposed CDN. In section 3.1, we present an overview of our framework and briefly introduce the pipeline. In section 3.2, we introduce the visual feature extractor. The cascade disentangling HOI decoder is introduced in section 3.3. Section 3.4 introduces a novel dynamic re-weighting mechanism that mitigates the long-tailed problem. The detailed training process and post-processing are discussed in section 3.5.
+
+# 3.1 Overview
+
+The architecture of our proposed CDN is illustrated in Figure 2. Our CDN is organized in a cascade manner with a visual feature extractor. Given an image, we first follow transformer-based detection methods [1, 39] to apply a CNN followed by a transformer encoder architecture to extract visual features into a sequence. Then we detect HOI triplets in two cascade decoders. Firstly, we apply the Human-Object Pair Decoder (HO-PD) to predict a set of human-object bounding-boxes pairs based on a set of learnable queries. Next, taking the output of the last layer of HO-PD as queries, an isolated interaction decoder is utilized to predict the action category for each query. Finally, the HOI triplets are formed by the output of the above two cascade decoders.
+
+# 3.2 Visual Feature Extractor
+
+We define the visual feature extractor by combining a CNN and a transformer encoder. Fed with an input image $\pmb { I }$ with shape $( H , W , C )$ , the CNN generates a feature map of shape $( H ^ { ' } , W ^ { ' } , D _ { b } )$
+
+![](images/19c437351374d41e649928a72a1f04db513b4e3046280a5c9c3b2ded7a27550e.jpg)  
+Figure 2: The framework of our CDN. It is comprised of three components:Visual Feature Extractor, Human-Object Pair Decoder (HO-PD) and Interaction Decoder. We first apply a CNN-transformer combined architecture to extract sequenced visual features $X _ { s }$ . Then, we divide HOI detection into two cascade transformer-based decoders. Firstly, we regress the human-object bounding-box pairs based on $X _ { s }$ and a set of random-initialized queries $Q _ { d }$ by HO-PD. The interactive score is from a binary classification to determine whether the human-object pair is an interactive pair or not. Secondly, we predict one or many action categories for each predicted human-object pairs, where we take the output of HO-PD $\pmb { Q } _ { d } ^ { o u t }$ to initialize the interaction queries $Q _ { c }$ and aggregate information with $X _ { s }$ . Finally, the HOI triplets are formed by the output of the cascade decoders.
+
+Then, $D _ { b }$ is reduced to $D _ { c }$ by a projection convolution layer with a kernel size $1 \times 1$ . Next, a flatten operator is used to generating the flatten feature $\mathbf { \boldsymbol { X } } _ { v } \in \mathcal { R } ^ { ( \boldsymbol { H } ^ { \prime } \times \boldsymbol { W } ^ { \prime } ) \times \boldsymbol { D _ { c } } }$ by collapsing the spatial dimensions into one dimension. This flatten feature is then fed into a transformer encoder and the position encoding $E _ { p o s } \in \mathcal { R } ^ { ( H ^ { ' } \times W ^ { ' } ) \times D _ { c } }$ , which distinguishes the relative position in the sequence $\boldsymbol { X } _ { s } \in \mathcal { R } ^ { ( H ^ { ' } \times W ^ { ' } ) \times D _ { c } }$ . Thanks to the multi-head self-attention mechanism, the transformer encoder produces a feature map with richer contextual information by summarizing global information. The output of the encoder is denoted as global memory with a dimension of $D _ { c }$ .
+
+# 3.3 Cascade Disentangling HOI Decoder
+
+The cascade disentangling HOI decoder consists of two decoders: Human-Object Pair Decoder (HOPD) and interaction decoder. Both decoders share the same architecture, a transformer-based decoder, with independent weights. In this subsection, we first introduce the general architecture of the decoder and then elaborate on the two decoders in detail, respectively.
+
+Transformer-based decoder. We follow the transformer-based object detector DETR [1] to design the basic architecture in our cascade disentangling HOI decoder. We apply $N$ transformer decoder layers for each decoder and equip each decoder layer with several FFN heads for intermediate supervision. Specifically, each decoder layer is comprised of a self-attention module and a multi-head co-attention module. During feed-forward, fed into a set of learnable queries $Q \in \mathcal { R } ^ { N _ { q } \times C _ { q } }$ , each decoder layer first applies a self-attention module on all queries and then conducts a multi-head co-attention operation between queries and the sequenced visual features, and outputs a set of updated queries. For the FFN heads, each head is comprised of one or several MLP branches, and each branch is for a specific task, e.g., regression, or classification. All queries share the same FFN heads. Therefore, each decoder can be simply represented as:
+
+$$
+P = f ( Q , X _ { s } , E _ { p o s } ) .
+$$
+
+Besides, the number of queries $N _ { q }$ is determined by the number of positive samples of an image.
+
+HO-PD. Firstly, we design the HO-PD to predict a set of human-object pairs from the sequenced visual features. To this end, we first randomly initialize a set of learnable queries $Q _ { d } \in \mathcal { R } ^ { N _ { d } ^ { \bullet } \times C _ { q } }$ as HO queries. Then we apply a transformer-based decoder, which takes HO queries $Q _ { d }$ and sequenced visual features as input and applies three FFN heads for each query to predict human bounding-box, object bounding-box, and object class, which form a human-object pair. We also utilize an additional interactive score head to simply determine whether the human-object pair is an interactive pair or not by a binary classification. In this case, $_ { r }$ is instantiated as $P _ { h o }$ , which is consist of a set of human-object pairs $\{ ( b _ { i } ^ { h } , b _ { i } ^ { o } ) , i \in \{ 1 , 2 , \cdot \cdot \cdot , N _ { d } \} \}$ . Thus, HO-PD can be denoted as:
+
+$$
+P _ { h o } = f _ { d } ( Q _ { d } , X _ { s } , E _ { p o s } ) .
+$$
+
+In addition, we keep the output queries of the last layer of HO-PD as $\pmb { Q } _ { d } ^ { o u t }$ for the following step.
+
+Interaction Decoder. Secondly, we propose the interaction decoder to classify the human-object queries and assign one or several action categories for each human-object query. To classify each human-object query one-to-one, we initialize $Q _ { c }$ with the output of HO-PD $\dot { \pmb { Q } } _ { d } ^ { o u t }$ . In this way, $\pmb { Q } _ { d } ^ { o u t }$ can provide prior knowledge to guide $Q _ { c }$ to learn the corresponding action categories for each human-object query. The other components and inputs are the same as HO-PD, which conducts self-attention among queries and co-attention with $X _ { s }$ and $E _ { p o s }$ . The final output is a set of action categories $P _ { c l s } : \{ \bar { a _ { i } } , \bar { i } \in \{ 1 , 2 , \cdots , N _ { d } \} \}$ . Therefore, this process can be formulated as:
+
+$$
+P _ { c l s } = f _ { c l s } ( Q _ { d } ^ { o u t } , X _ { s } , E _ { p o s } ) .
+$$
+
+In our proposed cascade disentangling HOI decoder, the task of HOI detection is disentangled into two relatively independent steps: human-object pairs detection and interaction classification. Therefore, each step can aggregate more related features to concentrate on its corresponding task.
+
+# 3.4 Decoupling Dynamic Re-weighting
+
+The HOI datasets usually have long-tail class distribution for both object class and action class. To alleviate the long-tail problem, we design a dynamic re-weighting mechanism for further improvements with a decoupling training strategy. In detail, we first train the whole model with regular losses. Then, we freeze the parameters of the visual feature extractor and only train the cascade disentangling decoders with a relatively small learning rate and the designed dynamic re-weighted losses.
+
+During decoupling training, at each iteration, we apply two similar queues to accumulate number of each object class or action class. The queues are used as memory banks to accumulate training samples and truncate the accumulation with length $L _ { Q }$ as sliding windows. In detail, $Q _ { o }$ with length $L _ { Q } ^ { o }$ to accumulate object number $N _ { i } ^ { o }$ for each object class $i \in \{ 1 , 2 , \cdots , C _ { o } \}$ , and $Q _ { a }$ with length $L _ { Q } ^ { a }$ to accumulate interaction number $N _ { i } ^ { a }$ for each action category $i \in \{ 1 , 2 , \cdots , C _ { a } \}$ . The dynamic re-weighting coefficients $w _ { d y n a m i c }$ are presented as follow:
+
+$$
+w _ { i } ^ { a } \big | _ { i \in \{ 1 , 2 , \cdots , C _ { a } \} } = \bigg ( \frac { \sum _ { i = 1 } ^ { C _ { a } } N _ { i } } { N _ { i } } \bigg ) ^ { p _ { a } } , \quad w _ { b g } ^ { a } = \bigg ( \frac { \sum _ { i = 1 } ^ { C _ { a } } N _ { i } } { N _ { b g } ^ { a } } \bigg ) ^ { p _ { a } } ,
+$$
+
+$$
+w _ { i } ^ { o } \big | _ { i \in \{ 1 , 2 , \cdots , C _ { o } \} } = \bigg ( \frac { \sum _ { i = 1 } ^ { C _ { o } } N _ { i } } { N _ { i } } \bigg ) ^ { p _ { o } } , \quad w _ { b g } ^ { o } = \bigg ( \frac { \sum _ { i = 1 } ^ { C _ { o } } N _ { i } } { N _ { b g } ^ { o } } \bigg ) ^ { p _ { o } } ,
+$$
+
+where $N _ { i }$ is the number of accumulated positive samples of category $i$ by the queues $Q _ { o }$ and $Q _ { a }$ , $N _ { b g }$ is the number of accumulated background samples, $C$ is the number of categories, and exponent $p$ is a hyper-parameter that adapts the magnitude of mitigation. Specifically, the weight of background class, $w _ { b g }$ , is designed to balance the positives and negatives. For the stability of the dynamic re-weighted training, the weight coefficients are initialized as $w _ { s t a t i c }$ with those calculated by 4 and 5 using the static number of object and action categories. The final dynamic weights are given as $w = \gamma w _ { s t a t i c } + ( 1 - \gamma ) w _ { d y n a m i c }$ , where $\gamma$ is a smooth factor, given as $m i n ( 0 . \bar { 9 9 9 } ^ { L _ { Q } } , 0 . \bar { 9 } )$ . The factor $\gamma$ transits $w$ from $w _ { s t a t i c }$ to wdynamic with the increasing of $L _ { Q }$ . Finally, the weights are used to the classification losses in a traditional way by multiplying each coefficient to each class and then calculating the summation.
+
+# 3.5 Training and Post-processing
+
+In this section, we introduce the training and inference processes in detail. Especially, we will introduce a novel Pair-wise Non-Maximal Suppression (PNMS) strategy in the inference process.
+
+Training. Following the set-based training process of HOI-Trans [39] and QPIC [28], we first match each ground-truth with its best-matching prediction by the bipartite matching with the Hungarian algorithm. Then the loss is produced between the matched predictions and the corresponding ground truths for the final back-propagation. During matching, we consider the predictions of two cascade decoders together. The loss of CDN follows QPIC which is composed by five parts: the box regression loss $L _ { b }$ , the intersection-over-union loss $L _ { G I o U }$ [26], the interactive score loss $L _ { p }$ , the object class loss $L _ { c } ^ { o }$ , and the action category loss $L _ { c } ^ { a }$ . The target loss is the weighted sum of these parts as:
+
+$$
+L = \sum _ { k \in ( h , o ) } \bigl ( \lambda _ { b } L _ { b } ^ { k } + \lambda _ { G I o U } L _ { G I o U } ^ { k } \bigr ) + \lambda _ { p } L _ { p } + \lambda _ { o } L _ { c } ^ { o } + \lambda _ { a } L _ { c } ^ { a } ,
+$$
+
+where $\lambda _ { b } , \lambda _ { G I o U } , \lambda _ { p } , \lambda _ { o }$ and $\lambda _ { a }$ are the hyper-parameters for adjusting the weights of each loss.
+
+Inference. The inference process is to composite the output of instance-related FFNs and the interaction-related FFN to form HOI triplets. By our cascade disentangling decoder architecture, the instance queries and the interaction queries are one-to-one corresponding, therefore, the five components <human bounding box, object bounding box, object class, interactive score, action class> can be homologous in each of the $N _ { d }$ dimensions per FFN head. Formally, we generate the $i$ -th output prediction as $< b _ { i } ^ { h }$ , $b _ { i } ^ { o }$ , argmax $k ^ { c _ { i } ^ { h o i } ( k ) > }$ . The HOI triplet score $c _ { i } ^ { h o i }$ is given by $c _ { i } ^ { h o i } = c _ { i } ^ { a } c _ { i } ^ { o } c _ { i } ^ { p }$ where $c _ { i } ^ { a }$ and $c _ { i } ^ { o }$ are the scores of interaction and object classification, respectively, and $c _ { i } ^ { p }$ is the interactive score from the interactive FFN head for the query vector being an human-object pair.
+
+PNMS. After sorting $c _ { i } ^ { h o i }$ in descending order and generating the top $K$ HOI triplets, we design a pair-wise non-maximal suppression (PNMS) method to further filter out human-object pairs from pair-wise bounding boxes overlapping perspective. For two HOI triplets $m$ and $n$ , the pair-wise overlap $P I o U$ is calculated as:
+
+$$
+P I o U ( m , n ) = \Big ( \frac { I ( b _ { m } ^ { h } , b _ { n } ^ { h } ) } { U ( b _ { m } ^ { h } , b _ { n } ^ { h } ) } \Big ) ^ { \alpha } \Big ( \frac { I ( b _ { m } ^ { o } , b _ { n } ^ { o } ) } { U ( b _ { m } ^ { o } , b _ { n } ^ { o } ) } \Big ) ^ { \beta } ,
+$$
+
+where the operators $I$ and $U$ compute the intersection and union areas between the two boxes of $m$ and $n$ , respectively. $\alpha$ and $\beta$ are the balancing parameters between humans and objects.
+
+# 4 Experiments
+
+In this section, we conduct comprehensive experiments to demonstrate the superiority of our designed CDN. In section 4.1, we briefly introduce the experimental benchmarks. Section 4.2 presents implementation details. Next, It is a detailed experimental comparison and analysis of two-stage and one-stage methods in section 4.3. In section 4.4, we compare our methods with the previous state-of-the-art methods. The ablation studies and components analysis are included in 4.5.
+
+# 4.1 Datasets and Evaluation Metrics
+
+Datasets. We carry out experiments on two widely-used HOI detection benchmarks: HICO-Det [2] and V-COCO [8]. We follow the standard evaluation scheme. HICO-Det consists of 47, 776 Creative Common images from Flickr (38, 118 for training and 9, 658 for test) with more than 150K humanobject pairs. It contains the same 80 object categories as MS-COCO [21] and 117 action categories. The objects and actions form 600 classes of HOI triplets. V-COCO is derived from MS-COCO dataset, which consists of 5, 400 images in the trainval subset and 4, 946 images in the test subset. It has 29 action categories (25 HOIs and 4 body motions) and 80 object categories. For both datasets, one person can interact with multiple objects in different ways at the same time.
+
+Evaluation Metrics. Following the standard evaluation [2], we use the mean average precision (mAP) as the evaluation metric. For one positively predicted HOI triplet <human, object, action>, it needs to contain accurate human and object locations (box IoU with reference to GT box is greater than 0.5) and correct object and action categories. Specifically, for HICO-Det, besides the full set of $6 0 0 \mathrm { H O I }$ classes, we also report the mAP over a rare set of 138 HOI classes that have less than 10 training instances and a non-rare set of the other 462 HOI classes. For V-COCO, we report the role mAP for two scenarios: scenario 1 includes the cases even without any objects (for the four action categories of body motions), and scenario 2 ignores these cases.
+
+# 4.2 Implementation Details
+
+We implement three variant architectures of CDN: CDN-S, CDN-B, and CDN-L, where ‘S’, ‘B’, and ‘L’ denote small, base, and large, respectively. For CDN-S and CDN-B, we adopt ResNet-50 with a 6-layer transformer encoder as the visual feature extractor. For the cascade decoders, CDN-S is equipped with both 3-layer transformers, while CDN-B has a 6-layer transformer for each decoder. CDN-L only replaces the ResNet-50 with ResNet-101 in CDN-B. The reduced dimension size $D _ { c }$ is set to 256. The number of queries $N _ { d }$ is set to 64 for HICO-Det and 100 for V-COCO since the average number of positives for variant human-object pairs per image of HICO-Det is smaller than V-COCO. The human and object box FFNs have 3 linear layers with ReLU, while the object and action category FFNs have one linear layer. The code is provided in supplemental material.
+
+During training, we initialize the network with the parameters of DETR [1] trained with the MSCOCO dataset. We set the weight coefficients $\lambda _ { b }$ , $\lambda _ { G I o U }$ , $\lambda _ { p }$ , $\lambda _ { o }$ and $\lambda _ { a }$ to 2.5, 1, 1, 1 and 1, respectively, which are exactly same with QPIC [28]. We optimize the network by AdamW [23] with the weight decay $1 0 ^ { - 4 }$ . We first train the whole model for 90 epochs with a learning rate of $1 0 ^ { - 4 }$ decreased by 10 times at the 60th epoch. Then, during the decoupling training process, we fine-tune the cascade disentangling decoders together with the box, object, and action FFNs for 10 epochs with a learning rate of $1 0 ^ { = 5 }$ . We use both object and action dynamic re-weighting for HICO-Det and only action dynamic re-weighting for V-COCO. The re-weighting parameter $p$ is set to 0.7 for both object and action. The length $L _ { Q }$ of training sample queue $Q$ for both object and action is set to $2 \times N _ { s }$ , where $N _ { s }$ is the sample number of the training set. All experiments are conducted on the 8 Tesla V100 GPUs and CUDA10.2, with a batch size of 16.
+
+For validation, we select 100 detection results with the highest scores and then adopt PNMS to further filter results. The threshold, $\alpha$ , and $\beta$ of PNMS are set to 0.7, 1, and 0.5, respectively.
+
+# 4.3 Experiment Analysis of Two-stage and One-stage Methods
+
+In this part, we introduce a detailed experimental analysis of conventional two-stage and one-stage methods and our proposed CDN from the following three aspects.
+
+Human-object Pair Generation. We first explore the quality of the human-object pairs generation between two-stage and one-stage methods. To attain this, we conduct a detailed experiment based on a representative two-stage method iCAN [6]. We first implement a PyTorch version iCAN as the baseline model, denoted as $\mathrm { i } { \mathrm { C A N } } ^ { * }$ , which only applies human and object appearance with a COCO-pretrained Faster-RCNN detector [25]. For a fair comparison, we first fine-tune DETR on HICO-Det for 100 epochs only with the instance detection annotation based on COCO-pretrained weights. Then we combine the detected human and object bounding-boxes, whose confidences are greater than a threshold, one by one to generate human-object pairs denoted as $\mathrm { i } { \mathrm { C A N } } ^ { \dagger }$ in Table 1. We train our CDN only with HO-PD for 100 epochs and get the human-object pairs from the output directly. Then, we graft the human-object pairs to the baseline model to extract box features and utilize the same interaction classifier in the second stage of $\mathrm { i } { \mathrm { C A N } } ^ { * }$ . In this way, we degrade the number of pairs from $M \times N$ to $K ^ { \prime }$ , which means time complexity is reduced from $\mathcal { O } ( M \times N )$ to $\mathcal { O } ( K ^ { \prime } )$ . Primarily, HO-PD significantly promotes mAP from 15.37 to 24.05, as shown in Table 1. This indicates that one-stage methods are much superior in human-object pair generation.
+
+<table><tr><td>Strategy</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>iCAN*</td><td>14.16</td><td>12.26</td><td>14.73</td></tr><tr><td>iCAN t</td><td>15.37</td><td>13.23</td><td>16.01</td></tr><tr><td>HO-PD+iCAN*</td><td>24.05</td><td>18.32</td><td>25.76</td></tr><tr><td>QPIC [28]</td><td>29.07</td><td>21.85</td><td>31.23</td></tr><tr><td>CDN-S base</td><td>30.96</td><td>27.02</td><td>32.14</td></tr></table>
+
+Table 1: Analysis of Two-stage and Onestage Methods. ∗ denotes our implemented PyTorch version iCAN [6] baseline model. † denotes replacing instance detection boxes given by a HICO-Det fine-tuned DETR detector to extract box features. ‘HO$\mathrm { P D + i C A N ^ { * } }$ ’ denotes replacing original oneby-one generated human-object pairs with our HO-PD generated. ‘CDN-S base’ denotes CDN-S w/o re-weighting and PNMS strategies.
+
+![](images/606fe2d92b8b9bfee5d048534bea82d09e67a83b86212cf8ea8f31e0b33bef19.jpg)  
+Figure 3: Visualization of Feature Maps for Queries. Visual attended features for query with top-1 score extracted from the last layer of the decoder of (a) QPIC, (b) HO-PD in CDN, and (c) interaction decoder in CDN. Zoom in for details.
+
+Interaction Classification. We aim to study the interaction classification between conventional multi-task one-stage methods and our disentangled one-stage detector. We can regard QPIC [28] as a multi-task version of our CDN. Table 1 shows that our ‘CDN-S base’ (w/o re-weighting and PNMS strategies) has achieved mAP 30.96 with $6 . 5 0 \%$ relative mAP gain compared to QPIC. Especially, our ‘CDN-S base’ significantly outperforms QPIC for rare classes with a $\mathrm { { \bar { 2 3 . 6 6 \% } } }$ improvement. The performance of rare classes can partly reflect the accuracy of interaction classification.
+
+Table 2: Performance comparison on the HICO-Det test set. The ‘P’, ‘T’ represent human pose information and the language feature, respectively.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Detector</td><td rowspan="2">Backbone</td><td rowspan="2">Extra</td><td colspan="3">Default</td><td rowspan="2"></td><td colspan="2">Know Object</td></tr><tr><td>Full</td><td>Rare</td><td>Non-Rare Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>Two-stageMethod:</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>InteractNet [7]</td><td>COCO</td><td>ResNet-50-FPN</td><td>X</td><td>9.94</td><td>7.16</td><td>10.77</td><td></td><td></td><td>=</td></tr><tr><td>GPNN [24]</td><td>CoCO</td><td>Res-DCN-152</td><td>X</td><td>13.11</td><td>9.34</td><td>14.23</td><td></td><td></td><td></td></tr><tr><td>iCAN [6]</td><td>CoCO</td><td>ResNet-50</td><td>X</td><td>14.84</td><td>10.45</td><td>16.15</td><td>16.26</td><td>11.33</td><td>17.73</td></tr><tr><td>No-Frills [9]</td><td>CoCo</td><td>ResNet-152</td><td>P</td><td>17.18</td><td>12.17</td><td>18.68</td><td>=</td><td>=</td><td>=</td></tr><tr><td>PMFNet [30]</td><td>COCO</td><td>ResNet-50-FPN</td><td>P</td><td>17.46</td><td>15.65</td><td>18.00</td><td>20.34</td><td>17.47</td><td>21.20</td></tr><tr><td>CHGNet [31]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>17.57</td><td>16.85</td><td>17.78</td><td>21.00</td><td>20.74</td><td>21.08</td></tr><tr><td>DRG [5]</td><td>CoCO</td><td>ResNet-50-FPN</td><td>T</td><td>19.26</td><td>17.74</td><td>19.71</td><td>23.40</td><td>21.75</td><td>23.89</td></tr><tr><td>VCL[12]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>19.43</td><td>16.55</td><td>20.29</td><td>22.00</td><td>19.09</td><td>22.87</td></tr><tr><td>IP-Net [32]</td><td>CoCO</td><td>Hourglass-104</td><td>X</td><td>19.56</td><td>12.79</td><td>21.58</td><td>22.05</td><td>15.77</td><td>23.92</td></tr><tr><td>VSGNet [29]</td><td>CoCO</td><td>ResNet-152</td><td>X</td><td>19.80</td><td>16.05</td><td>20.91</td><td>=</td><td>=</td><td>=</td></tr><tr><td>FCMNet [22]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>20.41</td><td>17.34</td><td>21.56</td><td>22.04</td><td>18.97</td><td>23.12</td></tr><tr><td>ACP[15]</td><td>CoCO</td><td>ResNet-152</td><td>T</td><td>20.59</td><td>15.92</td><td>21.98</td><td></td><td></td><td></td></tr><tr><td>PD-Net [35]</td><td>COCO</td><td>ResNet-152-FPN</td><td>T</td><td>20.81</td><td>15.90</td><td>22.28</td><td>24.78</td><td>18.88</td><td>26.54</td></tr><tr><td>DJ-RN[16]</td><td>COCO</td><td>ResNet-50</td><td>P</td><td>21.34</td><td>18.53</td><td>22.18</td><td>23.69</td><td>20.64</td><td>24.60</td></tr><tr><td>IDN[17]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>23.36</td><td>22.47</td><td>23.63</td><td>26.43</td><td>25.01</td><td>26.85</td></tr><tr><td>One-stage Method:</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>UnionDet[13]</td><td>CoCO</td><td>ResNet-50-FPN</td><td>X</td><td>17.58</td><td>11.72</td><td>19.33</td><td>19.76</td><td>14.68</td><td>21.27</td></tr><tr><td>DIRV [4]</td><td>COCo</td><td>EfficientDet-d3</td><td>X</td><td>21.78</td><td>16.38</td><td>23.39</td><td>25.52</td><td>20.84</td><td>26.92</td></tr><tr><td>PPDM-Hourglass [20]</td><td>HICO-DET</td><td>Hourglass-104</td><td>X</td><td>21.94</td><td>13.97</td><td>24.32</td><td>24.81</td><td>17.09</td><td>27.12</td></tr><tr><td>HOI-Trans [39]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>23.46</td><td>16.91</td><td>25.41</td><td>26.15</td><td>19.24</td><td>28.22</td></tr><tr><td>GG-Net [37]</td><td>HICO-DET</td><td>Hourglass-104</td><td>X</td><td>23.47</td><td>16.48</td><td>25.60</td><td>27.36</td><td>20.23</td><td>29.48</td></tr><tr><td>ATL [11]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>23.81</td><td>17.43</td><td>25.72</td><td>27.38</td><td>22.09</td><td>28.96</td></tr><tr><td>HOTR[14]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>25.10</td><td>17.34</td><td>27.42</td><td></td><td>=</td><td></td></tr><tr><td>AS-Net [3]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>28.87</td><td>24.25</td><td>30.25</td><td>31.74</td><td>27.07</td><td>33.14</td></tr><tr><td>QPIC [28]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>29.07</td><td>21.85</td><td>31.23</td><td>31.68</td><td>24.14</td><td>33.93</td></tr><tr><td>CDN-S</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>31.44</td><td>27.39</td><td>32.64</td><td>34.09</td><td>29.63</td><td>35.42</td></tr><tr><td>CDN-B</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>31.78</td><td>27.55</td><td>33.05</td><td>34.53</td><td>29.73</td><td>35.96</td></tr><tr><td>CDN-L</td><td>HICO-DET</td><td>ResNet-101</td><td>×</td><td>32.07</td><td>27.19</td><td>33.53</td><td>34.79</td><td>29.48</td><td>36.38</td></tr></table>
+
+Feature Learning. This part discusses the differences in feature learning between the conventional one-stage method, QPIC, and our CDN from a qualitative view. As shown in Figure 3, we visualized the feature maps extracted from the last layer of the decoder of QPIC, the HO-PD, and the interaction decoder in our CDN. We can see that HO-PD and QPIC attend very similar regions, e.g., the boundaries of humans and objects and the human-object contact areas, which are beneficial for locating the interactive human-object pairs. However, the interaction decoder concentrates on humanpose and the regions that contribute to understanding human actions. As for the specific case, for example, for ‘hold cake’, HO-PD in CDN attends to the boundaries of the cake while the interaction decoder in CDN concentrates on the interaction context, i.e., the human’s hands holding the cake. Thus, it shows that CDN disentangles the human-object detection and interaction classification. For ‘ride horse’, HO-PD in CDN emphasizes the overall feature of the human and the horse, and the highlight parts are the edges of the human and horse. For the interaction decoder in CDN, the highlighted part emphasizes the interaction context, i.e., the human carries the rope when riding a horse. Finally, QPIC somehow combines the two highlights, but both are not obvious.
+
+# 4.4 Comparison to State-of-the-Art
+
+We conduct experiments on HICO-Det and V-COCO benchmarks to verify the effectiveness of our proposed methods. For HICO-Det dataset as shown in Table 2, comparing to the previous state-of-theart two-stage method FCMNet [22] with ResNet-50 as backbone, our CDN-B significantly promotes mAP from 20.41 to 31.78, with a relative gain of $5 5 . 7 1 \%$ . Even compared with PD-Net [36] which adopts extra language feature and DJ-RN [16] which utilizes extra human pose features, CDN-B achieves $5 2 . 7 1 \%$ and $4 8 . 9 2 \%$ relative mAP gains, respectively. When comparing to the one-stage method AS-Net [3] and QPIC [28] which also adopt transformer-based detector architecture, CDN-B attains $1 0 . 0 8 \%$ and $9 . 3 2 \%$ point relative mAP gains, respectively. Table 3 shows the comparisons on V-COCO dataset. CDN-B achieves 62.29 $A P _ { r o l e }$ on Scenario 1 and 64.42 $A P _ { r o l e }$ on Scenario 2, which significantly outperform previous state-of-the-art method QPIC with relative $5 . 9 4 \%$ and $5 . 6 1 \%$ gains, respectively. As for efficiency analysis, CDN-S has almost the same number of parameters and flops compared to QPIC, but CDN-S achieves mAP 31.44 on HICO-Det, $8 . 1 5 \%$ higher than QPIC.
+
+Table 3: Performance comparison on the V-COCO test set. The ‘P’, ‘T’ represent the human pose information and the language feature, respectively.   
+
+<table><tr><td>Method</td><td>Extra</td><td>APST role</td><td>APS2 role</td></tr><tr><td>Two-stage Method:</td><td></td><td></td><td></td></tr><tr><td>InteractNet [7]</td><td>X</td><td>40.0</td><td></td></tr><tr><td>GPNN [24]</td><td>×</td><td>44.0</td><td></td></tr><tr><td>iCAN[6]</td><td>X</td><td>45.3</td><td>52.4</td></tr><tr><td>TIN [18]</td><td>X</td><td>47.8</td><td>54.2</td></tr><tr><td>VCL [12]</td><td>X</td><td>48.3</td><td>-</td></tr><tr><td>DRG [5]</td><td>T</td><td>51.0</td><td>=</td></tr><tr><td>IP-Net [32]</td><td>X</td><td>51.0</td><td>-</td></tr><tr><td>VSGNet [29]</td><td>X</td><td>51.8</td><td>57.0</td></tr><tr><td>PMFNet [30]</td><td>P</td><td>52.0</td><td>=</td></tr><tr><td>PD-Net [35]</td><td>T</td><td>52.6</td><td>=</td></tr><tr><td>CHGNet [31]</td><td>X</td><td>52.7</td><td>=</td></tr><tr><td>FCMNet [22]</td><td>X</td><td>53.1</td><td>=</td></tr><tr><td>ACP [15]</td><td>T</td><td>53.23</td><td>=</td></tr><tr><td>IDN[17]</td><td>X</td><td>53.3</td><td>60.3</td></tr><tr><td>One-stage Method:</td><td></td><td></td><td></td></tr><tr><td>UnionDet[13]</td><td>X</td><td>47.5</td><td>56.2</td></tr><tr><td>HOI-Trans [39]</td><td></td><td>52.9</td><td>1</td></tr><tr><td>AS-Net [3]</td><td>xx</td><td>53.9</td><td>=</td></tr><tr><td>GG-Net [37]</td><td>X</td><td>54.7</td><td>=</td></tr><tr><td>HOTR [14]</td><td>X</td><td>55.2</td><td>64.4</td></tr><tr><td>DIRV [4]</td><td>X</td><td>56.1</td><td>■</td></tr><tr><td>QPIC [28]</td><td>X</td><td>58.8</td><td>61.0</td></tr><tr><td>CDN-S</td><td>X</td><td>61.68</td><td>63.77</td></tr><tr><td>CDN-B</td><td>X</td><td>62.29</td><td>64.42</td></tr><tr><td>CDN-L</td><td>X</td><td>63.91</td><td>65.89</td></tr></table>
+
+(a) Strategies: Analysis of improvements by various training strategies.   
+
+<table><tr><td>Strategy</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>QPIC [28]</td><td>29.07</td><td>21.85</td><td>31.23</td></tr><tr><td>base</td><td>31.06</td><td>26.68</td><td>32.36</td></tr><tr><td>+ re-weighting</td><td>31.38</td><td>27.36</td><td>32.58</td></tr><tr><td>+PNMS</td><td>31.78</td><td>27.55</td><td>33.05</td></tr></table>
+
+<table><tr><td>Strategy</td><td>LQ</td><td>p</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>base</td><td>1</td><td>-</td><td>31.06</td><td>26.68</td><td>32.36</td></tr><tr><td>decouple</td><td>-</td><td>1</td><td>30.90</td><td>26.09</td><td>32.33</td></tr><tr><td>static</td><td>-</td><td>0.7</td><td>31.25</td><td>27.12</td><td>32.49</td></tr><tr><td>dynamic</td><td>2×Ns</td><td>0.8</td><td>31.33</td><td>27.45</td><td>32.49</td></tr><tr><td>dynamic</td><td>1×Ns</td><td>0.7</td><td>31.34</td><td>27.48</td><td>32.49</td></tr><tr><td>dynamic</td><td>2×Ns</td><td>0.7</td><td>31.38</td><td>27.36</td><td>32.58</td></tr></table>
+
+(b) Dynamic re-weighting: Analysis of decouple training with dynamic re-weighted losses, i.e., different queue length $L _ { Q }$ , coefficient $p$ and dynamic or static.
+
+Table 4: Ablation studies of our proposed method on the HICO-Det test set. We carry out all experiments based on the base model (CDN-B).   
+
+<table><tr><td>α</td><td>β</td><td>thres</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>=</td><td>-</td><td>1</td><td>31.38</td><td>27.36</td><td>32.58</td></tr><tr><td>1</td><td>1</td><td>0.8</td><td>31.66</td><td>27.46</td><td>32.91</td></tr><tr><td>1</td><td>1</td><td>0.7</td><td>31.75</td><td>27.50</td><td>33.03</td></tr><tr><td>1</td><td>0.7</td><td>0.7</td><td>31.77</td><td>27.54</td><td>33.03</td></tr><tr><td>1</td><td>0.5</td><td>0.8</td><td>31.75</td><td>27.51</td><td>33.02</td></tr><tr><td>1</td><td>0.5</td><td>0.7</td><td>31.78</td><td>27.55</td><td>33.05</td></tr></table>
+
+(c) PNMS: The effects of different settings of PNMS coefficients, i.e., α, $\beta$ , and thres denotes threshold.
+
+# 4.5 Ablation Study
+
+In this subsection, we analyse the effectiveness of the proposed strategies and components in detail. All experiments are eventuated on the HICO-Det dataset. The performance of each strategy is evaluated in Table 4a. The five hyper-parameters of the training loss in 7 follow QPIC [28]. The ablation study of the two hyper-parameters in the re-weighting is shown in Table 4b, and that of the three hyper-parameters in the PNMS is shown in Table 4c. We carry out all experiments based on the model CDN-B with ResNet-50 as backbone.
+
+Strategies. As shown Table 4a, our pure model without any additional post-processing operation, namely base model, achieves mAP 31.06, promoting 1.99 compared with QPIC [28]. Especially, the base model significantly promotes mAP for rare classes from 21.85 to 26.68 compared to QPIC. It indicates the superiority of the architecture of disentangling human-object detection and interaction classification. The re-weighted training further promotes mAP to 31.38, with a gain of 0.32, and the gain mainly lies in rare classes. Finally, the PNMS further improves mAP to 31.78.
+
+Dynamic re-weighting. In this part, we conduct experiments to evaluate the components in the dynamic re-weighted training strategy based on the base model as shown in Table 4b. If we only decouple training without re-weighting, the model achieves mAP 30.90, which is lower than the base model. Therefore, it shows that the performance gain does not come from a longer training process. Adding static weights $w _ { s t a t i c }$ to losses promotes mAP to 31.25. The dynamic re-weighting method improves the re-weighting effect since it captures the real-time weight of each class for each real-time sample during training. Thus it can sufficiently dig information from every single sample to achieve the best overall performance. Our method obtains best result mAP 31.38 when $L _ { Q } = 2 \times N _ { s }$ and $p =$ 0.7.
+
+PNMS. On the basis of the model after re-weighted training, we compare the variance by different parameter settings of the PNMS strategy, which is shown in Table $\cdot$ . We fix the human box balance factor $\alpha$ to 1. Then we tune the object box balance factor $\beta$ and the threshold of the $P I o U$ to filter pair-wise boxes. We achieve best performance mAP 31.78 when $\beta = 0 . 5$ and $t h r e s = 0 . 7$ . The fact that $\beta$ is smaller than $\alpha$ , indicates that the overall performance is more sensitive to human boxes compared with object boxes in our framework.
+
+# 5 Related Work
+
+Two-stage Methods. Most previous HOI detectors are with a two-stage paradigm [6, 2, 18, 5]. Firstly, a fine-tuned detector [25, 10] is applied to detect the instances. Secondly, generating the human-object pairs by matching detected human and object one by one, and then feeding them into an interaction classifier. To improve the interaction classification, some extra features were applied, such as human pose [27, 19, 9], human parts [38, 30, 16], and language features [33, 5, 22, 15]. Besides, some two-stage methods [24, 29, 31, 34, 38] applied graph neural networks to model the interactions.
+
+One-stage Methods. One-stage methods detect HOI triplets directly [20, 32, 13, 39, 3, 28, 14]. In detail, [20, 32] proposed a point-based interaction detection method which performs inference at each interaction key point. [13] proposed an anchor-based method to predict the interactions for each human-object union box. Recently, set-based detection approach has been proposed to handle HOI detection as a set prediction problem [39, 3, 28]. Specifically, [39, 28] designed a transformer encoder-decoder architecture to directly predict HOI detection results in an end-to-end manner, while [3] utilized parallel instance and interaction decoder branches to adaptively aggregate the HOI triplets.
+
+# 6 Conclusion
+
+In this paper, we explore the essential pros and cons of two-stage and one-stage HOI detection in detail. We propose a novel one-stage framework with disentangling human-object detection and interaction classification in a cascade manner. Our CDN can keep the advantage of one-stage methods, directly and accurately locating the interactive human-object pairs, and bring the benefit of two-stage methods, disentangling detection and interaction classification. Our novel paradigm has outperformed previous methods by margins. However, we only implement a specific version to mine the benefits of two-stage and one-stage methods. In the future, we plan to apply our idea with more general one-stage methods and introduce more advantages of two-stage methods into the one-stage framework.
+
+# Potential Negative Societal Impacts
+
+Similar to many other AI technologies, our proposed CDN itself is harmless. However, someone might utilize it for military purposes or apply it to any other malicious human activities detection, which might negatively impact society. Therefore, we encourage well-intentioned consideration before adopting our technique.
+
+# Acknowledgments and Disclosure of Funding
+
+This research is partly supported by National Natural Science Foundation of China (Grant 61876177), Beijing Natural Science Foundation (4202034), Fundamental Research Funds for the Central Universities, Zhejiang Lab (No. 2019KD0AB04).
+
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+[30] Bo Wan, Desen Zhou, Yongfei Liu, Rongjie Li, and Xuming He. Pose-aware multi-level feature network for human object interaction detection. In ICCV, 2019. 8, 9, 10   
+[31] Hai Wang, Wei-shi Zheng, and Ling Yingbiao. Contextual heterogeneous graph network for human-object interaction detection. In ECCV, 2020. 8, 9, 10   
+[32] Tiancai Wang, Tong Yang, Martin Danelljan, Fahad Shahbaz Khan, Xiangyu Zhang, and Jian Sun. Learning human-object interaction detection using interaction points. In CVPR, 2020. 8, 9, 10   
+[33] Bingjie Xu, Yongkang Wong, Junnan Li, Qi Zhao, and Mohan S. Kankanhalli. Learning to detect human-object interactions with knowledge. In CVPR, 2019. 10   
+[34] Dongming Yang and Yuexian Zou. A graph-based interactive reasoning for human-object interaction detection. In IJCAI, 2020. 10   
+[35] Xubin Zhong, Changxing Ding, Xian Qu, and Dacheng Tao. Polysemy deciphering network for humanobject interaction detection. In ECCV, 2020. 8, 9   
+[36] Xubin Zhong, Changxing Ding, Xian Qu, and Dacheng Tao. Polysemy deciphering network for robust human–object interaction detection. IJCV, 2021. 8   
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+[38] Penghao Zhou and Mingmin Chi. Relation parsing neural network for human-object interaction detection. In ICCV, 2019. 10   
+[39] Cheng Zou, Bohan Wang, Yue Hu, Junqi Liu, Qian Wu, Yu Zhao, Boxun Li, Chenguang Zhang, Chi Zhang, Yichen Wei, and Jian Sun. End-to-end human object interaction detection with hoi transformer. In CVPR, 2021. 2, 3, 5, 8, 9, 10

parse/train/qDrpme0FAi/qDrpme0FAi_content_list.json

@@ -0,0 +1,1168 @@
+[
+    {
+        "type": "text",
+        "text": "Mining the Benefits of Two-stage and One-stage HOI Detection ",
+        "text_level": 1,
+        "bbox": [
+            210,
+            122,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Aixi Zhang1∗ Yue Liao2\\* Si Liu2† Miao Lu1 Yongliang Wang1 Chen Gao2 Xiaobo Li1 1Alibaba Group 2Beihang University ",
+        "bbox": [
+            295,
+            219,
+            697,
+            266
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            301,
+            535,
+            318
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Two-stage methods have dominated Human-Object Interaction (HOI) detection for several years. Recently, one-stage HOI detection methods have become popular. In this paper, we aim to explore the essential pros and cons of two-stage and one-stage methods. With this as the goal, we find that conventional two-stage methods mainly suffer from positioning positive interactive human-object pairs, while one-stage methods are challenging to make an appropriate trade-off on multi-task learning, i.e., object detection, and interaction classification. Therefore, a core problem is how to take the essence and discard the dregs from the conventional two types of methods. To this end, we propose a novel one-stage framework with disentangling human-object detection and interaction classification in a cascade manner. In detail, we first design a human-object pair generator based on a state-of-the-art one-stage HOI detector by removing the interaction classification module or head and then design a relatively isolated interaction classifier to classify each human-object pair. Two cascade decoders in our proposed framework can focus on one specific task, detection or interaction classification. In terms of the specific implementation, we adopt a transformer-based HOI detector as our base model. The newly introduced disentangling paradigm outperforms existing methods by a large margin, with a significant relative mAP gain of $9 . 3 2 \\%$ on HICO-Det. The source codes are available at https://github.com/YueLiao/CDN. ",
+        "bbox": [
+            232,
+            333,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            621,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The goal of Human-Object Interaction (HOI) detection [2, 20, 6, 18, 7, 8, 17, 3] is to make a machine detailedly understand human activities from a static image. Human activities in this task are abstracted as a set of <human, object, action $\\mid >$ HOI triplets. Thus, an HOI detector is required to locate humanobject pairs and classify their corresponding action simultaneously. Based on this definition, we can summarize conventional HOI detection methods into two paradigms, i.e., two-stage methods, and one-stage methods. These two paradigms have made significant progress with the development of deep learning, but both paradigms still have their shortcomings due to their structural design. This paper aims to present a detailed analysis of methods under these two paradigms and propose a solution to mine the benefits of two-stage and one-stage methods. ",
+        "bbox": [
+            174,
+            648,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We first take a closer look at the conventional two-stage and one-stage HOI detectors. Conventional two-stage methods [6, 2, 18, 5] are mostly with a serial architecture. As shown in Figure 1 (a), two-stage methods detect humans and objects first and then feeds the human-object pairs, which are generated by matching humans and objects one by one, into an interaction classifier. The serial architecture suffers from locating the interactive human-object pairs under the interference of a large number of negative pairs only based on local region features. Otherwise, the efficiency of two-stage methods is also limited by the serial architecture. To alleviate these problems, one-stage methods [20, 13, 39, 3, 28, 14] are proposed to detect the HOI triplets directly and break HOI detection as multi-task learning, i.e., human-object detection and interaction classification, which is shown in Figure 1(b). Therefore, one-stage methods can easily focus on the interactive human-object pairs and effectively extract corresponding features in an end-to-end manner. However, it is difficult for a single model to make a good trade-off on multi-task learning since human-object detection and interaction classification are two very different tasks, which requires the model to focus on different visual features. As shown in Figure 1(c), though some previous methods [20, 3] design two parallel branches to detect instances and predict interaction respectively, the interaction classification branch still needs to regress additional offsets to associate humans and objects. Thus the interaction branch is also required to make a trade-off between interaction classification and human and object positioning. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/ac35478e213beafd7a15fa28c4e7cd0444a1562cc847359b60b9274bd73b91d5.jpg",
+        "image_caption": [
+            "Figure 1: (a) Two-stage framework, (b) one-stage end-to-end framework, (c) one-stage framework with parallel architecture, and (d) our one-stage framework with a cascade disentangling head. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            87,
+            823,
+            207
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Therefore, the intuitive idea is to take the essence and discard the dregs from the two paradigms. To attain this, we propose a novel end-to-end one-stage framework with disentangling human-object detection and interaction classification in a cascade manner, namely Cascade Disentangling Network (CDN). The original intention of our framework is to keep the advantages of conventional onestage methods, directly and accurately locating the interactive human-object pairs, and bring the advantages of two-stage methods into our one-stage framework, disentangling human-object detection and interaction classification. As shown in Figure 1(d), in our proposed framework, we design a human-object pair decoder based on the one-stage paradigm by removing the interaction classification function, namely HO-PD, and following an isolated interaction classifier. To instantiate our idea with an end-to-end manner, we design the HO-PD based on the previous state-of-the-art one-stage transformer-based HOI detector, HOI-Trans [39] and QPIC [28], where we remove the interaction classification head for each query and make it focus on human-object pairs detection. Otherwise, we design an independent HOI decoder for interaction classification to make the interaction classification unaffected by human-object detection. Therefore, there exists a core problem, i.e., how to link the human-object pair and the corresponding action class. To address this problem, we initialize the query embedding of the HOI decoder with the output of the last layer of the HO-PD. In this case, the HOI decoder is able to learn the corresponding action category under the guidance of the query embedding and free out from the human-object detection task. Moreover, we design a decoupling dynamic re-weighting manner to handle the long-tailed problems in HOI detection. ",
+        "bbox": [
+            173,
+            419,
+            826,
+            681
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions can be summarized threefold: (1) We conduct a detailed analysis of two conventional HOI detection paradigms, i.e., two-stage and one-stage. (2) We propose a novel one-stage framework with a cascade disentangling decoder to combine the advantages of two-stage and onestage methods. (3) Our method outperforms previous state-of-the-art methods by a large margin on the HOI detection task, especially achieves a $2 5 . 3 5 \\%$ performance gain on rare classes of HICO-Det. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Analysis of Two-stage and One-stage HOI detectors ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            775,
+            635,
+            794
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first introduce a unified formulation for the HOI detection problem. Given a human-centric image $\\pmb { I }$ , the model $T ( \\cdot )$ is required to predict a set of HOI triplets $\\mathbf { \\bar {  { S } } } = \\{ ( b _ { i } ^ { h } , b _ { i } ^ { o } , a _ { i } ) , i \\in \\{ 1 , 2 , \\cdot \\cdot \\cdot , K \\} \\}$ , where $b _ { i } ^ { h }$ , $b _ { i } ^ { o }$ and $a _ { i }$ denotes a human bounding-box, an object bounding-box and their corresponding action category, respectively. ",
+        "bbox": [
+            174,
+            805,
+            825,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Two-stage HOI detector. Two-stage detectors can be regarded as an instance-driven manner, detecting instances first and predicting interaction based on the detected instances. The two-stage detector divides $T ( \\cdot )$ into two stages, i.e., detection $T _ { d } ( \\cdot )$ and interaction classification $T _ { c } ( \\cdot )$ . In the first stage, we suppose that $T _ { d } ( \\cdot )$ produces $M$ human bounding-boxes and $N$ object bounding-boxes. Here the ‘object’ is a universal object which includes human as one class. Therefore, $T _ { d } ( \\cdot )$ generates $M \\times N$ human-object pairs. In general, the number of true-positive interactive human-object pairs, denoted as $K ^ { \\prime }$ , is much smaller than $M \\times N$ . However, in the second stage, $T _ { c } ( \\cdot )$ needs to scan all $M \\times N$ pairs one by one and predict an action category with its corresponding confidence score. In this case, $T _ { c } ( \\cdot )$ is required to inference $M \\times N$ times to find $K ^ { \\prime }$ interactive pairs from $M \\times N$ pairs. We argue that this manner causes three problems. Firstly, these models produce a more additional computational cost, whose time complexity is $\\mathcal { O } ( M \\times N ) \\gg \\mathcal { O } ( K ^ { \\prime } )$ . Secondly, the imbalance between positive and negative samples makes the model easily overfit to negative samples. Thus the model tends to assign a ‘no-interaction’ class for human-object pairs with very high confidence, suppressing the true-positive samples. Thirdly, the accuracy of interaction classification is influenced by the non-end-to-end pipeline. Because the interaction classification is mostly based on the region features extracted by $T _ { d } ( \\cdot )$ , while the core of $T _ { d } ( \\cdot )$ is to regress bounding-boxes and its extracted features pay more attention to the edge of regions, thereby such features are not good options for interaction classification, which needs more context. However, it is an excellent property for two-stage methods that disentangling detection and interaction classification makes each stage focus on its task and produce good results in each stage. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            90,
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+            325
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "One-stage HOI detector. As for one-stage methods, they detect all HOI triplets $S$ directly and simultaneously with an end-to-end framework. Such paradigm has greatly relieved the three problems of two-stage methods, especially for efficiency, where the time complexity is reduced to $\\mathcal { O } ( K ^ { \\prime } )$ . Most one-stage methods are interaction-driven, which directly locate the interaction point [20] or interactive human-object pairs [39], thereby reducing negative sample interference. However, coupling human-object detection and interaction classification limit their performance because it is hard to generate a unified feature representation for two very different tasks. Though the parallel one-stage methods break HOI detection into two parallel branches, their interaction branch still suffers from multi-task learning. Specifically, the optimization target of interaction branch is $\\mathcal { P } ( e _ { h } , e _ { o } , a | V )$ , where $e _ { h }$ and $e _ { o }$ are associative embeddings, e.g., offset, to match interaction with human and object respectively. Therefore, even if detection is organized as an independent branch, the interaction branch must position humans and objects for the association. The set-based detectors couple detection and interaction completely, whose optimization function is $\\mathcal { P } ( b ^ { h } , b ^ { o } , a | V )$ . ",
+        "bbox": [
+            174,
+            332,
+            825,
+            512
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Next, we introduce a simple one-stage framework with disentangling human-object detection and interaction classification, namely CDN, to mine the benefits of two-stage and one-stage HOI detectors. Our CDN disentangles the original set-based one-stage optimization function into two cascade decoders. Firstly, we predict human-object pair by ${ \\mathcal { P } } ( b ^ { h } , \\dot { b } ^ { o } | V )$ . Secondly, we apply an isolated decoder to predict the action category by $\\mathcal { P } ( a | V , b ^ { h } , b ^ { o } )$ . More details are in the following. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Method ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            603,
+            271,
+            619
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will present a detailed introduction to the pipeline of our proposed CDN. In section 3.1, we present an overview of our framework and briefly introduce the pipeline. In section 3.2, we introduce the visual feature extractor. The cascade disentangling HOI decoder is introduced in section 3.3. Section 3.4 introduces a novel dynamic re-weighting mechanism that mitigates the long-tailed problem. The detailed training process and post-processing are discussed in section 3.5. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Overview ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            715,
+            279,
+            729
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The architecture of our proposed CDN is illustrated in Figure 2. Our CDN is organized in a cascade manner with a visual feature extractor. Given an image, we first follow transformer-based detection methods [1, 39] to apply a CNN followed by a transformer encoder architecture to extract visual features into a sequence. Then we detect HOI triplets in two cascade decoders. Firstly, we apply the Human-Object Pair Decoder (HO-PD) to predict a set of human-object bounding-boxes pairs based on a set of learnable queries. Next, taking the output of the last layer of HO-PD as queries, an isolated interaction decoder is utilized to predict the action category for each query. Finally, the HOI triplets are formed by the output of the above two cascade decoders. ",
+        "bbox": [
+            174,
+            736,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 Visual Feature Extractor ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            861,
+            387,
+            876
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We define the visual feature extractor by combining a CNN and a transformer encoder. Fed with an input image $\\pmb { I }$ with shape $( H , W , C )$ , the CNN generates a feature map of shape $( H ^ { ' } , W ^ { ' } , D _ { b } )$ ",
+        "bbox": [
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+            881,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/19c437351374d41e649928a72a1f04db513b4e3046280a5c9c3b2ded7a27550e.jpg",
+        "image_caption": [
+            "Figure 2: The framework of our CDN. It is comprised of three components:Visual Feature Extractor, Human-Object Pair Decoder (HO-PD) and Interaction Decoder. We first apply a CNN-transformer combined architecture to extract sequenced visual features $X _ { s }$ . Then, we divide HOI detection into two cascade transformer-based decoders. Firstly, we regress the human-object bounding-box pairs based on $X _ { s }$ and a set of random-initialized queries $Q _ { d }$ by HO-PD. The interactive score is from a binary classification to determine whether the human-object pair is an interactive pair or not. Secondly, we predict one or many action categories for each predicted human-object pairs, where we take the output of HO-PD $\\pmb { Q } _ { d } ^ { o u t }$ to initialize the interaction queries $Q _ { c }$ and aggregate information with $X _ { s }$ . Finally, the HOI triplets are formed by the output of the cascade decoders. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            88,
+            821,
+            261
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Then, $D _ { b }$ is reduced to $D _ { c }$ by a projection convolution layer with a kernel size $1 \\times 1$ . Next, a flatten operator is used to generating the flatten feature $\\mathbf { \\boldsymbol { X } } _ { v } \\in \\mathcal { R } ^ { ( \\boldsymbol { H } ^ { \\prime } \\times \\boldsymbol { W } ^ { \\prime } ) \\times \\boldsymbol { D _ { c } } }$ by collapsing the spatial dimensions into one dimension. This flatten feature is then fed into a transformer encoder and the position encoding $E _ { p o s } \\in \\mathcal { R } ^ { ( H ^ { ' } \\times W ^ { ' } ) \\times D _ { c } }$ , which distinguishes the relative position in the sequence $\\boldsymbol { X } _ { s } \\in \\mathcal { R } ^ { ( H ^ { ' } \\times W ^ { ' } ) \\times D _ { c } }$ . Thanks to the multi-head self-attention mechanism, the transformer encoder produces a feature map with richer contextual information by summarizing global information. The output of the encoder is denoted as global memory with a dimension of $D _ { c }$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 Cascade Disentangling HOI Decoder ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            536,
+            467,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The cascade disentangling HOI decoder consists of two decoders: Human-Object Pair Decoder (HOPD) and interaction decoder. Both decoders share the same architecture, a transformer-based decoder, with independent weights. In this subsection, we first introduce the general architecture of the decoder and then elaborate on the two decoders in detail, respectively. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Transformer-based decoder. We follow the transformer-based object detector DETR [1] to design the basic architecture in our cascade disentangling HOI decoder. We apply $N$ transformer decoder layers for each decoder and equip each decoder layer with several FFN heads for intermediate supervision. Specifically, each decoder layer is comprised of a self-attention module and a multi-head co-attention module. During feed-forward, fed into a set of learnable queries $Q \\in \\mathcal { R } ^ { N _ { q } \\times C _ { q } }$ , each decoder layer first applies a self-attention module on all queries and then conducts a multi-head co-attention operation between queries and the sequenced visual features, and outputs a set of updated queries. For the FFN heads, each head is comprised of one or several MLP branches, and each branch is for a specific task, e.g., regression, or classification. All queries share the same FFN heads. Therefore, each decoder can be simply represented as: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1efe60a220ed232afcd20f07a092bcf883e96f13711a0a7d027ccbc9f163cadf.jpg",
+        "text": "$$\nP = f ( Q , X _ { s } , E _ { p o s } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            423,
+            763,
+            573,
+            781
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Besides, the number of queries $N _ { q }$ is determined by the number of positive samples of an image. ",
+        "bbox": [
+            171,
+            792,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "HO-PD. Firstly, we design the HO-PD to predict a set of human-object pairs from the sequenced visual features. To this end, we first randomly initialize a set of learnable queries $Q _ { d } \\in \\mathcal { R } ^ { N _ { d } ^ { \\bullet } \\times C _ { q } }$ as HO queries. Then we apply a transformer-based decoder, which takes HO queries $Q _ { d }$ and sequenced visual features as input and applies three FFN heads for each query to predict human bounding-box, object bounding-box, and object class, which form a human-object pair. We also utilize an additional interactive score head to simply determine whether the human-object pair is an interactive pair or not by a binary classification. In this case, $_ { r }$ is instantiated as $P _ { h o }$ , which is consist of a set of human-object pairs $\\{ ( b _ { i } ^ { h } , b _ { i } ^ { o } ) , i \\in \\{ 1 , 2 , \\cdot \\cdot \\cdot , N _ { d } \\} \\}$ . Thus, HO-PD can be denoted as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3daec2ea432925b8d0d52bd951e1c0d9294eabae9d596671248eaac28628d8fa.jpg",
+        "text": "$$\nP _ { h o } = f _ { d } ( Q _ { d } , X _ { s } , E _ { p o s } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            410,
+            113,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In addition, we keep the output queries of the last layer of HO-PD as $\\pmb { Q } _ { d } ^ { o u t }$ for the following step. ",
+        "bbox": [
+            176,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Interaction Decoder. Secondly, we propose the interaction decoder to classify the human-object queries and assign one or several action categories for each human-object query. To classify each human-object query one-to-one, we initialize $Q _ { c }$ with the output of HO-PD $\\dot { \\pmb { Q } } _ { d } ^ { o u t }$ . In this way, $\\pmb { Q } _ { d } ^ { o u t }$ can provide prior knowledge to guide $Q _ { c }$ to learn the corresponding action categories for each human-object query. The other components and inputs are the same as HO-PD, which conducts self-attention among queries and co-attention with $X _ { s }$ and $E _ { p o s }$ . The final output is a set of action categories $P _ { c l s } : \\{ \\bar { a _ { i } } , \\bar { i } \\in \\{ 1 , 2 , \\cdots , N _ { d } \\} \\}$ . Therefore, this process can be formulated as: ",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "equation",
+        "img_path": "images/c1c13c2e5eac2869c5dd1c1142aafccda07bc2166f4f2f74a3faa28af5089da1.jpg",
+        "text": "$$\nP _ { c l s } = f _ { c l s } ( Q _ { d } ^ { o u t } , X _ { s } , E _ { p o s } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In our proposed cascade disentangling HOI decoder, the task of HOI detection is disentangled into two relatively independent steps: human-object pairs detection and interaction classification. Therefore, each step can aggregate more related features to concentrate on its corresponding task. ",
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+    {
+        "type": "text",
+        "text": "3.4 Decoupling Dynamic Re-weighting ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The HOI datasets usually have long-tail class distribution for both object class and action class. To alleviate the long-tail problem, we design a dynamic re-weighting mechanism for further improvements with a decoupling training strategy. In detail, we first train the whole model with regular losses. Then, we freeze the parameters of the visual feature extractor and only train the cascade disentangling decoders with a relatively small learning rate and the designed dynamic re-weighted losses. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During decoupling training, at each iteration, we apply two similar queues to accumulate number of each object class or action class. The queues are used as memory banks to accumulate training samples and truncate the accumulation with length $L _ { Q }$ as sliding windows. In detail, $Q _ { o }$ with length $L _ { Q } ^ { o }$ to accumulate object number $N _ { i } ^ { o }$ for each object class $i \\in \\{ 1 , 2 , \\cdots , C _ { o } \\}$ , and $Q _ { a }$ with length $L _ { Q } ^ { a }$ to accumulate interaction number $N _ { i } ^ { a }$ for each action category $i \\in \\{ 1 , 2 , \\cdots , C _ { a } \\}$ . The dynamic re-weighting coefficients $w _ { d y n a m i c }$ are presented as follow: ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/27764b2119b17535752979b3e1c3fa857adb66fc4ef2cfe501636e8ac4c5a7d7.jpg",
+        "text": "$$\nw _ { i } ^ { a } \\big | _ { i \\in \\{ 1 , 2 , \\cdots , C _ { a } \\} } = \\bigg ( \\frac { \\sum _ { i = 1 } ^ { C _ { a } } N _ { i } } { N _ { i } } \\bigg ) ^ { p _ { a } } , \\quad w _ { b g } ^ { a } = \\bigg ( \\frac { \\sum _ { i = 1 } ^ { C _ { a } } N _ { i } } { N _ { b g } ^ { a } } \\bigg ) ^ { p _ { a } } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "img_path": "images/dc6f227a23a472214d9eb4f102e48a3b537c976a2b5e873ee0a6b17927798706.jpg",
+        "text": "$$\nw _ { i } ^ { o } \\big | _ { i \\in \\{ 1 , 2 , \\cdots , C _ { o } \\} } = \\bigg ( \\frac { \\sum _ { i = 1 } ^ { C _ { o } } N _ { i } } { N _ { i } } \\bigg ) ^ { p _ { o } } , \\quad w _ { b g } ^ { o } = \\bigg ( \\frac { \\sum _ { i = 1 } ^ { C _ { o } } N _ { i } } { N _ { b g } ^ { o } } \\bigg ) ^ { p _ { o } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            593,
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+            633
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $N _ { i }$ is the number of accumulated positive samples of category $i$ by the queues $Q _ { o }$ and $Q _ { a }$ , $N _ { b g }$ is the number of accumulated background samples, $C$ is the number of categories, and exponent $p$ is a hyper-parameter that adapts the magnitude of mitigation. Specifically, the weight of background class, $w _ { b g }$ , is designed to balance the positives and negatives. For the stability of the dynamic re-weighted training, the weight coefficients are initialized as $w _ { s t a t i c }$ with those calculated by 4 and 5 using the static number of object and action categories. The final dynamic weights are given as $w = \\gamma w _ { s t a t i c } + ( 1 - \\gamma ) w _ { d y n a m i c }$ , where $\\gamma$ is a smooth factor, given as $m i n ( 0 . \\bar { 9 9 9 } ^ { L _ { Q } } , 0 . \\bar { 9 } )$ . The factor $\\gamma$ transits $w$ from $w _ { s t a t i c }$ to wdynamic with the increasing of $L _ { Q }$ . Finally, the weights are used to the classification losses in a traditional way by multiplying each coefficient to each class and then calculating the summation. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.5 Training and Post-processing ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we introduce the training and inference processes in detail. Especially, we will introduce a novel Pair-wise Non-Maximal Suppression (PNMS) strategy in the inference process. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Training. Following the set-based training process of HOI-Trans [39] and QPIC [28], we first match each ground-truth with its best-matching prediction by the bipartite matching with the Hungarian algorithm. Then the loss is produced between the matched predictions and the corresponding ground truths for the final back-propagation. During matching, we consider the predictions of two cascade decoders together. The loss of CDN follows QPIC which is composed by five parts: the box regression loss $L _ { b }$ , the intersection-over-union loss $L _ { G I o U }$ [26], the interactive score loss $L _ { p }$ , the object class loss $L _ { c } ^ { o }$ , and the action category loss $L _ { c } ^ { a }$ . The target loss is the weighted sum of these parts as: ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/5f1f8be0530fe571a079dc5a41dea804947f213b310ec7b7fd25db36ecf728f4.jpg",
+        "text": "$$\nL = \\sum _ { k \\in ( h , o ) } \\bigl ( \\lambda _ { b } L _ { b } ^ { k } + \\lambda _ { G I o U } L _ { G I o U } ^ { k } \\bigr ) + \\lambda _ { p } L _ { p } + \\lambda _ { o } L _ { c } ^ { o } + \\lambda _ { a } L _ { c } ^ { a } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            294,
+            125,
+            702,
+            161
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda _ { b } , \\lambda _ { G I o U } , \\lambda _ { p } , \\lambda _ { o }$ and $\\lambda _ { a }$ are the hyper-parameters for adjusting the weights of each loss. ",
+        "bbox": [
+            168,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inference. The inference process is to composite the output of instance-related FFNs and the interaction-related FFN to form HOI triplets. By our cascade disentangling decoder architecture, the instance queries and the interaction queries are one-to-one corresponding, therefore, the five components <human bounding box, object bounding box, object class, interactive score, action class> can be homologous in each of the $N _ { d }$ dimensions per FFN head. Formally, we generate the $i$ -th output prediction as $< b _ { i } ^ { h }$ , $b _ { i } ^ { o }$ , argmax $k ^ { c _ { i } ^ { h o i } ( k ) > }$ . The HOI triplet score $c _ { i } ^ { h o i }$ is given by $c _ { i } ^ { h o i } = c _ { i } ^ { a } c _ { i } ^ { o } c _ { i } ^ { p }$ where $c _ { i } ^ { a }$ and $c _ { i } ^ { o }$ are the scores of interaction and object classification, respectively, and $c _ { i } ^ { p }$ is the interactive score from the interactive FFN head for the query vector being an human-object pair. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "PNMS. After sorting $c _ { i } ^ { h o i }$ in descending order and generating the top $K$ HOI triplets, we design a pair-wise non-maximal suppression (PNMS) method to further filter out human-object pairs from pair-wise bounding boxes overlapping perspective. For two HOI triplets $m$ and $n$ , the pair-wise overlap $P I o U$ is calculated as: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/85125336592a642d8b4c840c1e2db4266e492506056ee4d2f84394c64e68a4a4.jpg",
+        "text": "$$\nP I o U ( m , n ) = \\Big ( \\frac { I ( b _ { m } ^ { h } , b _ { n } ^ { h } ) } { U ( b _ { m } ^ { h } , b _ { n } ^ { h } ) } \\Big ) ^ { \\alpha } \\Big ( \\frac { I ( b _ { m } ^ { o } , b _ { n } ^ { o } ) } { U ( b _ { m } ^ { o } , b _ { n } ^ { o } ) } \\Big ) ^ { \\beta } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            364,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where the operators $I$ and $U$ compute the intersection and union areas between the two boxes of $m$ and $n$ , respectively. $\\alpha$ and $\\beta$ are the balancing parameters between humans and objects. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct comprehensive experiments to demonstrate the superiority of our designed CDN. In section 4.1, we briefly introduce the experimental benchmarks. Section 4.2 presents implementation details. Next, It is a detailed experimental comparison and analysis of two-stage and one-stage methods in section 4.3. In section 4.4, we compare our methods with the previous state-of-the-art methods. The ablation studies and components analysis are included in 4.5. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Datasets and Evaluation Metrics ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets. We carry out experiments on two widely-used HOI detection benchmarks: HICO-Det [2] and V-COCO [8]. We follow the standard evaluation scheme. HICO-Det consists of 47, 776 Creative Common images from Flickr (38, 118 for training and 9, 658 for test) with more than 150K humanobject pairs. It contains the same 80 object categories as MS-COCO [21] and 117 action categories. The objects and actions form 600 classes of HOI triplets. V-COCO is derived from MS-COCO dataset, which consists of 5, 400 images in the trainval subset and 4, 946 images in the test subset. It has 29 action categories (25 HOIs and 4 body motions) and 80 object categories. For both datasets, one person can interact with multiple objects in different ways at the same time. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Evaluation Metrics. Following the standard evaluation [2], we use the mean average precision (mAP) as the evaluation metric. For one positively predicted HOI triplet <human, object, action>, it needs to contain accurate human and object locations (box IoU with reference to GT box is greater than 0.5) and correct object and action categories. Specifically, for HICO-Det, besides the full set of $6 0 0 \\mathrm { H O I }$ classes, we also report the mAP over a rare set of 138 HOI classes that have less than 10 training instances and a non-rare set of the other 462 HOI classes. For V-COCO, we report the role mAP for two scenarios: scenario 1 includes the cases even without any objects (for the four action categories of body motions), and scenario 2 ignores these cases. ",
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+    {
+        "type": "text",
+        "text": "4.2 Implementation Details ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We implement three variant architectures of CDN: CDN-S, CDN-B, and CDN-L, where ‘S’, ‘B’, and ‘L’ denote small, base, and large, respectively. For CDN-S and CDN-B, we adopt ResNet-50 with a 6-layer transformer encoder as the visual feature extractor. For the cascade decoders, CDN-S is equipped with both 3-layer transformers, while CDN-B has a 6-layer transformer for each decoder. CDN-L only replaces the ResNet-50 with ResNet-101 in CDN-B. The reduced dimension size $D _ { c }$ is set to 256. The number of queries $N _ { d }$ is set to 64 for HICO-Det and 100 for V-COCO since the average number of positives for variant human-object pairs per image of HICO-Det is smaller than V-COCO. The human and object box FFNs have 3 linear layers with ReLU, while the object and action category FFNs have one linear layer. The code is provided in supplemental material. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "During training, we initialize the network with the parameters of DETR [1] trained with the MSCOCO dataset. We set the weight coefficients $\\lambda _ { b }$ , $\\lambda _ { G I o U }$ , $\\lambda _ { p }$ , $\\lambda _ { o }$ and $\\lambda _ { a }$ to 2.5, 1, 1, 1 and 1, respectively, which are exactly same with QPIC [28]. We optimize the network by AdamW [23] with the weight decay $1 0 ^ { - 4 }$ . We first train the whole model for 90 epochs with a learning rate of $1 0 ^ { - 4 }$ decreased by 10 times at the 60th epoch. Then, during the decoupling training process, we fine-tune the cascade disentangling decoders together with the box, object, and action FFNs for 10 epochs with a learning rate of $1 0 ^ { = 5 }$ . We use both object and action dynamic re-weighting for HICO-Det and only action dynamic re-weighting for V-COCO. The re-weighting parameter $p$ is set to 0.7 for both object and action. The length $L _ { Q }$ of training sample queue $Q$ for both object and action is set to $2 \\times N _ { s }$ , where $N _ { s }$ is the sample number of the training set. All experiments are conducted on the 8 Tesla V100 GPUs and CUDA10.2, with a batch size of 16. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For validation, we select 100 detection results with the highest scores and then adopt PNMS to further filter results. The threshold, $\\alpha$ , and $\\beta$ of PNMS are set to 0.7, 1, and 0.5, respectively. ",
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+    {
+        "type": "text",
+        "text": "4.3 Experiment Analysis of Two-stage and One-stage Methods ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this part, we introduce a detailed experimental analysis of conventional two-stage and one-stage methods and our proposed CDN from the following three aspects. ",
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+    {
+        "type": "text",
+        "text": "Human-object Pair Generation. We first explore the quality of the human-object pairs generation between two-stage and one-stage methods. To attain this, we conduct a detailed experiment based on a representative two-stage method iCAN [6]. We first implement a PyTorch version iCAN as the baseline model, denoted as $\\mathrm { i } { \\mathrm { C A N } } ^ { * }$ , which only applies human and object appearance with a COCO-pretrained Faster-RCNN detector [25]. For a fair comparison, we first fine-tune DETR on HICO-Det for 100 epochs only with the instance detection annotation based on COCO-pretrained weights. Then we combine the detected human and object bounding-boxes, whose confidences are greater than a threshold, one by one to generate human-object pairs denoted as $\\mathrm { i } { \\mathrm { C A N } } ^ { \\dagger }$ in Table 1. We train our CDN only with HO-PD for 100 epochs and get the human-object pairs from the output directly. Then, we graft the human-object pairs to the baseline model to extract box features and utilize the same interaction classifier in the second stage of $\\mathrm { i } { \\mathrm { C A N } } ^ { * }$ . In this way, we degrade the number of pairs from $M \\times N$ to $K ^ { \\prime }$ , which means time complexity is reduced from $\\mathcal { O } ( M \\times N )$ to $\\mathcal { O } ( K ^ { \\prime } )$ . Primarily, HO-PD significantly promotes mAP from 15.37 to 24.05, as shown in Table 1. This indicates that one-stage methods are much superior in human-object pair generation. ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/6cc4b82545748d56f15eb47ee546117b45d53fbe407710013dece42049188140.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Strategy</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>iCAN*</td><td>14.16</td><td>12.26</td><td>14.73</td></tr><tr><td>iCAN t</td><td>15.37</td><td>13.23</td><td>16.01</td></tr><tr><td>HO-PD+iCAN*</td><td>24.05</td><td>18.32</td><td>25.76</td></tr><tr><td>QPIC [28]</td><td>29.07</td><td>21.85</td><td>31.23</td></tr><tr><td>CDN-S base</td><td>30.96</td><td>27.02</td><td>32.14</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Analysis of Two-stage and Onestage Methods. ∗ denotes our implemented PyTorch version iCAN [6] baseline model. † denotes replacing instance detection boxes given by a HICO-Det fine-tuned DETR detector to extract box features. ‘HO$\\mathrm { P D + i C A N ^ { * } }$ ’ denotes replacing original oneby-one generated human-object pairs with our HO-PD generated. ‘CDN-S base’ denotes CDN-S w/o re-weighting and PNMS strategies. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/606fe2d92b8b9bfee5d048534bea82d09e67a83b86212cf8ea8f31e0b33bef19.jpg",
+        "image_caption": [
+            "Figure 3: Visualization of Feature Maps for Queries. Visual attended features for query with top-1 score extracted from the last layer of the decoder of (a) QPIC, (b) HO-PD in CDN, and (c) interaction decoder in CDN. Zoom in for details. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Interaction Classification. We aim to study the interaction classification between conventional multi-task one-stage methods and our disentangled one-stage detector. We can regard QPIC [28] as a multi-task version of our CDN. Table 1 shows that our ‘CDN-S base’ (w/o re-weighting and PNMS strategies) has achieved mAP 30.96 with $6 . 5 0 \\%$ relative mAP gain compared to QPIC. Especially, our ‘CDN-S base’ significantly outperforms QPIC for rare classes with a $\\mathrm { { \\bar { 2 3 . 6 6 \\% } } }$ improvement. The performance of rare classes can partly reflect the accuracy of interaction classification. ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/148915c9bfaaf9b9e9723c5b8747a127d9fcea4d0004923aba7e06c699d551d6.jpg",
+        "table_caption": [
+            "Table 2: Performance comparison on the HICO-Det test set. The ‘P’, ‘T’ represent human pose information and the language feature, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Detector</td><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">Extra</td><td colspan=\"3\">Default</td><td rowspan=\"2\"></td><td colspan=\"2\">Know Object</td></tr><tr><td>Full</td><td>Rare</td><td>Non-Rare Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>Two-stageMethod:</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>InteractNet [7]</td><td>COCO</td><td>ResNet-50-FPN</td><td>X</td><td>9.94</td><td>7.16</td><td>10.77</td><td></td><td></td><td>=</td></tr><tr><td>GPNN [24]</td><td>CoCO</td><td>Res-DCN-152</td><td>X</td><td>13.11</td><td>9.34</td><td>14.23</td><td></td><td></td><td></td></tr><tr><td>iCAN [6]</td><td>CoCO</td><td>ResNet-50</td><td>X</td><td>14.84</td><td>10.45</td><td>16.15</td><td>16.26</td><td>11.33</td><td>17.73</td></tr><tr><td>No-Frills [9]</td><td>CoCo</td><td>ResNet-152</td><td>P</td><td>17.18</td><td>12.17</td><td>18.68</td><td>=</td><td>=</td><td>=</td></tr><tr><td>PMFNet [30]</td><td>COCO</td><td>ResNet-50-FPN</td><td>P</td><td>17.46</td><td>15.65</td><td>18.00</td><td>20.34</td><td>17.47</td><td>21.20</td></tr><tr><td>CHGNet [31]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>17.57</td><td>16.85</td><td>17.78</td><td>21.00</td><td>20.74</td><td>21.08</td></tr><tr><td>DRG [5]</td><td>CoCO</td><td>ResNet-50-FPN</td><td>T</td><td>19.26</td><td>17.74</td><td>19.71</td><td>23.40</td><td>21.75</td><td>23.89</td></tr><tr><td>VCL[12]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>19.43</td><td>16.55</td><td>20.29</td><td>22.00</td><td>19.09</td><td>22.87</td></tr><tr><td>IP-Net [32]</td><td>CoCO</td><td>Hourglass-104</td><td>X</td><td>19.56</td><td>12.79</td><td>21.58</td><td>22.05</td><td>15.77</td><td>23.92</td></tr><tr><td>VSGNet [29]</td><td>CoCO</td><td>ResNet-152</td><td>X</td><td>19.80</td><td>16.05</td><td>20.91</td><td>=</td><td>=</td><td>=</td></tr><tr><td>FCMNet [22]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>20.41</td><td>17.34</td><td>21.56</td><td>22.04</td><td>18.97</td><td>23.12</td></tr><tr><td>ACP[15]</td><td>CoCO</td><td>ResNet-152</td><td>T</td><td>20.59</td><td>15.92</td><td>21.98</td><td></td><td></td><td></td></tr><tr><td>PD-Net [35]</td><td>COCO</td><td>ResNet-152-FPN</td><td>T</td><td>20.81</td><td>15.90</td><td>22.28</td><td>24.78</td><td>18.88</td><td>26.54</td></tr><tr><td>DJ-RN[16]</td><td>COCO</td><td>ResNet-50</td><td>P</td><td>21.34</td><td>18.53</td><td>22.18</td><td>23.69</td><td>20.64</td><td>24.60</td></tr><tr><td>IDN[17]</td><td>COCO</td><td>ResNet-50</td><td>X</td><td>23.36</td><td>22.47</td><td>23.63</td><td>26.43</td><td>25.01</td><td>26.85</td></tr><tr><td>One-stage Method:</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>UnionDet[13]</td><td>CoCO</td><td>ResNet-50-FPN</td><td>X</td><td>17.58</td><td>11.72</td><td>19.33</td><td>19.76</td><td>14.68</td><td>21.27</td></tr><tr><td>DIRV [4]</td><td>COCo</td><td>EfficientDet-d3</td><td>X</td><td>21.78</td><td>16.38</td><td>23.39</td><td>25.52</td><td>20.84</td><td>26.92</td></tr><tr><td>PPDM-Hourglass [20]</td><td>HICO-DET</td><td>Hourglass-104</td><td>X</td><td>21.94</td><td>13.97</td><td>24.32</td><td>24.81</td><td>17.09</td><td>27.12</td></tr><tr><td>HOI-Trans [39]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>23.46</td><td>16.91</td><td>25.41</td><td>26.15</td><td>19.24</td><td>28.22</td></tr><tr><td>GG-Net [37]</td><td>HICO-DET</td><td>Hourglass-104</td><td>X</td><td>23.47</td><td>16.48</td><td>25.60</td><td>27.36</td><td>20.23</td><td>29.48</td></tr><tr><td>ATL [11]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>23.81</td><td>17.43</td><td>25.72</td><td>27.38</td><td>22.09</td><td>28.96</td></tr><tr><td>HOTR[14]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>25.10</td><td>17.34</td><td>27.42</td><td></td><td>=</td><td></td></tr><tr><td>AS-Net [3]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>28.87</td><td>24.25</td><td>30.25</td><td>31.74</td><td>27.07</td><td>33.14</td></tr><tr><td>QPIC [28]</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>29.07</td><td>21.85</td><td>31.23</td><td>31.68</td><td>24.14</td><td>33.93</td></tr><tr><td>CDN-S</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>31.44</td><td>27.39</td><td>32.64</td><td>34.09</td><td>29.63</td><td>35.42</td></tr><tr><td>CDN-B</td><td>HICO-DET</td><td>ResNet-50</td><td>X</td><td>31.78</td><td>27.55</td><td>33.05</td><td>34.53</td><td>29.73</td><td>35.96</td></tr><tr><td>CDN-L</td><td>HICO-DET</td><td>ResNet-101</td><td>×</td><td>32.07</td><td>27.19</td><td>33.53</td><td>34.79</td><td>29.48</td><td>36.38</td></tr></table>",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "Feature Learning. This part discusses the differences in feature learning between the conventional one-stage method, QPIC, and our CDN from a qualitative view. As shown in Figure 3, we visualized the feature maps extracted from the last layer of the decoder of QPIC, the HO-PD, and the interaction decoder in our CDN. We can see that HO-PD and QPIC attend very similar regions, e.g., the boundaries of humans and objects and the human-object contact areas, which are beneficial for locating the interactive human-object pairs. However, the interaction decoder concentrates on humanpose and the regions that contribute to understanding human actions. As for the specific case, for example, for ‘hold cake’, HO-PD in CDN attends to the boundaries of the cake while the interaction decoder in CDN concentrates on the interaction context, i.e., the human’s hands holding the cake. Thus, it shows that CDN disentangles the human-object detection and interaction classification. For ‘ride horse’, HO-PD in CDN emphasizes the overall feature of the human and the horse, and the highlight parts are the edges of the human and horse. For the interaction decoder in CDN, the highlighted part emphasizes the interaction context, i.e., the human carries the rope when riding a horse. Finally, QPIC somehow combines the two highlights, but both are not obvious. ",
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+    {
+        "type": "text",
+        "text": "4.4 Comparison to State-of-the-Art ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We conduct experiments on HICO-Det and V-COCO benchmarks to verify the effectiveness of our proposed methods. For HICO-Det dataset as shown in Table 2, comparing to the previous state-of-theart two-stage method FCMNet [22] with ResNet-50 as backbone, our CDN-B significantly promotes mAP from 20.41 to 31.78, with a relative gain of $5 5 . 7 1 \\%$ . Even compared with PD-Net [36] which adopts extra language feature and DJ-RN [16] which utilizes extra human pose features, CDN-B achieves $5 2 . 7 1 \\%$ and $4 8 . 9 2 \\%$ relative mAP gains, respectively. When comparing to the one-stage method AS-Net [3] and QPIC [28] which also adopt transformer-based detector architecture, CDN-B attains $1 0 . 0 8 \\%$ and $9 . 3 2 \\%$ point relative mAP gains, respectively. Table 3 shows the comparisons on V-COCO dataset. CDN-B achieves 62.29 $A P _ { r o l e }$ on Scenario 1 and 64.42 $A P _ { r o l e }$ on Scenario 2, which significantly outperform previous state-of-the-art method QPIC with relative $5 . 9 4 \\%$ and $5 . 6 1 \\%$ gains, respectively. As for efficiency analysis, CDN-S has almost the same number of parameters and flops compared to QPIC, but CDN-S achieves mAP 31.44 on HICO-Det, $8 . 1 5 \\%$ higher than QPIC. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5f664d4816b43461e406b6f02ed43a86a298f950db99a05e512748ab53f5892a.jpg",
+        "table_caption": [
+            "Table 3: Performance comparison on the V-COCO test set. The ‘P’, ‘T’ represent the human pose information and the language feature, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Extra</td><td>APST role</td><td>APS2 role</td></tr><tr><td>Two-stage Method:</td><td></td><td></td><td></td></tr><tr><td>InteractNet [7]</td><td>X</td><td>40.0</td><td></td></tr><tr><td>GPNN [24]</td><td>×</td><td>44.0</td><td></td></tr><tr><td>iCAN[6]</td><td>X</td><td>45.3</td><td>52.4</td></tr><tr><td>TIN [18]</td><td>X</td><td>47.8</td><td>54.2</td></tr><tr><td>VCL [12]</td><td>X</td><td>48.3</td><td>-</td></tr><tr><td>DRG [5]</td><td>T</td><td>51.0</td><td>=</td></tr><tr><td>IP-Net [32]</td><td>X</td><td>51.0</td><td>-</td></tr><tr><td>VSGNet [29]</td><td>X</td><td>51.8</td><td>57.0</td></tr><tr><td>PMFNet [30]</td><td>P</td><td>52.0</td><td>=</td></tr><tr><td>PD-Net [35]</td><td>T</td><td>52.6</td><td>=</td></tr><tr><td>CHGNet [31]</td><td>X</td><td>52.7</td><td>=</td></tr><tr><td>FCMNet [22]</td><td>X</td><td>53.1</td><td>=</td></tr><tr><td>ACP [15]</td><td>T</td><td>53.23</td><td>=</td></tr><tr><td>IDN[17]</td><td>X</td><td>53.3</td><td>60.3</td></tr><tr><td>One-stage Method:</td><td></td><td></td><td></td></tr><tr><td>UnionDet[13]</td><td>X</td><td>47.5</td><td>56.2</td></tr><tr><td>HOI-Trans [39]</td><td></td><td>52.9</td><td>1</td></tr><tr><td>AS-Net [3]</td><td>xx</td><td>53.9</td><td>=</td></tr><tr><td>GG-Net [37]</td><td>X</td><td>54.7</td><td>=</td></tr><tr><td>HOTR [14]</td><td>X</td><td>55.2</td><td>64.4</td></tr><tr><td>DIRV [4]</td><td>X</td><td>56.1</td><td>■</td></tr><tr><td>QPIC [28]</td><td>X</td><td>58.8</td><td>61.0</td></tr><tr><td>CDN-S</td><td>X</td><td>61.68</td><td>63.77</td></tr><tr><td>CDN-B</td><td>X</td><td>62.29</td><td>64.42</td></tr><tr><td>CDN-L</td><td>X</td><td>63.91</td><td>65.89</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e3390817e3a2985110172a7941bc88ffdd5d894853cd9a33ed956d09b49809cf.jpg",
+        "table_caption": [
+            "(a) Strategies: Analysis of improvements by various training strategies. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Strategy</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>QPIC [28]</td><td>29.07</td><td>21.85</td><td>31.23</td></tr><tr><td>base</td><td>31.06</td><td>26.68</td><td>32.36</td></tr><tr><td>+ re-weighting</td><td>31.38</td><td>27.36</td><td>32.58</td></tr><tr><td>+PNMS</td><td>31.78</td><td>27.55</td><td>33.05</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5ac63a6377873afdd2ffeb7340f679eb5743c83424a9438082b0ff1a26520b29.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "(b) Dynamic re-weighting: Analysis of decouple training with dynamic re-weighted losses, i.e., different queue length $L _ { Q }$ , coefficient $p$ and dynamic or static. "
+        ],
+        "table_body": "<table><tr><td>Strategy</td><td>LQ</td><td>p</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>base</td><td>1</td><td>-</td><td>31.06</td><td>26.68</td><td>32.36</td></tr><tr><td>decouple</td><td>-</td><td>1</td><td>30.90</td><td>26.09</td><td>32.33</td></tr><tr><td>static</td><td>-</td><td>0.7</td><td>31.25</td><td>27.12</td><td>32.49</td></tr><tr><td>dynamic</td><td>2×Ns</td><td>0.8</td><td>31.33</td><td>27.45</td><td>32.49</td></tr><tr><td>dynamic</td><td>1×Ns</td><td>0.7</td><td>31.34</td><td>27.48</td><td>32.49</td></tr><tr><td>dynamic</td><td>2×Ns</td><td>0.7</td><td>31.38</td><td>27.36</td><td>32.58</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/39759f0c3630b5c3bbe51acb46d73bff34000e53afc162e6e4caba8f19b61741.jpg",
+        "table_caption": [
+            "Table 4: Ablation studies of our proposed method on the HICO-Det test set. We carry out all experiments based on the base model (CDN-B). "
+        ],
+        "table_footnote": [
+            "(c) PNMS: The effects of different settings of PNMS coefficients, i.e., α, $\\beta$ , and thres denotes threshold. "
+        ],
+        "table_body": "<table><tr><td>α</td><td>β</td><td>thres</td><td>Full</td><td>Rare</td><td>Non-Rare</td></tr><tr><td>=</td><td>-</td><td>1</td><td>31.38</td><td>27.36</td><td>32.58</td></tr><tr><td>1</td><td>1</td><td>0.8</td><td>31.66</td><td>27.46</td><td>32.91</td></tr><tr><td>1</td><td>1</td><td>0.7</td><td>31.75</td><td>27.50</td><td>33.03</td></tr><tr><td>1</td><td>0.7</td><td>0.7</td><td>31.77</td><td>27.54</td><td>33.03</td></tr><tr><td>1</td><td>0.5</td><td>0.8</td><td>31.75</td><td>27.51</td><td>33.02</td></tr><tr><td>1</td><td>0.5</td><td>0.7</td><td>31.78</td><td>27.55</td><td>33.05</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "4.5 Ablation Study ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this subsection, we analyse the effectiveness of the proposed strategies and components in detail. All experiments are eventuated on the HICO-Det dataset. The performance of each strategy is evaluated in Table 4a. The five hyper-parameters of the training loss in 7 follow QPIC [28]. The ablation study of the two hyper-parameters in the re-weighting is shown in Table 4b, and that of the three hyper-parameters in the PNMS is shown in Table 4c. We carry out all experiments based on the model CDN-B with ResNet-50 as backbone. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Strategies. As shown Table 4a, our pure model without any additional post-processing operation, namely base model, achieves mAP 31.06, promoting 1.99 compared with QPIC [28]. Especially, the base model significantly promotes mAP for rare classes from 21.85 to 26.68 compared to QPIC. It indicates the superiority of the architecture of disentangling human-object detection and interaction classification. The re-weighted training further promotes mAP to 31.38, with a gain of 0.32, and the gain mainly lies in rare classes. Finally, the PNMS further improves mAP to 31.78. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Dynamic re-weighting. In this part, we conduct experiments to evaluate the components in the dynamic re-weighted training strategy based on the base model as shown in Table 4b. If we only decouple training without re-weighting, the model achieves mAP 30.90, which is lower than the base model. Therefore, it shows that the performance gain does not come from a longer training process. Adding static weights $w _ { s t a t i c }$ to losses promotes mAP to 31.25. The dynamic re-weighting method improves the re-weighting effect since it captures the real-time weight of each class for each real-time sample during training. Thus it can sufficiently dig information from every single sample to achieve the best overall performance. Our method obtains best result mAP 31.38 when $L _ { Q } = 2 \\times N _ { s }$ and $p =$ 0.7. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "PNMS. On the basis of the model after re-weighted training, we compare the variance by different parameter settings of the PNMS strategy, which is shown in Table $\\cdot$ . We fix the human box balance factor $\\alpha$ to 1. Then we tune the object box balance factor $\\beta$ and the threshold of the $P I o U$ to filter pair-wise boxes. We achieve best performance mAP 31.78 when $\\beta = 0 . 5$ and $t h r e s = 0 . 7$ . The fact that $\\beta$ is smaller than $\\alpha$ , indicates that the overall performance is more sensitive to human boxes compared with object boxes in our framework. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            166,
+            321,
+            183
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Two-stage Methods. Most previous HOI detectors are with a two-stage paradigm [6, 2, 18, 5]. Firstly, a fine-tuned detector [25, 10] is applied to detect the instances. Secondly, generating the human-object pairs by matching detected human and object one by one, and then feeding them into an interaction classifier. To improve the interaction classification, some extra features were applied, such as human pose [27, 19, 9], human parts [38, 30, 16], and language features [33, 5, 22, 15]. Besides, some two-stage methods [24, 29, 31, 34, 38] applied graph neural networks to model the interactions. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "One-stage Methods. One-stage methods detect HOI triplets directly [20, 32, 13, 39, 3, 28, 14]. In detail, [20, 32] proposed a point-based interaction detection method which performs inference at each interaction key point. [13] proposed an anchor-based method to predict the interactions for each human-object union box. Recently, set-based detection approach has been proposed to handle HOI detection as a set prediction problem [39, 3, 28]. Specifically, [39, 28] designed a transformer encoder-decoder architecture to directly predict HOI detection results in an end-to-end manner, while [3] utilized parallel instance and interaction decoder branches to adaptively aggregate the HOI triplets. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we explore the essential pros and cons of two-stage and one-stage HOI detection in detail. We propose a novel one-stage framework with disentangling human-object detection and interaction classification in a cascade manner. Our CDN can keep the advantage of one-stage methods, directly and accurately locating the interactive human-object pairs, and bring the benefit of two-stage methods, disentangling detection and interaction classification. Our novel paradigm has outperformed previous methods by margins. However, we only implement a specific version to mine the benefits of two-stage and one-stage methods. In the future, we plan to apply our idea with more general one-stage methods and introduce more advantages of two-stage methods into the one-stage framework. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Potential Negative Societal Impacts ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Similar to many other AI technologies, our proposed CDN itself is harmless. However, someone might utilize it for military purposes or apply it to any other malicious human activities detection, which might negatively impact society. Therefore, we encourage well-intentioned consideration before adopting our technique. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
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+        "text": "This research is partly supported by National Natural Science Foundation of China (Grant 61876177), Beijing Natural Science Foundation (4202034), Fundamental Research Funds for the Central Universities, Zhejiang Lab (No. 2019KD0AB04). ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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Uniondet: Union-level detector towards real-time human-object interaction detection. In ECCV, 2020. 2, 8, 9, 10   \n[14] Bumsoo Kim, Junhyun Lee, Jaewoo Kang, Eun-Sol Kim, and Hyunwoo J. Kim. Hotr: End-to-end human-object interaction detection with transformers. In CVPR, 2021. 2, 8, 9, 10   \n[15] Dong-Jin Kim, Xiao Sun, Jinsoo Choi, Stephen Lin, and In So Kweon. Detecting human-object interactions with action co-occurrence priors. In ECCV, 2020. 8, 9, 10   \n[16] Yong-Lu Li, Xinpeng Liu, Han Lu, Shiyi Wang, Junqi Liu, Jiefeng Li, and Cewu Lu. Detailed 2d-3d joint representation for human-object interaction. In CVPR, 2020. 8, 10   \n[17] Yong-Lu Li, Xinpeng Liu, Xiaoqian Wu, Yizhuo Li, and Cewu Lu. Hoi analysis: Integrating and decomposing human-object interaction. Advances in Neural Information Processing Systems, 33, 2020. 1, 8, 9   \n[18] Yong-Lu Li, Siyuan Zhou, Xijie Huang, Liang Xu, Ze Ma, Hao-Shu Fang, Yan-Feng Wang, and Cewu Lu. 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Vsgnet: Spatial attention network for detecting human object interactions using graph convolutions. In CVPR, 2020. 8, 9, 10   \n[30] Bo Wan, Desen Zhou, Yongfei Liu, Rongjie Li, and Xuming He. Pose-aware multi-level feature network for human object interaction detection. In ICCV, 2019. 8, 9, 10   \n[31] Hai Wang, Wei-shi Zheng, and Ling Yingbiao. Contextual heterogeneous graph network for human-object interaction detection. In ECCV, 2020. 8, 9, 10   \n[32] Tiancai Wang, Tong Yang, Martin Danelljan, Fahad Shahbaz Khan, Xiangyu Zhang, and Jian Sun. Learning human-object interaction detection using interaction points. In CVPR, 2020. 8, 9, 10   \n[33] Bingjie Xu, Yongkang Wong, Junnan Li, Qi Zhao, and Mohan S. Kankanhalli. Learning to detect human-object interactions with knowledge. In CVPR, 2019. 10   \n[34] Dongming Yang and Yuexian Zou. A graph-based interactive reasoning for human-object interaction detection. In IJCAI, 2020. 10   \n[35] Xubin Zhong, Changxing Ding, Xian Qu, and Dacheng Tao. Polysemy deciphering network for humanobject interaction detection. In ECCV, 2020. 8, 9   \n[36] Xubin Zhong, Changxing Ding, Xian Qu, and Dacheng Tao. Polysemy deciphering network for robust human–object interaction detection. IJCV, 2021. 8   \n[37] Xubin Zhong, Xian Qu, Changxing Ding, and Dacheng Tao. Glance and gaze: Inferring action-aware points for one-stage human-object interaction detection. In CVPR, 2021. 8, 9   \n[38] Penghao Zhou and Mingmin Chi. Relation parsing neural network for human-object interaction detection. In ICCV, 2019. 10   \n[39] Cheng Zou, Bohan Wang, Yue Hu, Junqi Liu, Qian Wu, Yu Zhao, Boxun Li, Chenguang Zhang, Chi Zhang, Yichen Wei, and Jian Sun. End-to-end human object interaction detection with hoi transformer. In CVPR, 2021. 2, 3, 5, 8, 9, 10 ",
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parse/train/rylwJxrYDS/rylwJxrYDS.md

@@ -0,0 +1,278 @@
+# VQ-WAV2VEC: SELF-SUPERVISED LEARNING OF DISCRETE SPEECH REPRESENTATIONS
+
+Alexei Baevski∗4 Steffen Schneider∗5† Michael Auli4 4 Facebook AI Research, Menlo Park, CA, USA $\bigtriangledown$ University of Tubingen, Germany ¨
+
+# ABSTRACT
+
+We propose vq-wav2vec to learn discrete representations of audio segments through a wav2vec-style self-supervised context prediction task. The algorithm uses either a Gumbel-Softmax or online $\mathbf { k }$ -means clustering to quantize the dense representations. Discretization enables the direct application of algorithms from the NLP community which require discrete inputs. Experiments show that BERT pre-training achieves a new state of the art on TIMIT phoneme classification and WSJ speech recognition.1
+
+# 1 INTRODUCTION
+
+Learning discrete representations of speech has gathered much recent interest (Versteegh et al., 2016; Dunbar et al., 2019). A popular approach to discover discrete units is via autoencoding (Tjandra et al., 2019; Eloff et al., 2019; Chorowski et al., 2019) sometimes coupled with an autoregressive model (Chung et al., 2019). Another line of research is to learn continuous speech representations in a self-supervised way via predicting context information (Chung & Glass, 2018; van den Oord et al., 2018; Schneider et al., 2019).
+
+In this paper, we combine these two lines of research by learning discrete representations of speech via a context prediction task instead of reconstructing the input. This enables us to directly apply well performing NLP algorithms to speech data (Figure 1a).
+
+![](images/86edb3a37578dfa8b9f0740a1d208509f0b19ccd6f8ec50c3ef988eb4c858f82.jpg)  
+Figure 1: (a) The vq-wav2vec encoder maps raw audio $( \mathcal { X } )$ to a dense representation $( { \mathcal { Z } } )$ which is quantized (q) to $\hat { \mathcal { Z } }$ and aggregated into context representations $( \mathcal { C } )$ ; training requires future time step prediction. (b) Acoustic models are trained by quantizing the raw audio with vq-wav2vec, then applying BERT to the discretized sequence and feeding the resulting representations into the acoustic model to output transcriptions.
+
+Our new discretization algorithm, vq-wav2vec, learns discrete representations of fixed length segments of audio signal by utilizing the wav2vec loss and architecture (Schneider et al, 2019; $\ S 2$ ). To choose the discrete variables, we consider a Gumbel-Softmax approach (Jang et al., 2016) as well as online k-means clustering, similar to VQ-VAE (Oord et al., 2017; Eloff et al., 2019; §3).
+
+We then train a Deep Bidirectional Transformer (BERT; Devlin et al., 2018; Liu et al., 2019) on the discretized unlabeled speech data and input these representations to a standard acoustic model (Figure 1b; $\ S 4 _ { , }$ ). Our experiments show that BERT representations perform better than log-mel filterbank inputs as well as dense wav2vec representations on both TIMIT and WSJ benchmarks. Discretization of audio enables the direct application of a whole host of algorithms from the NLP literature to speech data. For example, we show that a standard sequence to sequence model from the NLP literature can be used to perform speech recognition over discrete audio tokens (§5, §6).
+
+# 2 BACKGROUND
+
+# 2.1 WAV2VEC
+
+wav2vec (Schneider et al., 2019) learns representations of audio data by solving a self-supervised context-prediction task with the same loss function as word2vec (Mikolov et al., 2013; van den Oord et al., 2018). The model is based on two convolutional neural networks where the the encoder produces a representation $\mathbf { z } _ { i }$ for each time step $i$ at a rate of $1 0 0 ~ \mathrm { H z }$ and the aggregator combines multiple encoder time steps into a new representation $\mathbf { c } _ { i }$ for each time step $i$ . Given an aggregated representation $\mathbf { c } _ { i }$ , the model is trained to distinguish a sample $\mathbf { z } _ { i + k }$ that is $k$ steps in the future from distractor samples $\tilde { \mathbf { z } }$ drawn from a distribution $p _ { n }$ , by minimizing the contrastive loss for steps $k = 1 , \ldots , K$ :
+
+$$
+\mathcal { L } _ { k } ^ { \mathrm { w a v 2 v e c } } = - \sum _ { i = 1 } ^ { T - k } \Big ( \log \sigma ( \mathbf { z } _ { i + k } ^ { \top } h _ { k } ( \mathbf { c } _ { i } ) ) + \underset { \ b { \tilde { \mathbf { z } } } \sim p _ { n } } { \mathbb { E } } [ \log \sigma ( - \tilde { \mathbf { z } } ^ { \top } h _ { k } ( \mathbf { c } _ { i } ) ) ] \Big )
+$$
+
+where $T$ is the sequence length, $\sigma ( x ) ~ = ~ 1 / ( 1 + \exp ( - x ) )$ , and where $\sigma ( \mathbf { z } _ { i + k } ^ { \top } h _ { k } ( \mathbf { c } _ { i } ) )$ is the probability of $\mathbf { z } _ { i + k }$ being the true sample. We consider a step-specific affine transformation $h _ { k } ( \mathbf { c } _ { i } ) \ : = \ : W _ { k } \mathbf { c } _ { i } + \mathbf { b } _ { k }$ that is applied to $\mathbf { c } _ { i }$ (van den Oord et al., 2018). We optimize the loss $\begin{array} { r } { \mathcal { L } = \sum _ { k = 1 } ^ { K } \mathcal { L } _ { k } } \end{array}$ , summing (1) over different step sizes. After training, the representations produced by the context network $\mathbf { c } _ { i }$ are input to the acoustic model instead of log-mel filterbank features.
+
+# 2.2 BERT
+
+BERT (Devlin et al., 2018) is a pre-training approach for NLP tasks, which uses a transformer encoder model to build a representation of text. Transformers uses self-attention to encode the input sequence as well as an optional source sequence (Vaswani et al., 2017). The original BERT model combined two tasks for training: first, masked language modeling randomly removes some of the input tokens and the model has to predict those missing tokens. Second, next sentence prediction splices two different text passages together into a single example and the model needs to predict whether the passages are from the same document.
+
+# 3 VQ-WAV2VEC
+
+Our approach, vq-wav2vec, learns vector quantized (VQ) representations of audio data using a future time-step prediction task. We follow the same architectual choices as wav2vec $( \ S 2 . 1 )$ with two convolutional networks $f : \mathcal X \mapsto \mathcal Z$ and $g : \hat { \mathcal { Z } } \mapsto \mathcal { C }$ for feature extraction and aggregation, as well as a new quantization module $q : \mathcal { Z } \mapsto \hat { \mathcal { Z } }$ to build discrete representations (Figure 1a).
+
+We first map $3 0 \mathrm { m s }$ segments of raw speech to a dense feature representation $\mathbf { z }$ at a stride of $1 0 \mathrm { m s }$ using the encoder network $f$ . Next, the quantizer $( q )$ turns these dense representations into discrete indices which are mapped to a reconstruction $\hat { \mathbf { z } }$ of the original representation $\mathbf { z }$ . We feed $\hat { \mathbf { z } }$ into the aggregator $g$ and optimize the same context prediction task as wav2vec outlined in $\ S 2 . 1$ .
+
+The quantization module replaces the original representation $\mathbf { z }$ by $\hat { \mathbf { z } } = \mathbf { e } _ { i }$ from a fixed size codebook $\mathbf { e } \in { \dot { \mathbb { R } } } ^ { V \times d }$ which contains $V$ representations of size $d$ . We consider the Gumbel-Softmax which is a differentiable approximation of the argmax for computing one-hot representations $\ 8 3 . 1$ ; Figure 2a)
+
+![](images/b84b2048219dbcb8e1923e6a38273d68fd55cd2e07be0807a17f530a48662446.jpg)  
+Figure 2: (a) The Gumbel-Softmax quantization computes logits representing the codebook vectors (e). In the forward pass the argmax codeword $\left( \mathbf { e } _ { 2 } \right)$ is chosen and for backward (not shown) the exact probabilities are used. (b) K-means vector quantization computes the distance to all codeword vector and chooses the closest (argmin).
+
+as well as online $\mathbf { k }$ -means clustering, similar to the vector quantized variational autoencoder (VQVAE; Oord et al., 2017; $\ S 3 . 2$ ; Figure 2b). Finally, we perform multiple vector quantizations over different parts of $\mathbf { z }$ to mitigate mode collapse (§3.3).
+
+# 3.1 GUMBEL-SOFTMAX
+
+The Gumbel-Softmax (Gumbel, 1954; Jang et al., 2016; Maddison et al., 2014) enables selecting discrete codebook variables in a fully differentiable way and we use the straight-through estimator of Jang et al. (2016). Given the dense representation $\mathbf { z }$ , we apply a linear layer, followed by a ReLU and another linear which outputs $1 \in \mathbb { R } ^ { V }$ logits for the Gumbel-Softmax. At inference, we simply pick the largest index in $l$ . At training, the output probabilities for choosing the $j$ -th variable are
+
+$$
+p _ { j } = \frac { \exp ( l _ { j } + v _ { j } ) / \tau } { \sum _ { k = 1 } ^ { V } \exp ( l _ { k } + v _ { k } ) / \tau } ,
+$$
+
+where $v = - \log ( - \log ( u ) )$ and $u$ are uniform samples from $\mathcal { U } ( 0 , 1 )$ . During the forward pass, $i = \mathrm { a r g m a x } _ { j } p _ { j }$ and in the backward pass, the true gradient of the Gumbel-Softmax outputs is used.
+
+# 3.2 K-MEANS
+
+The vector quantization approach of van den Oord et al. (2017) is an alternative to making the index selection procedure fully differentiable. Different to their setup, we optimize a future time step prediction loss instead of the reconstruction loss of an autoencoder.
+
+We choose the codebook variable representation by finding the closest variable to the input features $\mathbf { z }$ in terms of the Euclidean distance, yielding $i = \mathrm { a r g m i n } _ { j } \| \mathbf { z } - \mathbf { e } _ { j } \| _ { 2 } ^ { 2 }$ . During the forward pass, we select $\hat { \mathbf { z } } = \mathbf { e } _ { i }$ by choosing the corresponding variable from the codebook. We obtain gradients for the encoder network by back-propagating $\mathrm { d } \bar { \mathcal { L } } ^ { \mathrm { w a v 2 v e c } } / \mathrm { d } \hat { \mathbf { z } }$ (van den Oord et al., 2017). The final loss has two additional terms:
+
+$$
+\mathcal { L } = \sum _ { k = 1 } ^ { K } \mathcal { L } _ { k } ^ { \mathrm { w a v 2 v e c } } + \Big ( \| \mathbf { s g } ( \mathbf { z } ) - \hat { \mathbf { z } } \| ^ { 2 } + \gamma \| \mathbf { z } - \mathbf { s g } ( \hat { \mathbf { z } } ) \| ^ { 2 } \Big ) ,
+$$
+
+where $\operatorname { s g } ( x ) \equiv x$ , $\begin{array} { r } { \frac { \mathrm { d } } { \mathrm { d } x } \mathbf { s } \mathbf { g } ( x ) \equiv 0 } \end{array}$ is the stop gradient operator and $\gamma$ is a hyperparameter. The first term is the future prediction task and gradients do not change the codebook because of the straightthrough gradient estimation of mapping $\mathbf { z }$ to $\hat { \mathbf { z } }$ . The second term $\| \mathbf { s g } ( \mathbf { z } ) - \hat { \mathbf { z } } \| ^ { 2 }$ moves the codebook vectors closer to the encoder output, and the third term $\| \mathbf { z } - \mathrm { s g } ( \hat { \mathbf { z } } ) \| ^ { 2 }$ makes sure that the encoder outputs are close to a centroid (codeword).
+
+# 3.3 VECTOR QUANTIZATION WITH MULTIPLE VARIABLE GROUPS
+
+So far, we considered replacing the encoder feature vector $\mathbf { z }$ by a single entry $\mathbf { e } _ { i }$ in the codebook. This is prone to mode collapse where only some of the codewords are actually used. Previously, this problem has been mitigated by workarounds such as re-initializing codewords or applying additional regularizers to the loss function (Caron et al., 2019). In the following, we describe another strategy where we independently quantize partitions of $\mathbf { z }$ , similar to product quantization (Jegou et al., 2011). This results in larger dictionaries and increased downstream performance (Appendix A).
+
+The dense feature vector $\textbf { z } \in \mathbb { R } ^ { d }$ is first organized into multiple groups $G$ into the matrix form $\mathbf { z } ^ { \prime } \in \mathbb { R } ^ { G \times ( d / G ) }$ . We then represent each row by an integer index, and hence can represent the full feature vector by the indices $\mathbf { \hat { i } } \in [ V ] ^ { G }$ , where $V$ again denotes the possible number of variables for this particular group and each element $\mathbf { i } _ { j }$ corresponds to a fixed codebook vector. For each of the $G$ groups, we apply either one of the two VQ approaches $\ S 3 . 1$ and $\ S 3 . 2 )$ .
+
+The codebook itself can be initialized in two possible ways: Codebook variables can be shared across groups, i.e., a particular index in group $j$ would reference the same vector as the same index in group $j ^ { \prime }$ . This yields a codebook $\mathbf { e } \in \mathbb { R } ^ { V \times ( d / G ) }$ . In contrast, not sharing the codebook variables yields a codebook of size $\mathbf { e } \in \mathbb { R } ^ { V \times G \times ( d / G ) }$ . In practise, we observe that sharing the codebook variables generally yields competitive results to a non-shared representation.
+
+# 4 BERT PRE-TRAINING ON QUANTIZED SPEECH
+
+Once we trained a vq-wav2vec model we can discretize audio data and make it applicable to algorithms that require discrete inputs. One possibility is to use the discretized training data and apply BERT pre-training where the task is to predict masked input tokens based on an encoding of the surrounding context (Devlin et al., 2018). Once the BERT model is trained, we can use it to build representations and feed them into an acoustic model to improve speech recognition. We follow recent advances in BERT training which only use the masked input token prediction (Liu et al., 2019).
+
+Since each of the discretized tokens represents around $1 0 \mathrm { m s }$ of audio it is likely too easy to predict a single masked input token. We therefore change BERT training by masking spans of consecutive discretized speech tokens, similar to Joshi et al. (2019). To mask the input sequence, we randomly sample $p = 0 . 0 5$ of all tokens to be a starting index, without replacement, and mask $M = 1 0$ consecutive tokens from every sampled index; spans may overlap. This makes the masked token prediction harder and we show later that it improves accuracy over masking individual tokens $( \ S 6 . 5 )$ .
+
+# 5 EXPERIMENTAL SETUP
+
+# 5.1 DATASETS
+
+We generally pre-train vq-wav2vec and BERT on the full 960h of Librispeech (Panayotov et al., 2015) and after vq-wav2vec training it is discretized to 345M tokens. Where indicated we perform ablations on a clean 100h subset which is discretized to 39.9M tokens. We evaluate models on two benchmarks: TIMIT (Garofolo et al., 1993b) is a 5h dataset with phoneme labels and Wall Street Journal (WSJ; Garofolo et al. 1993a) is a 81h dataset for speech recognition. For TIMIT, we apply the standard evaluation protocol and consider 39 different phonemes. For WSJ, we train acoustic models directly on 31 graphemes, including the English alphabet, the apostrophe, the silence token and tokens for repeating characters.
+
+# 5.2 VQ-WAV2VEC
+
+We adapt the fairseq implementation of wav2vec (Schneider et al., 2019; Ott et al., 2019) and use vqwav2vec/wav2vec models with $3 4 \times 1 0 ^ { 6 }$ parameters. The encoder has 8 layers with 512 channels each, kernel sizes (10,8,4,4,4,1,1,1) and strides (5,4,2,2,2,1,1,1), yielding a total stride of 160. Each layer contains a convolution, followed by dropout, group normalization with a single group (Wu & He, 2018) and a ReLU non-linearity. The aggregator is composed of 12 layers, with 512 channels, stride 1, and kernel sizes starting at 2 and increasing by 1 for every subsequent layer. The block structure is the same as for the encoder network, except we introduce skip connections between each subsequent block.
+
+We train with the wav2vec context prediction loss (Equation 1) for $4 0 0 \mathrm { k }$ updates, predicting $K = 8$ steps into the future and sample 10 negatives from the same audio example. Training is warmed up for 500 steps where the learning rate is increased from $1 \times 1 0 ^ { - 7 }$ to $5 \times 1 0 ^ { - 3 }$ , and then annealed to $1 \times 1 0 ^ { - 6 }$ using a cosine schedule (Loshchilov & Hutter, 2016). The batch size is 10, and we crop a random section of $1 5 0 \mathrm { k }$ frames for each example (approximately 9.3 seconds for 16kHz sampling rate). All models are trained on 8 GPUs.
+
+For ablations and experiments on the 100h Librispeech subset, we use a smaller model with kernels (10,8,4,4,4) and strides (5,4,2,2,2) in the encoder and seven convolutional layers with stride one and kernel size three in the aggregator. This model is trained for $4 0 \mathrm { k }$ updates.
+
+Gumbel-Softmax Models. We use $G = 2$ groups and $V = 3 2 0$ latents per group and the linear layer projects the features produced by the encoder into $G \cdot V = 6 4 0$ logits. The Gumbel-Softmax produces a one-hot vector for each group $G$ . The temperature $\tau$ is linearly annealed from 2 to 0.5 over the first $70 \%$ of updates and then kept constant at 0.5. This enables the model to learn which latents work best for each input before committing to a single latent. After training this model on 960h of Librispeech and quantizing the training dataset, we are left with $1 3 . 5 \mathrm { k }$ unique codewords combinations (out of $V ^ { G } = 1 0 2 \mathrm { k \Omega }$ possible codewords).
+
+$\mathbf { k }$ -means Models. We use $G = 2$ groups and $V = 3 2 0$ variables per group. vq-wav2vec on full Librispeech yields $2 3 \mathrm { k }$ unique codewords. Following van den Oord et al. (2017), we found $\gamma = 0 . 2 5$ to be a robust choice for balancing the VQ auxiliary loss.
+
+# 5.3 BERT
+
+BERT base models have 12 layers, model dimension 768, inner dimension (FFN) 3072 and 12 attention heads (Devlin et al., 2018). The learning rate is warmed up over the first 10,000 updates to a peak value of $1 \times 1 0 ^ { - 5 }$ , and then linearly decayed over a total of $2 5 0 \mathrm { k }$ updates. We train on 128 GPUs with a batch size of 3072 tokens per GPU giving a total batch size of $3 9 3 \mathrm { k }$ tokens (Ott et al., 2018). Each token represents $1 0 \mathrm { m s }$ of audio data.
+
+BERT small. For ablations we use a smaller setup with model dimension 512, FFN size 2048, 8 attention heads and dropout 0.05. Models are trained for 250k updates with a batch size of 2 examples per GPU.
+
+# 5.4 ACOUSTIC MODEL
+
+We use wav2letter as accoustic model (Collobert et al., 2016; 2019) and train for 1,000 epochs on 8 GPUs for both TIMIT and WSJ using the auto segmentation criterion. For decoding the emissions from the acoustic model on WSJ we use a lexicon as well as a separate language model trained on the WSJ language modeling data only. We consider a 4-gram KenLM language model (Heafield et al., 2013) and a character based convolutional language model (Likhomanenko et al., 2019) and tune the models with the same protocol as Schneider et al. (2019).
+
+# 6 RESULTS
+
+# 6.1 WSJ SPEECH RECOGNITION
+
+We first evaluate on the WSJ speech recognition benchmark. We train a vq-wav2vec model on the unlabeled version of Librispeech, then discretize the same data with the resulting model to estimate a BERT model. Finally, we train a wav2letter acoustic model on WSJ by inputting either the BERT or vq-wav2vec representations instead of log-mel filterbanks.2
+
+We compare to various results from the literature, including wav2vec (Schneider et al., 2019) and we consider three setups: performance without any language model (No LM), with an n-gram LM (4-gram LM) and with a character convolutional LM (Char ConvLM). We report the accuracy of wav2letter with log-mel filterbanks as input (Baseline) and wav2vec. For vq-wav2vec we first experiment with the Gumbel-Softmax, with and without a BERT base model (§5.3).
+
+Table 1: WSJ accuracy of vq-wav2vec on the development (nov93dev) and test set (nov92) in terms of letter error rate (LER) and word error rate (WER) without language modeling (No LM), a 4-gram LM and a character convolutional LM. vq-wav2vec with BERT pre-training improves over the best wav2vec model (Schneider et al., 2019).   
+
+<table><tr><td rowspan="2"></td><td colspan="2">nov93dev</td><td colspan="2">nov92</td></tr><tr><td>LER</td><td>WER</td><td>LER</td><td>WER</td></tr><tr><td>Deep Speech 2 (12K h labeled speech; Amodei et al., 2016)</td><td>1</td><td>4.42</td><td>1</td><td>3.1</td></tr><tr><td>Trainable frontend (Zeghidour et al., 2018)</td><td></td><td>6.8</td><td>=</td><td>3.5</td></tr><tr><td>Lattice-free MMI (Hadian et al., 2018)</td><td></td><td>5.66t</td><td></td><td>2.8†</td></tr><tr><td>Supervised transfer-learning (Ghahremani et al., 2017)</td><td></td><td>4.99t</td><td>1</td><td>2.53†</td></tr><tr><td>No LM</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>6.28</td><td>19.46</td><td>4.14</td><td>13.93</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>5.07</td><td>16.24</td><td>3.26</td><td>11.20</td></tr><tr><td>vq-wav2vec Gumbel</td><td>7.04</td><td>20.44</td><td>4.51</td><td>14.67</td></tr><tr><td>+BERT base</td><td>4.13</td><td>13.40</td><td>2.62</td><td>9.39</td></tr><tr><td>4-GRAM LM (Heafield et al., 2013)</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>3.32</td><td>8.57</td><td>2.19</td><td>5.64</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.73</td><td>6.96</td><td>1.57</td><td>4.32</td></tr><tr><td>vq-wav2vec Gumbel</td><td>3.93</td><td>9.55</td><td>2.40</td><td>6.10</td></tr><tr><td>+ BERT base</td><td>2.41</td><td>6.28</td><td>1.26</td><td>3.62</td></tr><tr><td>CHAR CoNvLM (Likhomanenko et al., 2019)</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>2.77</td><td>6.67</td><td>1.53</td><td>3.46</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.11</td><td>5.10</td><td>0.99</td><td>2.43</td></tr><tr><td>vq-wav2vec Gumbel + BERT base</td><td>1.79</td><td>4.46</td><td>0.93</td><td>2.34</td></tr></table>
+
+Table 2: Comparison of Gumbel-Softmax and k-means vector quantization on WSJ (cf. Table 1).   
+
+<table><tr><td></td><td colspan="2">nov93dev</td><td colspan="2">nov92</td></tr><tr><td></td><td>LER</td><td>WER</td><td>LER</td><td>WER</td></tr><tr><td>No LM</td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>5.07</td><td>16.24</td><td>3.26</td><td>11.20</td></tr><tr><td>vq-wav2vec Gumbel</td><td>7.04</td><td>20.44</td><td>4.51</td><td>14.67</td></tr><tr><td>+ BERT small</td><td>4.52</td><td>14.14</td><td>2.81</td><td>9.69</td></tr><tr><td>vq-wav2vec k-means (39M codewords)</td><td>5.41</td><td>17.11</td><td>3.63</td><td>12.17</td></tr><tr><td>vq-wav2vec k-means</td><td>7.33</td><td>21.64</td><td>4.72</td><td>15.17</td></tr><tr><td>+ BERT small</td><td>4.31</td><td>13.87</td><td>2.70</td><td>9.62</td></tr><tr><td>4-GRAM LM (Heafield et al., 2013)</td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.73</td><td>6.96</td><td>1.57</td><td>4.32</td></tr><tr><td>vq-wav2vec Gumbel</td><td>3.93</td><td>9.55</td><td>2.40</td><td>6.10</td></tr><tr><td>+ BERT small</td><td>2.67</td><td>6.67</td><td>1.46</td><td>4.09</td></tr><tr><td>vq-wav2vec k-means (39M codewords)</td><td>3.05</td><td>7.74</td><td>1.71</td><td>4.82</td></tr><tr><td>vq-wav2vec k-means</td><td>4.37</td><td>10.26</td><td>2.28</td><td>5.71</td></tr><tr><td>+ BERT small</td><td>2.60</td><td>6.62</td><td>1.45</td><td>4.08</td></tr></table>
+
+Table 1 shows that vq-wav2vec together with BERT training can achieve a new state of the art of 2.34 WER on nov92. Gains are largest when no language model is used which is the fastest setting. vq-wav2vec with Gumbel-Softmax uses only $1 3 . 5 \mathrm { k }$ distinct codewords to represent the audio signal and this limited set of codewords is not sufficient to outperform the baseline. However, it does enable training BERT models which require a relatively small vocabulary.
+
+Table 3: TIMIT phoneme recognition in terms of phoneme error rate (PER). All our models use the CNN-8L-PReLU-do0.7 architecture (Zeghidour et al., 2018).   
+
+<table><tr><td></td><td>dev PER</td><td>test PER</td></tr><tr><td>CNN + TD-filterbanks (Zeghidour et al., 2018)</td><td>15.6</td><td>18.0</td></tr><tr><td>Li-GRU + fMLLR (Ravanelli et al.,2018)</td><td>1</td><td>14.9</td></tr><tr><td>wav2vec (Schneider et al.,2019)</td><td>12.9</td><td>14.7</td></tr><tr><td>Baseline (log-mel)</td><td>16.9</td><td>17.6</td></tr><tr><td>vq-wav2vec, Gumbel</td><td>15.34</td><td>17.78</td></tr><tr><td>+ BERT small</td><td>9.64</td><td>11.64</td></tr><tr><td>vq-wav2vec, k-means</td><td>15.65</td><td>18.73</td></tr><tr><td>+ BERT small</td><td>9.80</td><td>11.40</td></tr></table>
+
+Table 4: Librispeech results for a standard sequence to sequence model trained on discretized audio without BERT pre-training and results from the literature. All results are without a language model.   
+
+<table><tr><td></td><td>dev clean</td><td>dev other</td><td> test clean</td><td> test other</td></tr><tr><td>Mohamed et al. (2019)</td><td>4.8</td><td>12.7</td><td>4.7</td><td>12.9</td></tr><tr><td>Irie et al. (2019)</td><td>4.4</td><td>13.2</td><td>4.7</td><td>13.4</td></tr><tr><td>Park et al. (2019)</td><td>2.8</td><td>6.8</td><td>2.5</td><td>5.8</td></tr><tr><td>vq-wav2vec Gumbel + Transformer Big</td><td>5.6</td><td>15.5</td><td>6.2</td><td>18.2</td></tr></table>
+
+Next, we compare Gumbel-Softmax to $\mathbf { k }$ -means for vector quantization. For this experiment we use the faster to train BERT small configuration (§5.3). We also train a vq-wav2vec $\mathbf { k }$ -means model with a very large number of codewords (39.9M) to test whether a more expressive model can close the gap to wav2vec. Table 2 shows that Gumbel-Softmax and $\mathbf { k }$ -means clustering perform relatively comparably: in the no language model setup without BERT, Gumbel-Softmax is more accurate than k-means but these differences disappear with BERT. For 4-gram LM setup, k-means is better but those differences disappear again after BERT training. Finally, the large codeword model can substantially reduce the gap to the original wav2vec model.
+
+# 6.2 TIMIT PHONEME RECOGNITION
+
+Next, we experiment on the much smaller TIMIT phoneme recognition task where we also pre-train vq-wav2vec on the full Librispeech corpus. Table 3 shows that vq-wav2vec and BERT achieve a new state of the art of 11.64 PER which corresponds to a $21 \%$ reduction in error over the previous best result of wav2vec.
+
+# 6.3 SEQUENCE TO SEQUENCE MODELING
+
+So far we used vq-wav2vec to train BERT on discretized speech. However, once the audio is discretized we can also train a standard sequence to sequence model to perform speech recognition. In preliminary experiments, we trained an off-the-shelf Big Transformer (Vaswani et al., 2017; Ott et al., 2019) on the vq-wav2vec Gumbel-Softmax discretized Librispeech corpus and evaluated on the Librispeech dev/test sets; we use a 4k BPE output vocabulary (Sennrich et al., 2016). Table 4 shows that results are promising, even though they are not as good as the state of the art (Park et al., 2019) which depends on data augmentation that we do not use.
+
+# 6.4 ACCURACY VS. BITRATE
+
+Next, we investigate how well vq-wav2vec can compress the audio data. Specifically, we train models with different numbers of groups $G$ and variables $V$ to vary the size of the possible codebook size $V ^ { G }$ and measure accuracy on TIMIT phoneme recognition without BERT training.
+
+![](images/9a15bf936d6d1265ca3cbbb31d5044033640a5533378629fdaf1a547978f7ec4.jpg)  
+Figure 3: Comparison of PER on the TIMIT dev set for various audio codecs and vq-wav2vec $\mathbf { k }$ -means trained on Librispeech 100h.
+
+We measure compression with the bitrate $r \cdot G \log _ { 2 } V$ at sampling rate $r \ = \ 1 0 0 \mathrm { H z }$ and report the trade-off between bitrate and accuracy on our phoneme recognition task. We experiment with vq-wav2vec $\mathbf { k }$ -means and train models with 1,2,4,8,16 and 32 groups, using $4 0 , 8 0 , 1 6 0 , . . . , 1 2 8 0$ variables, spanning a bitrate range from 0.53 kbit/s $\mathrm { G } = 1$ , ${ \mathrm { V } = 4 0 }$ ) to 33.03 kbit/s $\mathrm { G } = 3 2$ , $\mathrm { V } = 1 2 8 0$ ). We place the quantization module after the aggregator module and train all models in the small vq-wav2vec setup (§5.2) on the 100h clean Librispeech subset.
+
+As baselines, we consider various lossy compression algorithms applied to the TIMIT audio data and train wav2letter models on the resulting audio: Codec23 as a low bitrate codec, Opus (Terriberry & Vos, 2012) as a medium bitrate codec and MP3 and $\mathrm { O g g }$ Vorbis (Montgomery, 2004) as high bitrate codecs. We use the whole spectrum of both variable and constant bitrate settings of the codecs; we encode and decode with ffmpeg (ffmpeg developers, 2016). Figure 3 shows the trade-off between the bitrate and TIMIT accuracy. Acoustic models on vq-wav2vec achieve the best results across most bitrate settings.
+
+# 6.5 ABLATIONS
+
+Table 5a shows that masking entire spans of tokens performs significantly better than individual tokens $M = 1$ ). Furthermore, BERT training on discretized audio data is fairly robust to masking large parts of the input (Table 5b).
+
+<table><tr><td>p</td><td>dev</td><td>test</td></tr><tr><td>0.015</td><td>12.65</td><td>15.28</td></tr><tr><td>0.020</td><td>12.51</td><td>14.43</td></tr><tr><td>0.025</td><td>12.16</td><td>13.96</td></tr><tr><td>0.030</td><td>11.68</td><td>14.48</td></tr><tr><td>0.050</td><td>11.45</td><td>13.62</td></tr></table>
+
+(b) Mask probabilities.
+
+Table 5: TIMIT PER for (a) different mask sizes $M$ with $p M = 0 . 1 5$ in BERT training and (b) mask probabilities $p$ for a fixed mask length $M = 1 0$ .   
+
+<table><tr><td>M</td><td>dev</td><td>test</td></tr><tr><td>1</td><td>14.94</td><td>17.38</td></tr><tr><td>5</td><td>13.62</td><td>15.78</td></tr><tr><td>10</td><td>12.65</td><td>15.28</td></tr><tr><td>20</td><td>13.04</td><td>15.56</td></tr><tr><td>30</td><td>13.18</td><td>15.64</td></tr></table>
+
+(a) Mask length.
+
+# 7 CONCLUSION
+
+vq-wav2vec is a self-supervised algorithm that quantizes unlabeled audio data which makes it amenable to algorithms requiring discrete data. This approach improves the state of the art on the WSJ and TIMIT benchmarks by leveraging BERT pre-training. In future work, we plan to apply other algorithms requiring discrete inputs to audio data and to explore self-supervised pre-training algorithms which mask part of the continuous audio input. Another future work avenue is to finetune the pre-trained model to output transcriptions instead of feeding the pre-trained features to a custom ASR model.
+
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+# APPENDIX A NUMBER OF VARIABLES VS. GROUPS
+
+We investigate the relationship between number of variables $V$ and groups $G$ . Table 6 shows that multiple groups are beneficial compared to a single group with a large number of variables. Table 7 shows that with a single group and many variables, only a small number of codewords survive.   
+
+<table><tr><td>V</td><td>1 group</td><td>2 groups</td><td>4 groups</td><td>8 groups</td><td>16 groups</td><td>32 groups</td></tr><tr><td>40</td><td>33.44 ± 0.24</td><td>23.52 ± 0.53</td><td>18.76 ± 0.20</td><td>17.43 ± 0.14</td><td>15.97 ± 0.21</td><td>15.44 ± 0.32</td></tr><tr><td>80</td><td>29.14 ± 0.70</td><td>25.36 ± 4.62</td><td>17.32 ± 0.28</td><td>16.36 ± 0.27</td><td>17.55 ± 0.27</td><td>15.49 ± 0.14</td></tr><tr><td>160</td><td></td><td>24.27 ± 0.35</td><td>17.55 ± 0.03</td><td>16.36 ± 0.13</td><td>15.64 ± 0.03</td><td>15.11 ± 0.10</td></tr><tr><td>320</td><td>27.22 ± 0.25</td><td>20.86 ± 0.09</td><td>16.49 ± 0.07</td><td>15.88 ± 0.10</td><td>15.74 ± 0.18</td><td>15.18 ± 0.02</td></tr><tr><td>640</td><td>26.53 ± 2.02</td><td>18.64 ± 0.12</td><td>16.60 ± 0.22</td><td>15.62 ± 0.16</td><td>15.45 ± 0.13</td><td>15.54 ± 0.31</td></tr><tr><td>1280</td><td>32.63 ± 5.73</td><td>18.04 ± 0.26</td><td>16.37 ± 0.07</td><td>15.85 ± 0.05</td><td>15.13 ± 0.29</td><td>15.18 ± 0.05</td></tr></table>
+
+Table 6: PER on TIMIT dev set for vq-wav2vec models trained on Libri100. Results are based on three random seeds.   
+
+<table><tr><td>V</td><td>1 group</td><td>2 groups</td><td>4 groups</td><td>8 groups</td><td>16 groups</td><td>32 groups</td></tr><tr><td>40</td><td>100 % (40)</td><td>95.3 % (1.6k)</td><td>27.4 % (2.56M)</td><td>74.8 % (39.9M)</td><td>99.6 % (39.9M)</td><td>99.9 % (39.9M)</td></tr><tr><td>80</td><td>92.5% (80)</td><td>78.5% (6.4k)</td><td>11.8 % (39.9M)</td><td>91.5 % (39.9M)</td><td>99.3% (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>160</td><td>95 % (160)</td><td>57.2% (25.6k)</td><td>35.2 % (39.9M)</td><td>97.6 % (39.9M)</td><td>99.8 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>320</td><td>33.8% (320)</td><td>24.6 % (102.4k)</td><td>57.3 % (39.9M)</td><td>98.7 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>640</td><td>24.6% (640)</td><td>10 % (409.6k)</td><td>60.2 % (39.9M)</td><td>99.3 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>1280</td><td>7.2% (1.28k)</td><td>4.9 % (1.63M)</td><td>67.9 % (39.9M)</td><td>99.5 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr></table>
+
+Table 7: Fraction of used codewords vs. number of theoretically possible codewords $V ^ { G }$ in brackets; $3 9 . 9 \mathbf { M }$ is the number of tokens in Librispeech $1 0 0 \mathrm { { h } }$ .

parse/train/rylwJxrYDS/rylwJxrYDS_content_list.json

@@ -0,0 +1,1517 @@
+[
+    {
+        "type": "text",
+        "text": "VQ-WAV2VEC: SELF-SUPERVISED LEARNING OF DISCRETE SPEECH REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Alexei Baevski∗4 Steffen Schneider∗5† Michael Auli4 4 Facebook AI Research, Menlo Park, CA, USA $\\bigtriangledown$ University of Tubingen, Germany ¨ ",
+        "bbox": [
+            181,
+            169,
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+            214
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            251,
+            544,
+            266
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We propose vq-wav2vec to learn discrete representations of audio segments through a wav2vec-style self-supervised context prediction task. The algorithm uses either a Gumbel-Softmax or online $\\mathbf { k }$ -means clustering to quantize the dense representations. Discretization enables the direct application of algorithms from the NLP community which require discrete inputs. Experiments show that BERT pre-training achieves a new state of the art on TIMIT phoneme classification and WSJ speech recognition.1 ",
+        "bbox": [
+            233,
+            284,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            410,
+            336,
+            426
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Learning discrete representations of speech has gathered much recent interest (Versteegh et al., 2016; Dunbar et al., 2019). A popular approach to discover discrete units is via autoencoding (Tjandra et al., 2019; Eloff et al., 2019; Chorowski et al., 2019) sometimes coupled with an autoregressive model (Chung et al., 2019). Another line of research is to learn continuous speech representations in a self-supervised way via predicting context information (Chung & Glass, 2018; van den Oord et al., 2018; Schneider et al., 2019). ",
+        "bbox": [
+            173,
+            444,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we combine these two lines of research by learning discrete representations of speech via a context prediction task instead of reconstructing the input. This enables us to directly apply well performing NLP algorithms to speech data (Figure 1a). ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/86edb3a37578dfa8b9f0740a1d208509f0b19ccd6f8ec50c3ef988eb4c858f82.jpg",
+        "image_caption": [
+            "Figure 1: (a) The vq-wav2vec encoder maps raw audio $( \\mathcal { X } )$ to a dense representation $( { \\mathcal { Z } } )$ which is quantized (q) to $\\hat { \\mathcal { Z } }$ and aggregated into context representations $( \\mathcal { C } )$ ; training requires future time step prediction. (b) Acoustic models are trained by quantizing the raw audio with vq-wav2vec, then applying BERT to the discretized sequence and feeding the resulting representations into the acoustic model to output transcriptions. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            183,
+            592,
+            799,
+            742
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Our new discretization algorithm, vq-wav2vec, learns discrete representations of fixed length segments of audio signal by utilizing the wav2vec loss and architecture (Schneider et al, 2019; $\\ S 2$ ). To choose the discrete variables, we consider a Gumbel-Softmax approach (Jang et al., 2016) as well as online k-means clustering, similar to VQ-VAE (Oord et al., 2017; Eloff et al., 2019; §3). ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+            103,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We then train a Deep Bidirectional Transformer (BERT; Devlin et al., 2018; Liu et al., 2019) on the discretized unlabeled speech data and input these representations to a standard acoustic model (Figure 1b; $\\ S 4 _ { , }$ ). Our experiments show that BERT representations perform better than log-mel filterbank inputs as well as dense wav2vec representations on both TIMIT and WSJ benchmarks. Discretization of audio enables the direct application of a whole host of algorithms from the NLP literature to speech data. For example, we show that a standard sequence to sequence model from the NLP literature can be used to perform speech recognition over discrete audio tokens (§5, §6). ",
+        "bbox": [
+            174,
+            138,
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+            236
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            256,
+            326,
+            273
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 WAV2VEC ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            289,
+            282,
+            303
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "wav2vec (Schneider et al., 2019) learns representations of audio data by solving a self-supervised context-prediction task with the same loss function as word2vec (Mikolov et al., 2013; van den Oord et al., 2018). The model is based on two convolutional neural networks where the the encoder produces a representation $\\mathbf { z } _ { i }$ for each time step $i$ at a rate of $1 0 0 ~ \\mathrm { H z }$ and the aggregator combines multiple encoder time steps into a new representation $\\mathbf { c } _ { i }$ for each time step $i$ . Given an aggregated representation $\\mathbf { c } _ { i }$ , the model is trained to distinguish a sample $\\mathbf { z } _ { i + k }$ that is $k$ steps in the future from distractor samples $\\tilde { \\mathbf { z } }$ drawn from a distribution $p _ { n }$ , by minimizing the contrastive loss for steps $k = 1 , \\ldots , K$ : ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/00a4189605dfc7224afdf60c2ff6830ba347e76b426ef9d7924acf3640d8eece.jpg",
+        "text": "$$\n\\mathcal { L } _ { k } ^ { \\mathrm { w a v 2 v e c } } = - \\sum _ { i = 1 } ^ { T - k } \\Big ( \\log \\sigma ( \\mathbf { z } _ { i + k } ^ { \\top } h _ { k } ( \\mathbf { c } _ { i } ) ) + \\underset { \\ b { \\tilde { \\mathbf { z } } } \\sim p _ { n } } { \\mathbb { E } } [ \\log \\sigma ( - \\tilde { \\mathbf { z } } ^ { \\top } h _ { k } ( \\mathbf { c } _ { i } ) ) ] \\Big )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            272,
+            433,
+            722,
+            477
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $T$ is the sequence length, $\\sigma ( x ) ~ = ~ 1 / ( 1 + \\exp ( - x ) )$ , and where $\\sigma ( \\mathbf { z } _ { i + k } ^ { \\top } h _ { k } ( \\mathbf { c } _ { i } ) )$ is the probability of $\\mathbf { z } _ { i + k }$ being the true sample. We consider a step-specific affine transformation $h _ { k } ( \\mathbf { c } _ { i } ) \\ : = \\ : W _ { k } \\mathbf { c } _ { i } + \\mathbf { b } _ { k }$ that is applied to $\\mathbf { c } _ { i }$ (van den Oord et al., 2018). We optimize the loss $\\begin{array} { r } { \\mathcal { L } = \\sum _ { k = 1 } ^ { K } \\mathcal { L } _ { k } } \\end{array}$ , summing (1) over different step sizes. After training, the representations produced by the context network $\\mathbf { c } _ { i }$ are input to the acoustic model instead of log-mel filterbank features. ",
+        "bbox": [
+            173,
+            484,
+            825,
+            559
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 BERT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            575,
+            259,
+            589
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "BERT (Devlin et al., 2018) is a pre-training approach for NLP tasks, which uses a transformer encoder model to build a representation of text. Transformers uses self-attention to encode the input sequence as well as an optional source sequence (Vaswani et al., 2017). The original BERT model combined two tasks for training: first, masked language modeling randomly removes some of the input tokens and the model has to predict those missing tokens. Second, next sentence prediction splices two different text passages together into a single example and the model needs to predict whether the passages are from the same document. ",
+        "bbox": [
+            174,
+            601,
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+            699
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3 VQ-WAV2VEC ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            718,
+            331,
+            736
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our approach, vq-wav2vec, learns vector quantized (VQ) representations of audio data using a future time-step prediction task. We follow the same architectual choices as wav2vec $( \\ S 2 . 1 )$ with two convolutional networks $f : \\mathcal X \\mapsto \\mathcal Z$ and $g : \\hat { \\mathcal { Z } } \\mapsto \\mathcal { C }$ for feature extraction and aggregation, as well as a new quantization module $q : \\mathcal { Z } \\mapsto \\hat { \\mathcal { Z } }$ to build discrete representations (Figure 1a). ",
+        "bbox": [
+            174,
+            751,
+            823,
+            811
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first map $3 0 \\mathrm { m s }$ segments of raw speech to a dense feature representation $\\mathbf { z }$ at a stride of $1 0 \\mathrm { m s }$ using the encoder network $f$ . Next, the quantizer $( q )$ turns these dense representations into discrete indices which are mapped to a reconstruction $\\hat { \\mathbf { z } }$ of the original representation $\\mathbf { z }$ . We feed $\\hat { \\mathbf { z } }$ into the aggregator $g$ and optimize the same context prediction task as wav2vec outlined in $\\ S 2 . 1$ . ",
+        "bbox": [
+            174,
+            818,
+            825,
+            875
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The quantization module replaces the original representation $\\mathbf { z }$ by $\\hat { \\mathbf { z } } = \\mathbf { e } _ { i }$ from a fixed size codebook $\\mathbf { e } \\in { \\dot { \\mathbb { R } } } ^ { V \\times d }$ which contains $V$ representations of size $d$ . We consider the Gumbel-Softmax which is a differentiable approximation of the argmax for computing one-hot representations $\\ 8 3 . 1$ ; Figure 2a) ",
+        "bbox": [
+            176,
+            881,
+            823,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/b84b2048219dbcb8e1923e6a38273d68fd55cd2e07be0807a17f530a48662446.jpg",
+        "image_caption": [
+            "Figure 2: (a) The Gumbel-Softmax quantization computes logits representing the codebook vectors (e). In the forward pass the argmax codeword $\\left( \\mathbf { e } _ { 2 } \\right)$ is chosen and for backward (not shown) the exact probabilities are used. (b) K-means vector quantization computes the distance to all codeword vector and chooses the closest (argmin). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            204,
+            99,
+            795,
+            282
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "as well as online $\\mathbf { k }$ -means clustering, similar to the vector quantized variational autoencoder (VQVAE; Oord et al., 2017; $\\ S 3 . 2$ ; Figure 2b). Finally, we perform multiple vector quantizations over different parts of $\\mathbf { z }$ to mitigate mode collapse (§3.3). ",
+        "bbox": [
+            174,
+            377,
+            821,
+            421
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 GUMBEL-SOFTMAX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            439,
+            352,
+            453
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The Gumbel-Softmax (Gumbel, 1954; Jang et al., 2016; Maddison et al., 2014) enables selecting discrete codebook variables in a fully differentiable way and we use the straight-through estimator of Jang et al. (2016). Given the dense representation $\\mathbf { z }$ , we apply a linear layer, followed by a ReLU and another linear which outputs $1 \\in \\mathbb { R } ^ { V }$ logits for the Gumbel-Softmax. At inference, we simply pick the largest index in $l$ . At training, the output probabilities for choosing the $j$ -th variable are ",
+        "bbox": [
+            173,
+            464,
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+            536
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1dceea2e6a6552d92068bd18f51a882b490b04217a9e52dd933d779c83e0d70e.jpg",
+        "text": "$$\np _ { j } = \\frac { \\exp ( l _ { j } + v _ { j } ) / \\tau } { \\sum _ { k = 1 } ^ { V } \\exp ( l _ { k } + v _ { k } ) / \\tau } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            553,
+            598,
+            592
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $v = - \\log ( - \\log ( u ) )$ and $u$ are uniform samples from $\\mathcal { U } ( 0 , 1 )$ . During the forward pass, $i = \\mathrm { a r g m a x } _ { j } p _ { j }$ and in the backward pass, the true gradient of the Gumbel-Softmax outputs is used. ",
+        "bbox": [
+            174,
+            595,
+            823,
+            625
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 K-MEANS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            642,
+            287,
+            656
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The vector quantization approach of van den Oord et al. (2017) is an alternative to making the index selection procedure fully differentiable. Different to their setup, we optimize a future time step prediction loss instead of the reconstruction loss of an autoencoder. ",
+        "bbox": [
+            174,
+            667,
+            825,
+            710
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We choose the codebook variable representation by finding the closest variable to the input features $\\mathbf { z }$ in terms of the Euclidean distance, yielding $i = \\mathrm { a r g m i n } _ { j } \\| \\mathbf { z } - \\mathbf { e } _ { j } \\| _ { 2 } ^ { 2 }$ . During the forward pass, we select $\\hat { \\mathbf { z } } = \\mathbf { e } _ { i }$ by choosing the corresponding variable from the codebook. We obtain gradients for the encoder network by back-propagating $\\mathrm { d } \\bar { \\mathcal { L } } ^ { \\mathrm { w a v 2 v e c } } / \\mathrm { d } \\hat { \\mathbf { z } }$ (van den Oord et al., 2017). The final loss has two additional terms: ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8eba2e4e439752fac583a9a844799a231d362c7d74a29660e8685c7cf5affe3d.jpg",
+        "text": "$$\n\\mathcal { L } = \\sum _ { k = 1 } ^ { K } \\mathcal { L } _ { k } ^ { \\mathrm { w a v 2 v e c } } + \\Big ( \\| \\mathbf { s g } ( \\mathbf { z } ) - \\hat { \\mathbf { z } } \\| ^ { 2 } + \\gamma \\| \\mathbf { z } - \\mathbf { s g } ( \\hat { \\mathbf { z } } ) \\| ^ { 2 } \\Big ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            792,
+            679,
+            837
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\operatorname { s g } ( x ) \\equiv x$ , $\\begin{array} { r } { \\frac { \\mathrm { d } } { \\mathrm { d } x } \\mathbf { s } \\mathbf { g } ( x ) \\equiv 0 } \\end{array}$ is the stop gradient operator and $\\gamma$ is a hyperparameter. The first term is the future prediction task and gradients do not change the codebook because of the straightthrough gradient estimation of mapping $\\mathbf { z }$ to $\\hat { \\mathbf { z } }$ . The second term $\\| \\mathbf { s g } ( \\mathbf { z } ) - \\hat { \\mathbf { z } } \\| ^ { 2 }$ moves the codebook vectors closer to the encoder output, and the third term $\\| \\mathbf { z } - \\mathrm { s g } ( \\hat { \\mathbf { z } } ) \\| ^ { 2 }$ makes sure that the encoder outputs are close to a centroid (codeword). ",
+        "bbox": [
+            174,
+            853,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3 VECTOR QUANTIZATION WITH MULTIPLE VARIABLE GROUPS",
+        "text_level": 1,
+        "bbox": [
+            183,
+            104,
+            635,
+            117
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "So far, we considered replacing the encoder feature vector $\\mathbf { z }$ by a single entry $\\mathbf { e } _ { i }$ in the codebook. This is prone to mode collapse where only some of the codewords are actually used. Previously, this problem has been mitigated by workarounds such as re-initializing codewords or applying additional regularizers to the loss function (Caron et al., 2019). In the following, we describe another strategy where we independently quantize partitions of $\\mathbf { z }$ , similar to product quantization (Jegou et al., 2011). This results in larger dictionaries and increased downstream performance (Appendix A). ",
+        "bbox": [
+            174,
+            128,
+            823,
+            213
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The dense feature vector $\\textbf { z } \\in \\mathbb { R } ^ { d }$ is first organized into multiple groups $G$ into the matrix form $\\mathbf { z } ^ { \\prime } \\in \\mathbb { R } ^ { G \\times ( d / G ) }$ . We then represent each row by an integer index, and hence can represent the full feature vector by the indices $\\mathbf { \\hat { i } } \\in [ V ] ^ { G }$ , where $V$ again denotes the possible number of variables for this particular group and each element $\\mathbf { i } _ { j }$ corresponds to a fixed codebook vector. For each of the $G$ groups, we apply either one of the two VQ approaches $\\ S 3 . 1$ and $\\ S 3 . 2 )$ . ",
+        "bbox": [
+            174,
+            219,
+            823,
+            291
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The codebook itself can be initialized in two possible ways: Codebook variables can be shared across groups, i.e., a particular index in group $j$ would reference the same vector as the same index in group $j ^ { \\prime }$ . This yields a codebook $\\mathbf { e } \\in \\mathbb { R } ^ { V \\times ( d / G ) }$ . In contrast, not sharing the codebook variables yields a codebook of size $\\mathbf { e } \\in \\mathbb { R } ^ { V \\times G \\times ( d / G ) }$ . In practise, we observe that sharing the codebook variables generally yields competitive results to a non-shared representation. ",
+        "bbox": [
+            174,
+            297,
+            825,
+            371
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 BERT PRE-TRAINING ON QUANTIZED SPEECH ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            390,
+            598,
+            406
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Once we trained a vq-wav2vec model we can discretize audio data and make it applicable to algorithms that require discrete inputs. One possibility is to use the discretized training data and apply BERT pre-training where the task is to predict masked input tokens based on an encoding of the surrounding context (Devlin et al., 2018). Once the BERT model is trained, we can use it to build representations and feed them into an acoustic model to improve speech recognition. We follow recent advances in BERT training which only use the masked input token prediction (Liu et al., 2019). ",
+        "bbox": [
+            174,
+            421,
+            825,
+            518
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since each of the discretized tokens represents around $1 0 \\mathrm { m s }$ of audio it is likely too easy to predict a single masked input token. We therefore change BERT training by masking spans of consecutive discretized speech tokens, similar to Joshi et al. (2019). To mask the input sequence, we randomly sample $p = 0 . 0 5$ of all tokens to be a starting index, without replacement, and mask $M = 1 0$ consecutive tokens from every sampled index; spans may overlap. This makes the masked token prediction harder and we show later that it improves accuracy over masking individual tokens $( \\ S 6 . 5 )$ . ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "5.1 DATASETS ",
+        "text_level": 1,
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "We generally pre-train vq-wav2vec and BERT on the full 960h of Librispeech (Panayotov et al., 2015) and after vq-wav2vec training it is discretized to 345M tokens. Where indicated we perform ablations on a clean 100h subset which is discretized to 39.9M tokens. We evaluate models on two benchmarks: TIMIT (Garofolo et al., 1993b) is a 5h dataset with phoneme labels and Wall Street Journal (WSJ; Garofolo et al. 1993a) is a 81h dataset for speech recognition. For TIMIT, we apply the standard evaluation protocol and consider 39 different phonemes. For WSJ, we train acoustic models directly on 31 graphemes, including the English alphabet, the apostrophe, the silence token and tokens for repeating characters. ",
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+    {
+        "type": "text",
+        "text": "5.2 VQ-WAV2VEC ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We adapt the fairseq implementation of wav2vec (Schneider et al., 2019; Ott et al., 2019) and use vqwav2vec/wav2vec models with $3 4 \\times 1 0 ^ { 6 }$ parameters. The encoder has 8 layers with 512 channels each, kernel sizes (10,8,4,4,4,1,1,1) and strides (5,4,2,2,2,1,1,1), yielding a total stride of 160. Each layer contains a convolution, followed by dropout, group normalization with a single group (Wu & He, 2018) and a ReLU non-linearity. The aggregator is composed of 12 layers, with 512 channels, stride 1, and kernel sizes starting at 2 and increasing by 1 for every subsequent layer. The block structure is the same as for the encoder network, except we introduce skip connections between each subsequent block. ",
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "We train with the wav2vec context prediction loss (Equation 1) for $4 0 0 \\mathrm { k }$ updates, predicting $K = 8$ steps into the future and sample 10 negatives from the same audio example. Training is warmed up for 500 steps where the learning rate is increased from $1 \\times 1 0 ^ { - 7 }$ to $5 \\times 1 0 ^ { - 3 }$ , and then annealed to $1 \\times 1 0 ^ { - 6 }$ using a cosine schedule (Loshchilov & Hutter, 2016). The batch size is 10, and we crop a random section of $1 5 0 \\mathrm { k }$ frames for each example (approximately 9.3 seconds for 16kHz sampling rate). All models are trained on 8 GPUs. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For ablations and experiments on the 100h Librispeech subset, we use a smaller model with kernels (10,8,4,4,4) and strides (5,4,2,2,2) in the encoder and seven convolutional layers with stride one and kernel size three in the aggregator. This model is trained for $4 0 \\mathrm { k }$ updates. ",
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+    },
+    {
+        "type": "text",
+        "text": "Gumbel-Softmax Models. We use $G = 2$ groups and $V = 3 2 0$ latents per group and the linear layer projects the features produced by the encoder into $G \\cdot V = 6 4 0$ logits. The Gumbel-Softmax produces a one-hot vector for each group $G$ . The temperature $\\tau$ is linearly annealed from 2 to 0.5 over the first $70 \\%$ of updates and then kept constant at 0.5. This enables the model to learn which latents work best for each input before committing to a single latent. After training this model on 960h of Librispeech and quantizing the training dataset, we are left with $1 3 . 5 \\mathrm { k }$ unique codewords combinations (out of $V ^ { G } = 1 0 2 \\mathrm { k \\Omega }$ possible codewords). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf { k }$ -means Models. We use $G = 2$ groups and $V = 3 2 0$ variables per group. vq-wav2vec on full Librispeech yields $2 3 \\mathrm { k }$ unique codewords. Following van den Oord et al. (2017), we found $\\gamma = 0 . 2 5$ to be a robust choice for balancing the VQ auxiliary loss. ",
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+    {
+        "type": "text",
+        "text": "5.3 BERT ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "BERT base models have 12 layers, model dimension 768, inner dimension (FFN) 3072 and 12 attention heads (Devlin et al., 2018). The learning rate is warmed up over the first 10,000 updates to a peak value of $1 \\times 1 0 ^ { - 5 }$ , and then linearly decayed over a total of $2 5 0 \\mathrm { k }$ updates. We train on 128 GPUs with a batch size of 3072 tokens per GPU giving a total batch size of $3 9 3 \\mathrm { k }$ tokens (Ott et al., 2018). Each token represents $1 0 \\mathrm { m s }$ of audio data. ",
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+    },
+    {
+        "type": "text",
+        "text": "BERT small. For ablations we use a smaller setup with model dimension 512, FFN size 2048, 8 attention heads and dropout 0.05. Models are trained for 250k updates with a batch size of 2 examples per GPU. ",
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+    {
+        "type": "text",
+        "text": "5.4 ACOUSTIC MODEL ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We use wav2letter as accoustic model (Collobert et al., 2016; 2019) and train for 1,000 epochs on 8 GPUs for both TIMIT and WSJ using the auto segmentation criterion. For decoding the emissions from the acoustic model on WSJ we use a lexicon as well as a separate language model trained on the WSJ language modeling data only. We consider a 4-gram KenLM language model (Heafield et al., 2013) and a character based convolutional language model (Likhomanenko et al., 2019) and tune the models with the same protocol as Schneider et al. (2019). ",
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+    {
+        "type": "text",
+        "text": "6 RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "6.1 WSJ SPEECH RECOGNITION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We first evaluate on the WSJ speech recognition benchmark. We train a vq-wav2vec model on the unlabeled version of Librispeech, then discretize the same data with the resulting model to estimate a BERT model. Finally, we train a wav2letter acoustic model on WSJ by inputting either the BERT or vq-wav2vec representations instead of log-mel filterbanks.2 ",
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+    {
+        "type": "text",
+        "text": "We compare to various results from the literature, including wav2vec (Schneider et al., 2019) and we consider three setups: performance without any language model (No LM), with an n-gram LM (4-gram LM) and with a character convolutional LM (Char ConvLM). We report the accuracy of wav2letter with log-mel filterbanks as input (Baseline) and wav2vec. For vq-wav2vec we first experiment with the Gumbel-Softmax, with and without a BERT base model (§5.3). ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/d118865a1a77c4ae2eea5a245d60cca20abb1d19c278e59c8c89e9c9a8dc6e99.jpg",
+        "table_caption": [
+            "Table 1: WSJ accuracy of vq-wav2vec on the development (nov93dev) and test set (nov92) in terms of letter error rate (LER) and word error rate (WER) without language modeling (No LM), a 4-gram LM and a character convolutional LM. vq-wav2vec with BERT pre-training improves over the best wav2vec model (Schneider et al., 2019). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">nov93dev</td><td colspan=\"2\">nov92</td></tr><tr><td>LER</td><td>WER</td><td>LER</td><td>WER</td></tr><tr><td>Deep Speech 2 (12K h labeled speech; Amodei et al., 2016)</td><td>1</td><td>4.42</td><td>1</td><td>3.1</td></tr><tr><td>Trainable frontend (Zeghidour et al., 2018)</td><td></td><td>6.8</td><td>=</td><td>3.5</td></tr><tr><td>Lattice-free MMI (Hadian et al., 2018)</td><td></td><td>5.66t</td><td></td><td>2.8†</td></tr><tr><td>Supervised transfer-learning (Ghahremani et al., 2017)</td><td></td><td>4.99t</td><td>1</td><td>2.53†</td></tr><tr><td>No LM</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>6.28</td><td>19.46</td><td>4.14</td><td>13.93</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>5.07</td><td>16.24</td><td>3.26</td><td>11.20</td></tr><tr><td>vq-wav2vec Gumbel</td><td>7.04</td><td>20.44</td><td>4.51</td><td>14.67</td></tr><tr><td>+BERT base</td><td>4.13</td><td>13.40</td><td>2.62</td><td>9.39</td></tr><tr><td>4-GRAM LM (Heafield et al., 2013)</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>3.32</td><td>8.57</td><td>2.19</td><td>5.64</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.73</td><td>6.96</td><td>1.57</td><td>4.32</td></tr><tr><td>vq-wav2vec Gumbel</td><td>3.93</td><td>9.55</td><td>2.40</td><td>6.10</td></tr><tr><td>+ BERT base</td><td>2.41</td><td>6.28</td><td>1.26</td><td>3.62</td></tr><tr><td>CHAR CoNvLM (Likhomanenko et al., 2019)</td><td></td><td></td><td></td><td></td></tr><tr><td>Baseline (log-mel)</td><td>2.77</td><td>6.67</td><td>1.53</td><td>3.46</td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.11</td><td>5.10</td><td>0.99</td><td>2.43</td></tr><tr><td>vq-wav2vec Gumbel + BERT base</td><td>1.79</td><td>4.46</td><td>0.93</td><td>2.34</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4b3c129e0bd2739d3e1368429d46418beeec408813e6cccf6968ac59c10b0a82.jpg",
+        "table_caption": [
+            "Table 2: Comparison of Gumbel-Softmax and k-means vector quantization on WSJ (cf. Table 1). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">nov93dev</td><td colspan=\"2\">nov92</td></tr><tr><td></td><td>LER</td><td>WER</td><td>LER</td><td>WER</td></tr><tr><td>No LM</td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>5.07</td><td>16.24</td><td>3.26</td><td>11.20</td></tr><tr><td>vq-wav2vec Gumbel</td><td>7.04</td><td>20.44</td><td>4.51</td><td>14.67</td></tr><tr><td>+ BERT small</td><td>4.52</td><td>14.14</td><td>2.81</td><td>9.69</td></tr><tr><td>vq-wav2vec k-means (39M codewords)</td><td>5.41</td><td>17.11</td><td>3.63</td><td>12.17</td></tr><tr><td>vq-wav2vec k-means</td><td>7.33</td><td>21.64</td><td>4.72</td><td>15.17</td></tr><tr><td>+ BERT small</td><td>4.31</td><td>13.87</td><td>2.70</td><td>9.62</td></tr><tr><td>4-GRAM LM (Heafield et al., 2013)</td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec (Schneider et al., 2019)</td><td>2.73</td><td>6.96</td><td>1.57</td><td>4.32</td></tr><tr><td>vq-wav2vec Gumbel</td><td>3.93</td><td>9.55</td><td>2.40</td><td>6.10</td></tr><tr><td>+ BERT small</td><td>2.67</td><td>6.67</td><td>1.46</td><td>4.09</td></tr><tr><td>vq-wav2vec k-means (39M codewords)</td><td>3.05</td><td>7.74</td><td>1.71</td><td>4.82</td></tr><tr><td>vq-wav2vec k-means</td><td>4.37</td><td>10.26</td><td>2.28</td><td>5.71</td></tr><tr><td>+ BERT small</td><td>2.60</td><td>6.62</td><td>1.45</td><td>4.08</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Table 1 shows that vq-wav2vec together with BERT training can achieve a new state of the art of 2.34 WER on nov92. Gains are largest when no language model is used which is the fastest setting. vq-wav2vec with Gumbel-Softmax uses only $1 3 . 5 \\mathrm { k }$ distinct codewords to represent the audio signal and this limited set of codewords is not sufficient to outperform the baseline. However, it does enable training BERT models which require a relatively small vocabulary. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/5dc3d9f580eb22ecccf936bd0b90505b2b73ceb5ff543df8d33072559bb7bd76.jpg",
+        "table_caption": [
+            "Table 3: TIMIT phoneme recognition in terms of phoneme error rate (PER). All our models use the CNN-8L-PReLU-do0.7 architecture (Zeghidour et al., 2018). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>dev PER</td><td>test PER</td></tr><tr><td>CNN + TD-filterbanks (Zeghidour et al., 2018)</td><td>15.6</td><td>18.0</td></tr><tr><td>Li-GRU + fMLLR (Ravanelli et al.,2018)</td><td>1</td><td>14.9</td></tr><tr><td>wav2vec (Schneider et al.,2019)</td><td>12.9</td><td>14.7</td></tr><tr><td>Baseline (log-mel)</td><td>16.9</td><td>17.6</td></tr><tr><td>vq-wav2vec, Gumbel</td><td>15.34</td><td>17.78</td></tr><tr><td>+ BERT small</td><td>9.64</td><td>11.64</td></tr><tr><td>vq-wav2vec, k-means</td><td>15.65</td><td>18.73</td></tr><tr><td>+ BERT small</td><td>9.80</td><td>11.40</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/8d9da95b17fa71b6b7d85b9d81f2dcda3931ba840dad2b086edf7a7993a7fa8a.jpg",
+        "table_caption": [
+            "Table 4: Librispeech results for a standard sequence to sequence model trained on discretized audio without BERT pre-training and results from the literature. All results are without a language model. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>dev clean</td><td>dev other</td><td> test clean</td><td> test other</td></tr><tr><td>Mohamed et al. (2019)</td><td>4.8</td><td>12.7</td><td>4.7</td><td>12.9</td></tr><tr><td>Irie et al. (2019)</td><td>4.4</td><td>13.2</td><td>4.7</td><td>13.4</td></tr><tr><td>Park et al. (2019)</td><td>2.8</td><td>6.8</td><td>2.5</td><td>5.8</td></tr><tr><td>vq-wav2vec Gumbel + Transformer Big</td><td>5.6</td><td>15.5</td><td>6.2</td><td>18.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we compare Gumbel-Softmax to $\\mathbf { k }$ -means for vector quantization. For this experiment we use the faster to train BERT small configuration (§5.3). We also train a vq-wav2vec $\\mathbf { k }$ -means model with a very large number of codewords (39.9M) to test whether a more expressive model can close the gap to wav2vec. Table 2 shows that Gumbel-Softmax and $\\mathbf { k }$ -means clustering perform relatively comparably: in the no language model setup without BERT, Gumbel-Softmax is more accurate than k-means but these differences disappear with BERT. For 4-gram LM setup, k-means is better but those differences disappear again after BERT training. Finally, the large codeword model can substantially reduce the gap to the original wav2vec model. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.2 TIMIT PHONEME RECOGNITION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we experiment on the much smaller TIMIT phoneme recognition task where we also pre-train vq-wav2vec on the full Librispeech corpus. Table 3 shows that vq-wav2vec and BERT achieve a new state of the art of 11.64 PER which corresponds to a $21 \\%$ reduction in error over the previous best result of wav2vec. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.3 SEQUENCE TO SEQUENCE MODELING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "So far we used vq-wav2vec to train BERT on discretized speech. However, once the audio is discretized we can also train a standard sequence to sequence model to perform speech recognition. In preliminary experiments, we trained an off-the-shelf Big Transformer (Vaswani et al., 2017; Ott et al., 2019) on the vq-wav2vec Gumbel-Softmax discretized Librispeech corpus and evaluated on the Librispeech dev/test sets; we use a 4k BPE output vocabulary (Sennrich et al., 2016). Table 4 shows that results are promising, even though they are not as good as the state of the art (Park et al., 2019) which depends on data augmentation that we do not use. ",
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+    },
+    {
+        "type": "text",
+        "text": "6.4 ACCURACY VS. BITRATE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we investigate how well vq-wav2vec can compress the audio data. Specifically, we train models with different numbers of groups $G$ and variables $V$ to vary the size of the possible codebook size $V ^ { G }$ and measure accuracy on TIMIT phoneme recognition without BERT training. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a15bf936d6d1265ca3cbbb31d5044033640a5533378629fdaf1a547978f7ec4.jpg",
+        "image_caption": [
+            "Figure 3: Comparison of PER on the TIMIT dev set for various audio codecs and vq-wav2vec $\\mathbf { k }$ -means trained on Librispeech 100h. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We measure compression with the bitrate $r \\cdot G \\log _ { 2 } V$ at sampling rate $r \\ = \\ 1 0 0 \\mathrm { H z }$ and report the trade-off between bitrate and accuracy on our phoneme recognition task. We experiment with vq-wav2vec $\\mathbf { k }$ -means and train models with 1,2,4,8,16 and 32 groups, using $4 0 , 8 0 , 1 6 0 , . . . , 1 2 8 0$ variables, spanning a bitrate range from 0.53 kbit/s $\\mathrm { G } = 1$ , ${ \\mathrm { V } = 4 0 }$ ) to 33.03 kbit/s $\\mathrm { G } = 3 2$ , $\\mathrm { V } = 1 2 8 0$ ). We place the quantization module after the aggregator module and train all models in the small vq-wav2vec setup (§5.2) on the 100h clean Librispeech subset. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As baselines, we consider various lossy compression algorithms applied to the TIMIT audio data and train wav2letter models on the resulting audio: Codec23 as a low bitrate codec, Opus (Terriberry & Vos, 2012) as a medium bitrate codec and MP3 and $\\mathrm { O g g }$ Vorbis (Montgomery, 2004) as high bitrate codecs. We use the whole spectrum of both variable and constant bitrate settings of the codecs; we encode and decode with ffmpeg (ffmpeg developers, 2016). Figure 3 shows the trade-off between the bitrate and TIMIT accuracy. Acoustic models on vq-wav2vec achieve the best results across most bitrate settings. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6.5 ABLATIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5a shows that masking entire spans of tokens performs significantly better than individual tokens $M = 1$ ). Furthermore, BERT training on discretized audio data is fairly robust to masking large parts of the input (Table 5b). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/a97a203a2b2796e5b5b9e943a8a24bd7176cd761d36cff345a00eff2eaef3fdc.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "(b) Mask probabilities. "
+        ],
+        "table_body": "<table><tr><td>p</td><td>dev</td><td>test</td></tr><tr><td>0.015</td><td>12.65</td><td>15.28</td></tr><tr><td>0.020</td><td>12.51</td><td>14.43</td></tr><tr><td>0.025</td><td>12.16</td><td>13.96</td></tr><tr><td>0.030</td><td>11.68</td><td>14.48</td></tr><tr><td>0.050</td><td>11.45</td><td>13.62</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1e52ec51969ae106cb253119aeec9a579332792aef73fa0f06c14db141855551.jpg",
+        "table_caption": [
+            "Table 5: TIMIT PER for (a) different mask sizes $M$ with $p M = 0 . 1 5$ in BERT training and (b) mask probabilities $p$ for a fixed mask length $M = 1 0$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>M</td><td>dev</td><td>test</td></tr><tr><td>1</td><td>14.94</td><td>17.38</td></tr><tr><td>5</td><td>13.62</td><td>15.78</td></tr><tr><td>10</td><td>12.65</td><td>15.28</td></tr><tr><td>20</td><td>13.04</td><td>15.56</td></tr><tr><td>30</td><td>13.18</td><td>15.64</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(a) Mask length. ",
+        "bbox": [
+            287,
+            744,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            827,
+            318,
+            842
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "vq-wav2vec is a self-supervised algorithm that quantizes unlabeled audio data which makes it amenable to algorithms requiring discrete data. This approach improves the state of the art on the WSJ and TIMIT benchmarks by leveraging BERT pre-training. In future work, we plan to apply other algorithms requiring discrete inputs to audio data and to explore self-supervised pre-training algorithms which mask part of the continuous audio input. Another future work avenue is to finetune the pre-trained model to output transcriptions instead of feeding the pre-trained features to a custom ASR model. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
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+        "page_idx": 8
+    },
+    {
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+    {
+        "type": "text",
+        "text": "APPENDIX A NUMBER OF VARIABLES VS. GROUPS ",
+        "text_level": 1,
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+    {
+        "type": "table",
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+        "table_caption": [
+            "We investigate the relationship between number of variables $V$ and groups $G$ . Table 6 shows that multiple groups are beneficial compared to a single group with a large number of variables. Table 7 shows that with a single group and many variables, only a small number of codewords survive. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>V</td><td>1 group</td><td>2 groups</td><td>4 groups</td><td>8 groups</td><td>16 groups</td><td>32 groups</td></tr><tr><td>40</td><td>33.44 ± 0.24</td><td>23.52 ± 0.53</td><td>18.76 ± 0.20</td><td>17.43 ± 0.14</td><td>15.97 ± 0.21</td><td>15.44 ± 0.32</td></tr><tr><td>80</td><td>29.14 ± 0.70</td><td>25.36 ± 4.62</td><td>17.32 ± 0.28</td><td>16.36 ± 0.27</td><td>17.55 ± 0.27</td><td>15.49 ± 0.14</td></tr><tr><td>160</td><td></td><td>24.27 ± 0.35</td><td>17.55 ± 0.03</td><td>16.36 ± 0.13</td><td>15.64 ± 0.03</td><td>15.11 ± 0.10</td></tr><tr><td>320</td><td>27.22 ± 0.25</td><td>20.86 ± 0.09</td><td>16.49 ± 0.07</td><td>15.88 ± 0.10</td><td>15.74 ± 0.18</td><td>15.18 ± 0.02</td></tr><tr><td>640</td><td>26.53 ± 2.02</td><td>18.64 ± 0.12</td><td>16.60 ± 0.22</td><td>15.62 ± 0.16</td><td>15.45 ± 0.13</td><td>15.54 ± 0.31</td></tr><tr><td>1280</td><td>32.63 ± 5.73</td><td>18.04 ± 0.26</td><td>16.37 ± 0.07</td><td>15.85 ± 0.05</td><td>15.13 ± 0.29</td><td>15.18 ± 0.05</td></tr></table>",
+        "bbox": [
+            173,
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+    },
+    {
+        "type": "table",
+        "img_path": "images/06d0e4176094bb3f2597ed9fd9a2478c34a0303be831afc2d8977348250bc900.jpg",
+        "table_caption": [
+            "Table 6: PER on TIMIT dev set for vq-wav2vec models trained on Libri100. Results are based on three random seeds. "
+        ],
+        "table_footnote": [
+            "Table 7: Fraction of used codewords vs. number of theoretically possible codewords $V ^ { G }$ in brackets; $3 9 . 9 \\mathbf { M }$ is the number of tokens in Librispeech $1 0 0 \\mathrm { { h } }$ . "
+        ],
+        "table_body": "<table><tr><td>V</td><td>1 group</td><td>2 groups</td><td>4 groups</td><td>8 groups</td><td>16 groups</td><td>32 groups</td></tr><tr><td>40</td><td>100 % (40)</td><td>95.3 % (1.6k)</td><td>27.4 % (2.56M)</td><td>74.8 % (39.9M)</td><td>99.6 % (39.9M)</td><td>99.9 % (39.9M)</td></tr><tr><td>80</td><td>92.5% (80)</td><td>78.5% (6.4k)</td><td>11.8 % (39.9M)</td><td>91.5 % (39.9M)</td><td>99.3% (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>160</td><td>95 % (160)</td><td>57.2% (25.6k)</td><td>35.2 % (39.9M)</td><td>97.6 % (39.9M)</td><td>99.8 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>320</td><td>33.8% (320)</td><td>24.6 % (102.4k)</td><td>57.3 % (39.9M)</td><td>98.7 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>640</td><td>24.6% (640)</td><td>10 % (409.6k)</td><td>60.2 % (39.9M)</td><td>99.3 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr><tr><td>1280</td><td>7.2% (1.28k)</td><td>4.9 % (1.63M)</td><td>67.9 % (39.9M)</td><td>99.5 % (39.9M)</td><td>99.9 % (39.9M)</td><td>100 % (39.9M)</td></tr></table>",
+        "bbox": [
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+            353,
+            885,
+            458
+        ],
+        "page_idx": 11
+    }
+]