Add files using upload-large-folder tool

parse/train/0-EYBhgw80y/0-EYBhgw80y.md

@@ -0,0 +1,332 @@
+# MOPRO: WEBLY SUPERVISED LEARNING WITHMOMENTUM PROTOTYPES
+
+Junnan Li, Caiming Xiong, Steven C.H. Hoi Salesforce Research {junnan.li,cxiong,shoi}@salesforce.com
+
+# ABSTRACT
+
+We propose a webly-supervised representation learning method that does not suffer from the annotation unscalability of supervised learning, nor the computation unscalability of self-supervised learning. Most existing works on weblysupervised representation learning adopt a vanilla supervised learning method without accounting for the prevalent noise in the training data, whereas most prior methods in learning with label noise are less effective for real-world large-scale noisy data. We propose momentum prototypes (MoPro), a simple contrastive learning method that achieves online label noise correction, out-of-distribution sample removal, and representation learning. MoPro achieves state-of-the-art performance on WebVision, a weakly-labeled noisy dataset. MoPro also shows superior performance when the pretrained model is transferred to down-stream image classification and detection tasks. It outperforms the ImageNet supervised pretrained model by $+ 1 0 . 5$ on 1-shot classification on VOC, and outperforms the best self-supervised pretrained model by $+ 1 7 . 3$ when finetuned on $1 \%$ of ImageNet labeled samples. Furthermore, MoPro is more robust to distribution shifts. Code and pretrained models are available at https://github.com/ salesforce/MoPro.
+
+# 1 INTRODUCTION
+
+Large-scale datasets with human-annotated labels have revolutionized computer vision. Supervised pretraining on ImageNet (Deng et al., 2009) has been the de facto formula of success for almost all state-of-the-art visual perception models. However, it is extremely labor intensive to manually annotate millions of images, which makes it a non-scalable solution. One alternative to reduce annotation cost is self-supervised representation learning, which leverages unlabeled data. However, self-supervised learning methods (Goyal et al., 2019; He et al., 2019; Chen et al., 2020a; Li et al., 2020b) have yet consistently shown superior performance compared to supervised learning, especially when transferred to downstream tasks with limited labels.
+
+With the help of commercial search engines, photo-sharing websites, and social media platforms, there is near-infinite amount of weakly-labeled images available on the web. Several works have exploited the scalable source of web images and demonstrated promising results with weblysupervised representation learning (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). However, there exists two competing claims on whether weakly-labeled noisy datasets lead to worse generalization performance. One claim argues that the effect of noise can be overpowered by the scale of data, and simply applies standard supervised learning method on web datasets (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). The other claim argues that deep models can easily memorize noisy labels, resulting in worse generalization (Zhang et al., 2017; Ma et al., 2018). In this paper, we show that both claims are partially true. While increasing the size of data does improve the model’s robustness to noise, our method can substantially boost the representation learning performance by addressing noise.
+
+There exists a large body of literature on learning with label noise (Jiang et al., 2018; Han et al., 2018; Guo et al., 2018; Tanaka et al., 2018; Arazo et al., 2019; Li et al., 2020a). However, existing methods have several limitations that make them less effective for webly-supervised representation learning. First, most methods do not consider out-of-distribution (OOD) samples, which is a major source of noise in real-world web datasets. Second, many methods perform computation-heavy procedures for noise cleaning (Jiang et al., 2018; Li et al., 2019; 2020a), or require access to a set of samples with clean labels (Vahdat, 2017; Veit et al., 2017; Lee et al., 2018), which limit their scalability in practice.
+
+![](images/7ecbcd588a47f787db2184fc5789e2871d9c82a7936417547c95e4d0aa45ea1f.jpg)  
+Figure 1: Illustration of the normalized embedding space learned with MoPro. Samples from the same class gather around their class prototype, whereas OOD samples are separated from in-distribution samples. Label correction and OOD removal are achieved based on a sample’s distance with the prototypes.
+
+We propose a new method for efficient representation learning from weakly-labeled web images. Our method is inspired by recent developments in contrastive learning for self-supervised learning (He et al., 2019; Chen et al., 2020a; Li et al., 2020b) We introduce Momentum Prototypes (MoPro), a simple component which is effective in label noise correction, OOD sample removal, and representation learning. A visual explanation of our method is shown in Figure 1. We use a deep network to project images into normalized low-dimensional embeddings, and calculate the prototype for a class as the moving-average embedding for clean samples in that class. We train the network such that embeddings are pulled closer to their corresponding prototypes, while pushed away from other prototypes. Images with corrupted labels are corrected either as another class or as an OOD sample based on their distance to the momentum prototypes.
+
+We experimentally show that:
+
+• MoPro achieves state-of-the-art performance on the upstream weakly-supervised learning task. • MoPro substantially improves representation learning performance when the pretrained model is transferred to downstream image classification and object detection tasks. For the first time, we show that weakly-supervised representation learning achieves similar performance as supervised representation learning, under the same data and computation budget. With a larger web dataset, MoPro outperforms ImageNet supervised learning by a large margin. • MoPro learns a more robust and calibrated model that generalizes better to distribution variations.
+
+# 2 RELATED WORK
+
+# 2.1 WEBLY-SUPERVISED REPRESENTATION LEARNING
+
+A number of prior works exploit large web datasets for visual representation learning (Divvala et al., 2014; Chen & Gupta, 2015; Joulin et al., 2016; Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). These datasets contain a considerable amount of noise. Approximately $20 \%$ of the labels in the JMT-300M dataset (Sun et al., 2017) are noisy, whereas $34 \%$ of images in the WebVision dataset (Li et al., 2017) are considered outliers. Surprisingly, most prior works have chosen to ignore the noise and applied vanilla supervised method, with the claim that the scale of data can overpower the noise (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017). However, we show that supervised method cannot fully harvest the power of large-scale weakly-labeled datasets.
+
+Our method achieves substantial improvement by addressing noise, and advances the potential of webly-supervised representation learning.
+
+# 2.2 LEARNING WITH LABEL NOISE
+
+Learning with label noise has been widely studied. Some methods require access to a small set of clean samples (Xiao et al., 2015; Vahdat, 2017; Veit et al., 2017; Lee et al., 2018; Zhang et al., 2020), and other methods assume that no clean labels are available. There exist two major types of approaches. The first type performs label correction using predictions from the network (Reed et al., 2015; Ma et al., 2018; Tanaka et al., 2018; Yi & Wu, 2019; Yang et al., 2020). The second type separates clean samples from corrupted samples, and trains the model on clean samples (Han et al., 2018; Arazo et al., 2019; Jiang et al., 2018; Wang et al., 2018; Chen et al., 2019; Li et al., 2020a). However, existing methods have yet shown promising results for large-scale weakly-supervised representation learning. The main reasons include: (1) most methods do not consider OOD samples, which commonly occur in real-world web datasets; (2) most methods are computational-heavy due to co-training (Han et al., 2018; Li et al., 2020a; Jiang et al., 2018; 2020), iterative training (Tanaka et al., 2018; Yi & Wu, 2019; Wang et al., 2018; Chen et al., 2019), or meta-learning (Li et al., 2019; Zhang et al., 2019).
+
+Different from existing methods, MoPro achieves both label correction and OOD sample removal on-the-fly with a single step, based on the similarity between an image embedding and the momentum prototypes. MoPro also leverages contrastive learning to learn a robust embedding space.
+
+# 2.3 SELF-SUPERVISED REPRESENTATION LEARNING
+
+Self-supervised methods have been proposed for representation learning using unlabeled data. The recent developments in self-supervised representation learning can be attributed to contrastive learning. Most methods (He et al., 2019; Chen et al., 2020a; Oord et al., 2018; Wu et al., 2018) leverage the task of instance discrimination, where augmented crops from the same source image are enforced to have similar embeddings. Prototypical contrastive learning (PCL) (Li et al., 2020b) performs clustering to find prototypical embeddings, and enforces an image embedding to be similar to its assigned prototypes. Different from PCL, we update prototypes on-the-fly in a weakly-supervised setting, where the momentum prototype of a class is the moving average of clean samples’ embeddings. Furthermore, we jointly optimize two contrastive losses and a cross-entropy loss.
+
+Current self-supervised representation learning methods are limited in (1) inferior performance in low-shot task adaptation, (2) huge computation cost, and (3) inadequate to harvest larger datasets. We show that weakly-supervised learning with MoPro addresses these limitations.
+
+# 3 METHOD
+
+In this section, we delineate the details of our method. First, we introduce the components in our representation learning framework. Then, we describe the loss functions. Finally, we explain the noise correction procedure for label correction and OOD sample removal. A pseudo-code of MoPro is provided in appendix B.
+
+# 3.1 REPRESENTATION LEARNING FRAMEWORK
+
+Our proposed framework consists of the following components. Figure 2 gives an illustration.
+
+• A noisy training dataset $\{ ( \pmb { x } _ { i } , y _ { i } ) \} _ { i = 1 } ^ { n }$ , where $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ is an image and $y _ { i } \in \{ 1 , . . . , K \}$ is its class label.   
+• A pseudo-label $\hat { y } _ { i }$ for each image $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ , which is its corrected label. Details for generating the pseudo-label is explained in Sec 3.3.   
+• An encoder network, which maps an augmented image $\tilde { \mathbf { x } } _ { i }$ to a representation vector $\pmb { v } _ { i } \in \mathbb { R } ^ { d _ { e } }$ . We experiment with ResNet-50 (He et al., 2016) as the encoder, where the activations of the final global pooling layer $\langle d _ { e } = 2 0 4 8 \rangle$ ) are used as the representation vector.   
+• A classifier (a fully-connected layer followed by softmax) which receives the representation ${ \mathbf { } } v _ { i }$ as input and outputs class predictions $\mathbf { \nabla } p _ { i }$ .
+
+![](images/996d567d2a9b08e3b048509f78a32a9841e8e3c1a949bf71cfe1559f14de6277.jpg)  
+Figure 2: Proposed weakly-supervised learning framework. We jointly optimize a prototypical contrastive loss using momentum prototypes, an instance contrastive loss using momentum embeddings, and a cross-entropy loss using pseudo-labels. The pseudo-label for a sample is generated based on its original training label, the model’s prediction, and the sample’s distance to the prototypes.
+
+• A projection network, which maps the representation ${ \mathbf { } } v _ { i }$ into a low-dimensional embedding $z _ { i } \in$ $\mathbb { R } ^ { \hat { d } _ { p } }$ $\bar { \boldsymbol { d } } _ { p } = 1 2 8 )$ . $z _ { i }$ is always normalized to the unit sphere. Following SimCLR (Chen et al., 2020a), we use a MLP with one hidden layer as the projection network. • Momentum embeddings $ { \boldsymbol { z } } _ { i } ^ { \prime }$ generated by a momentum encoder. The momentum encoder has the same architecture as the encoder followed by the projection network, and its parameters are the moving-average of the encoder’s and the projection network’s parameters. Same as in MoCo (He et al., 2019), we maintain a queue of momentum embeddings of past samples. • Momentum prototypes $C \in \mathbb { R } ^ { d _ { p } \times K }$ . The momentum prototype of the $k$ -th class, $\scriptstyle c _ { k }$ , is the normalized moving-average embedding for samples with pseudo-label ${ \hat { y } } _ { i } = k$ .
+
+# 3.2 CONTRASTIVE LOSS
+
+As illustrated in Figure 1, we aim to learn an embedding space where samples from the same class gather around its class prototype, while samples from different classes are seperated. We achieve it with two contrastive losses: (1) a prototypical contrastive loss $\mathcal { L } _ { \mathrm { { p r o } } }$ which increases the similarity between an embedding and its corresponding class prototype, $( z _ { i } , c _ { \hat { y } _ { i } } )$ , in contrast to other prototypes; (2) an instance contrastive loss ${ \mathcal { L } } _ { \mathrm { i n s } }$ which increases the similarity between two embeddings of the same source image, $( z _ { i } , z _ { i } ^ { \prime } )$ , in contrast to embeddings of other images. Specifically, the contrastive losses are defined as:
+
+$$
+\mathcal { L } _ { \mathrm { p r o } } ^ { i } = - \log \frac { \exp ( z _ { i } \cdot c _ { \hat { y } _ { i } } / \tau ) } { \sum _ { k = 1 } ^ { K } \exp ( z _ { i } \cdot c _ { k } / \tau ) } , ~ \mathcal { L } _ { \mathrm { i n s } } ^ { i } = - \log \frac { \exp ( z _ { i } \cdot z _ { i } ^ { \prime } / \tau ) } { \sum _ { r = 0 } ^ { R } \exp ( z _ { i } \cdot z _ { r } ^ { \prime } / \tau ) } ,
+$$
+
+where $\tau$ is a temperature parameter, and $\hat { y } _ { i }$ is the pseudo-label. We use $R$ negative momentum embeddings to construct the denominator of the instance contrastive loss.
+
+We train the classifier with cross-entropy loss, using pseudo-labels as targets.
+
+$$
+\mathcal { L } _ { \mathrm { c e } } ^ { i } = - \log ( p _ { i } ^ { \hat { y } _ { i } } )
+$$
+
+We jointly optimize the contrastive losses and the classification loss. The training objective is:
+
+$$
+{ \mathcal { L } } = \sum _ { i = 1 } ^ { n } ( { \mathcal { L } } _ { \mathrm { c e } } ^ { i } + \lambda _ { \mathrm { p r o } } { \mathcal { L } } _ { \mathrm { p r o } } ^ { i } + \lambda _ { \mathrm { i n s } } { \mathcal { L } } _ { \mathrm { i n s } } ^ { i } )
+$$
+
+For simplicity, we set $\lambda _ { \mathrm { p r o } } = \lambda _ { \mathrm { i n s } } = 1$ for all experiments.
+
+# 3.3 NOISE CORRECTION
+
+We propose a simple yet effective method for online noise correction during training, which cleans label noise and removes OOD samples. For each sample, we generate a soft pseudo-label $\pmb { q } _ { i }$ by
+
+combining the classifier’s output probability $\mathbf { \nabla } _ { \mathbf { p } _ { i } }$ with $\mathbf { \boldsymbol { s } } _ { i }$ , a class probability distribution calculated using the sample’s similarity $w . r . t$ the momentum prototypes:
+
+$$
+\begin{array} { l } { q _ { i } = \alpha { { p } _ { i } } + ( 1 - \alpha ) { { s } _ { i } } , } \\ { s _ { i } ^ { k } = \displaystyle \frac { \exp ( z _ { i } \cdot { { c } _ { k } } / \tau ) } { \sum _ { k = 1 } ^ { K } \exp ( z _ { i } \cdot { { c } _ { k } } / \tau ) } . } \end{array}
+$$
+
+where the combination weight is simply set as $\alpha = 0 . 5$ in all experiments.
+
+We convert $\pmb q _ { i }$ into a hard pseudo-label $\hat { y } _ { i }$ based on the following rules: (1) if the highest score of $\pmb q _ { i }$ is above certain threshold $T$ , use the class with the highest score as the pseudo-label; (2) otherwise, if the score for the original label $y _ { i }$ is higher than uniform probability, use $y _ { i }$ as the pseudo-label; (3) otherwise, label it as an OOD sample.
+
+$$
+\begin{array} { r } { \hat { y } _ { i } = \left\{ \begin{array} { l l } { \mathrm { a r g } \operatorname* { m a x } _ { k } q _ { i } ^ { k } } & { \mathrm { i f } \operatorname* { m a x } _ { k } q _ { i } ^ { k } > T , } \\ { y _ { i } } & { \mathrm { e l s e i f } q _ { i } ^ { y _ { i } } > 1 / K , } \\ { \mathrm { O O D } } & { \mathrm { o t h e r w i s e } . } \end{array} \right. } \end{array}
+$$
+
+We remove OOD samples from both the cross-entropy loss and the prototypical contrastive loss so that they do not affect class-specific learning, but include them in the instance contrastive loss to further separate them from in-distribution samples. Examples of OOD images and corrected pseudo-labels are shown in the appendices.
+
+# 3.4 MOMENTUM PROTOTYPES
+
+For each class $k$ , we calculate its momentum prototype as a moving-average of the normalized embeddings for samples with pseudo-label $k$ . Specifically, we update $c _ { k }$ by:
+
+$$
+\begin{array} { r } { \boldsymbol { c } _ { k } \gets \mathrm { N o r m a l i z e } ( m \boldsymbol { c } _ { k } + ( 1 - m ) \boldsymbol { z } _ { i } ) , \forall i \in \{ i \mid \hat { y } _ { i } = k \} , } \end{array}
+$$
+
+where ${ \mathrm { N o r m a l i z e } } ( c ) = c / \left\| c \right\| _ { 2 }$ . The momentum coefficient $m$ is set 0.999 in our experiments.
+
+# 4 EXPERIMENTS
+
+# 4.1 DATASET FOR UPSTREAM TRAINING
+
+We use the WebVision (Li et al., 2017) dataset as the noisy training data. It consists of images automatically crawled from Google and Flickr, using visual concepts from ImageNet as queries. We experiment with three versions of WebVision with different sizes: (1) WebVision-V1.0 contains $2 . 4 4 \mathrm { m }$ images with the same classes as the ImageNet-1k (ILSVRC 2012) dataset; (2) WebVisionV0.5 is a randomly sampled subset of WebVision-V1.0, which contains the same number of images $( 1 . 2 8 \mathrm { m } )$ as ImageNet-1k; (3) WebVision- $. \mathrm { V } 2 . 0$ contains $1 6 \mathrm m$ images with 5k classes.
+
+# 4.2 IMPLEMENTATION DETAILS
+
+We follow standard settings for ImageNet training: batch size is 256; total number of epochs is 90; optimizer is SGD with a momentum of 0.9; initial learning rate is 0.1, decayed at 40 and 80 epochs; weight decay is 0.0001. We use ResNet-50 (He et al., 2016) as the encoder. For MoProspecific hyperparameters, we set $\tau = 0 . 1 , \alpha = 0 . 5 , T = 0 . 8$ $T = 0 . 6$ for WebVision-V2.0). The momentum for both the momentum encoder and momentum prototypes is set as 0.999. The queue to store momentum embeddings has a size of 8192. We apply standard data augmentation (crop and horizontal flip) to the encoder’s input, and stronger data augmentation (color changes in MoCo (He et al., 2019)) to the momentum encoder’s input. We warm-up the model for 10 epochs by training on all samples with original labels, before applying noise correction.
+
+# 4.3 UPSTREAM TASK PERFORMANCE
+
+In Table 1, we compare MoPro with existing weakly-supervised learning methods trained on WebVision-V1.0, where MoPro achieves state-of-the-art performance. Since the training dataset has imbalanced number of samples per-class, inspired by Kang et al. (2020), we perform the following decoupled training steps to re-balance the classifier: (1) pretrain the model with MoPro; (2) perform noise correction on the training data using the pretrained model, following the method in Section 3.3; (3) keep the pretrained encoder fixed and finetune the classifier on the cleaned dataset, using square-root data sampling (Mahajan et al., 2018) which balances the classes. We retrain the classifier for 15 epochs, using a learning rate of 0.01 which is decayed at 5 and 10 epochs. Surprisingly, we also find that a vanilla cross-entropy method with decoupled classifier re-balancing can also achieve competitive performance, outperforming most existing baselines.
+
+Table 1: Comparison with state-of-the-art methods on WebVision-V1.0. Numbers denote accuracy $( \% )$ on the clean WebVision-V1.0 validation set and the ILSVRC 2012 validation set. CleanNet (Lee et al., 2018) and Distill (Zhang et al., 2020) require data with clean annotations.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Architecture</td><td colspan="2">WebVision</td><td colspan="2">ImageNet</td></tr><tr><td>top-1</td><td>top-5</td><td>top-1</td><td>top-5</td></tr><tr><td>Cross-Entropy (Tu et al., 2020)</td><td>ResNet-50</td><td>66.4</td><td>83.4</td><td>57.7</td><td>78.4</td></tr><tr><td>MentorNet (Jiang et al.,2018)</td><td>InceptionResNet-V2</td><td>70.8</td><td>88.0</td><td>62.5</td><td>83.0</td></tr><tr><td>CurriculumNet (Guo et al., 2018)</td><td>Inception-V2</td><td>72.1</td><td>89.1</td><td>64.8</td><td>84.9</td></tr><tr><td>CleanNet (Lee et al.,2018)</td><td>ResNet-50</td><td>70.3</td><td>87.8</td><td>63.4</td><td>84.6</td></tr><tr><td>CurriculumNet (Guo et al., 2018; Tu et al., 2020)</td><td>ResNet-50</td><td>70.7</td><td>88.6</td><td>62.7</td><td>83.4</td></tr><tr><td>SOM (Tu et al., 2020)</td><td>ResNet-50</td><td>72.2</td><td>89.5</td><td>65.0</td><td>85.1</td></tr><tr><td>Distill (Zhang et al.,2020)</td><td>ResNet-50</td><td>1</td><td>-</td><td>65.8</td><td>85.8</td></tr><tr><td>Cross-Entropy (decoupled)</td><td>ResNet-50</td><td>72.4</td><td>89.0</td><td>65.7</td><td>85.1</td></tr><tr><td>MoPro (ours)</td><td>ResNet-50</td><td>73.9</td><td>90.0</td><td>67.8</td><td>87.0</td></tr></table>
+
+# 5 TRANSFER LEARNING
+
+In this section, we transfer weakly-supervised learned models to a variety of downstream tasks. We show that MoPro yields superior performance in image classification, object detection, instance segmentation, and obtains better robustness to domain shifts. Implementation details for the transfer learning experiments are described in appendix C.
+
+# 5.1 LOW-SHOT IMAGE CLASSIFICATION ON FIXED REPRESENTATION
+
+First, we transfer the learned representation to downstream tasks with few training samples. We perform low-shot classification on two datasets: PASCAL VOC2007 (Everingham et al., 2010) for object classification and Places205 (Zhou et al., 2014) for scene recognition. Following the setup by Goyal et al. (2019); Li et al. (2020b), we train linear SVMs using fixed representations from pretrained models. We vary the number $k$ of samples per-class and report the average result across 5 independent runs. Table 2 shows the results. When pretrained on weakly-labeled datasets, MoPro consistently outperforms the vanilla CE method. The improvement of MoPro becomes less significant when the number of web images increases from $2 . 4 \mathrm { m }$ to $1 6 \mathrm m$ , suggesting that increasing dataset size is a viable solution to combat noise.
+
+Table 2: Low-shot image classification on VOC07 and Places205 using linear SVMs trained on fixed representations. We vary the number of labeled examples per-class $( k )$ , and report the average mAP (for VOC) and accuracy (for Places) across 5 independent runs. WebVision-V0.5 has the same number of training samples as ImageNet. The self-supervised learning methods∗ are trained for 200 epochs, while other methods are trained for 90 epochs. MoPro outperforms vanilla CE pretrained on Web datasets, as well as self-supervised learning and supervised learning methods pretrained on ImageNet.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Pretrain dataset</td><td colspan="5">vOC07</td><td colspan="5">Places205</td></tr><tr><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=16|</td><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=16</td></tr><tr><td>MoCo v2* PCL v2*</td><td>ImageNet ImageNet</td><td>46.3 47.9</td><td>58.4 59.6</td><td>64.9 66.2</td><td>72.5 74.5</td><td>76.1 78.3</td><td>11.9 12.5</td><td>17.0 17.5</td><td>22.6 23.2</td><td>28.1 28.1</td><td>32.4 32.3</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>54.3</td><td>67.8</td><td>73.9</td><td>79.6</td><td>82.3</td><td>14.9</td><td>21.0</td><td>26.9</td><td>32.1</td><td>36.0</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V0.5</td><td>49.8 54.3</td><td>63.9 67.8</td><td>69.9</td><td>76.1</td><td>79.2</td><td>13.5</td><td>19.3</td><td>24.7</td><td>29.5</td><td>33.8</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V1.0</td><td>54.5</td><td>67.1</td><td>73.5 72.8</td><td>79.2 78.4</td><td>81.8 81.4</td><td>15.0 15.1</td><td>21.2 21.5</td><td>26.6 27.2</td><td>31.8 32.1</td><td>36.0 36.4</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V2.0</td><td>59.5 63.0 64.8 74.8</td><td>71.3 73.8 79.9</td><td>76.5 78.7</td><td>81.4 83.0</td><td>83.7 85.4</td><td>16.9 21.8 22.2</td><td>23.2 28.6</td><td>29.2 35.1</td><td>34.5 40.0</td><td>38.7 43.6</td></tr></table>
+
+When compared with ImageNet pretrained models, MoPro substantially outperforms self-supervised learning (MoCo v2 (Chen et al., 2020b) and PCL v2 (Li et al., 2020b)), and achieves comparable performance with supervised learning when the same amount of web images (i.e. WebVision-V0.5) is used. Our results for the first time show that weakly-supervised representation learning can be as powerful as supervised representation learning under the same data and computation budget.
+
+# 5.2 LOW-RESOURCE TRANSFER WITH FINETUNING
+
+Next, we perform experiment to evaluate whether the pretrained model provides a good basis for finetuning when the downstream task has limited training data. Following the setup by Chen et al. (2020a), we finetune the pretrained model on $1 \%$ or $1 0 \%$ of ImageNet training samples. Table 3 shows the results. MoPro consistently outperforms CE when pretrained on Web datasets. Compared to self-supervised learning methods pretrained on ImageNet, weakly-supervised learning achieves significantly better performance with fewer number of epochs.
+
+Surprisingly, pretraining on the larger WebVision-V2 leads to worse performance compared to ${ \mathrm { V } } 0 . 5$ and V1.0. This is because WebVision- $. \mathrm { V } 0 . 5$ and $\mathrm { V } 1 . 0$ contain the same 1k class as ImageNet, whereas V2 also contains $4 \mathrm { k }$ extra classes. Hence, the representations learned from V2 are less task-specific and more difficult to adapt to ImageNet, especially with only $1 \%$ of samples for finetuning. This suggests that if the classes for a downstream task are known a priori, it is more effective to curate a task-specific weakly-labeled dataset with the same classes.
+
+Table 3: Low-resource finetuning on ImageNet. A pretrained model is finetuned with $1 \%$ or $10 \%$ of ImageNet training data. Weakly-supervised learning with MoPro substantially outperforms self-supervised learning methods: PCL (Li et al., 2020b), SimCLR (Chen et al., 2020a), BYOL (Grill et al., 2020), and SwAV (Caron et al., 2020). Result for random init. is from Zhai et al. (2019).   
+
+<table><tr><td></td><td>Pretrain Method</td><td>Pretrain dataset</td><td>#Pretrain epochs</td><td>Top-1 1% 10%</td><td>Top-5 1%</td><td>10%</td></tr><tr><td>Random init.</td><td>None</td><td>None</td><td>None</td><td>25.4 56.4</td><td>48.4</td><td>80.4</td></tr><tr><td rowspan="3">Self-supervised</td><td>PCL SimCLR</td><td>ImageNet</td><td>200 1000</td><td>48.8 48.3</td><td>62.9 75.3 65.6 75.5</td><td>85.6 87.8</td></tr><tr><td>BYOL</td><td></td><td>1000</td><td>53.2</td><td>68.8 78.4</td><td>89.0</td></tr><tr><td>SwAV</td><td></td><td>800</td><td>53.9</td><td>70.2 78.5</td><td>89.9</td></tr><tr><td rowspan="4">Weakly-supervised</td><td>CE MoPro (ours)</td><td>WebVision-V0.5</td><td>90</td><td>65.9 69.3</td><td>72.4 73.3</td><td>87.0 90.9 91.7</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V1.0</td><td>90</td><td>67.6 73.5</td><td>89.1 88.3</td><td>91.7</td></tr><tr><td>CE</td><td></td><td></td><td>71.2 74.8 62.1 72.9</td><td>90.5 86.9</td><td>92.4</td></tr><tr><td>MoPro (ours)</td><td>WebVision-V2.0</td><td>90</td><td>65.3 73.7</td><td>88.2</td><td>91.4 92.1</td></tr></table>
+
+# 5.3 OBJECT DETECTION AND INSTANCE SEGMENTATION
+
+We further transfer the pretrained model to object detection and instance segmentation tasks on COCO (Lin et al., 2014). Following the setup by He et al. (2019), we use the pretrained ResNet-50 as the backbone for a Mask-RCNN (He et al., 2017) with FPN (Lin et al., 2017). We finetune all layers end-to-end, including BN. The schedule is the default $1 \times$ or $2 \times$ in Girshick et al. (2018) Table 4 shows the results. Weakly-supervised learning with MoPro outperforms both supervised learning on ImageNet and self-supervised learning on one billion Instagram images.
+
+# 5.4 ROBUSTNESS
+
+It has been shown that deep models trained on ImageNet lack robustness to out-of-distribution samples, often falsely producing over-confident predictions. Hendricks et al. have curated two benchmark datasets to evaluate models’ robustness to real-world distribution variation: (1) ImageNetR (Hendrycks et al., 2020) which contains various artistic renditions of object classes from the original ImageNet dataset, and (2) ImageNet-A (Hendrycks et al., 2019) which contains natural images where ImageNet-pretrained models consistently fail due to variations in background elements, color, or texture. Both datasets contain 200 classes, a subset of ImageNet’s 1,000 classes.
+
+<table><tr><td>Method</td><td>Pretrain dataset</td><td>Apbb AP</td><td>AP</td><td>Apmk</td><td>AP</td><td>AP</td></tr><tr><td>random</td><td>None</td><td>31.0 49.5</td><td>33.2</td><td>28.5</td><td>46.8</td><td>30.4</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>38.9 59.6</td><td>42.7</td><td>35.4</td><td>56.5</td><td>38.1</td></tr><tr><td>MoCo</td><td>Instagram-1B</td><td>38.9 59.4</td><td>42.3</td><td>35.4</td><td>56.5</td><td>37.9</td></tr><tr><td>CE</td><td>WebVision-V1.0</td><td>39.2 60.0</td><td>42.9</td><td>35.6</td><td>56.8</td><td>38.0</td></tr><tr><td>MoPro MoPro</td><td>WebVision-V2.0</td><td>39.7 (+0.8) 40.7 (+1.8)</td><td>60.9 (+1.3) 43.1 (+0.4)</td><td>36.1 (+0.7) 36.8 (+1.4)</td><td>57.5 (+1.0) 58.4 (+1.9)</td><td>38.6 (+0.5) ）39.6 (+1.5)</td></tr><tr><td colspan="7">61.7 (+2.1) 44.5 (+1.8) (a) 1× schedule</td></tr><tr><td>Method</td><td>Pretrain dataset</td><td>Apbb AP</td><td>AP</td><td>Apmk</td><td></td><td></td></tr><tr><td>random</td><td>None</td><td>36.7</td><td>40.0</td><td>33.7</td><td>AP 53.8</td><td>AP 35.9</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>40.6</td><td>44.4</td><td>36.8</td><td>58.1</td><td>39.5</td></tr><tr><td>MoCo</td><td>Instagram-1B</td><td>41.1</td><td>45.1</td><td>37.4</td><td>59.1</td><td>40.2</td></tr><tr><td>CE MoPro</td><td>WebVision-V1.0</td><td>40.9</td><td>44.7</td><td>37.2</td><td>58.7</td><td>40.1</td></tr><tr><td>MoPro</td><td>WebVision-V2.0</td><td>41.2 (+0.6) 41.8 (+1.2)</td><td>62.2 (+0.9) 45.0 (+0.6) 62.6 (+1.3) 45.6 (+1.2)</td><td>37.4 (+0.6) 37.8 (+1.0)</td><td>58.9 (+0.8) 59.5 (+1.4)</td><td>40.3 (+0.8) 40.6 (+1.1)</td></tr></table>
+
+(a) $2 \times$ schedule
+
+Table 4: Object detection and instance segmentation using Mask-RCNN with R50-FPN fine-tuned on COCO train2017. We evaluate bounding-box AP $( \mathsf { A P } ^ { \mathsf { b b } } )$ and mask AP $( \mathbf { A P } ^ { \mathrm { m k } } )$ on $\mathtt { v a l } 2 0 1 7$ . Weaklysupervised learning with MoPro outperforms both supervised learning on ImageNet and self-supervised learning (MoCo (He et al., 2019)) on one billion Instagram images.   
+Table 5: Evaluation of model robustness on images with artistic and natural distribution shifts. Weakly supervised learning with MoPro leads to a more robust and well-calibrated model.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Pretrain dataset</td><td colspan="2">ImageNet-R</td><td colspan="2">ImageNet-A</td></tr><tr><td>Accuracy (↑)</td><td>Calib. Error(↓）</td><td>Accuracy (↑)</td><td>Calib. Error (↓)</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>36.14</td><td>19.66</td><td>0.03</td><td>62.50</td></tr><tr><td>CE</td><td rowspan="2">WebVision-V1.0</td><td>49.56</td><td>10.05</td><td>10.24</td><td>37.84</td></tr><tr><td>MoPro</td><td> 54.87</td><td> 5.73</td><td>11.93</td><td>35.85</td></tr></table>
+
+We evaluate weakly-supervised trained models on these two robustness benchmarks. We report both accuracy and the $\ell _ { 2 }$ calibration error (Kumar et al., 2019). The calibration error measures the misalignment between a model’s confidence and its accuracy. Concretely, a well-calibrated classifier which give examples $80 \%$ confidence should be correct $80 \%$ of the time. Results are shown in Table 5. Webly-supervised learning show significantly higher accuracy and lower calibration error. The robustness to distribution shift could come from the higher diversity of samples in Web images. Compared to vanilla CE, MoPro further improves the model’s robustness on both datasets. Note that we made sure that the training data of WebVision does not overlap with the test data.
+
+# 6 ABLATION STUDY
+
+We perform ablation study to verify the effectiveness of three important components in MoPro: (1) prototypical contrastive loss ${ \mathcal { L } } _ { \mathrm { p r o } }$ , (2) instance contrastive loss ${ \mathcal { L } } _ { \mathrm { i n s } }$ , (3) prototypical similarity $\mathbf { \boldsymbol { s } } _ { i }$ used for noise correction (equation 4). We choose low-resource finetuning on $1 \%$ of ImageNet training data as the benchmark, and report the top-1 accuracy for models pretrained on WebVisionV0.5. As shown in Table 6, all of the three components contribute to the efficacy of MoPro.
+
+# 7 CONCLUSION
+
+This paper introduces a new contrastive learning framework for webly-supervised representation learning. We propose momentum prototypes, a simple component that is effective in label noise
+
+<table><tr><td></td><td>MoPro</td><td>w/oLpro</td><td></td><td></td><td>w/o Linst |w/o si (i.e.α =1) | w/o Lpro &amp; Linst &amp;si</td><td>CE</td></tr><tr><td>ImageNet acc.</td><td>69.3</td><td>68.0</td><td>68.2 一</td><td>68.4</td><td>一 66.9</td><td>65.9</td></tr></table>
+
+Table 6: Ablation study where different components are removed from MoPro. Models are pre-trained on WebVision-V0.5 and finetuned on $1 \%$ of ImageNet data.
+
+correction, OOD sample removal, and representation learning. MoPro achieves state-of-the-art performance on the upstream task of learning from real-world noisy data, and superior representation learning performance on multiple down-stream tasks. Webly-supervised learning with MoPro does not require the expensive annotation cost in supervised learning, nor the huge computation budget in self-supervised learning. For future work, MoPro could be extended to utilize other sources of free Web data, such as weakly-labeled videos, for representation learning in other domains.
+
+# REFERENCES
+
+Eric Arazo, Diego Ortego, Paul Albert, Noel E. O’Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In ICML, pp. 312–321, 2019.   
+Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. arXiv preprint arXiv:2006.09882, 2020.   
+Pengfei Chen, Benben Liao, Guangyong Chen, and Shengyu Zhang. Understanding and utilizing deep neural networks trained with noisy labels. In ICML, pp. 1062–1070, 2019.   
+Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, 2020a.   
+Xinlei Chen and Abhinav Gupta. Webly supervised learning of convolutional networks. In ICCV, pp. 1431–1439, 2015.   
+Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He. Improved baselines with momentum contrastive learning. arXiv preprint arXiv:2003.04297, 2020b.   
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Fei-Fei Li. Imagenet: A large-scale hierarchical image database. In CVPR, pp. 248–255, 2009.   
+Santosh Kumar Divvala, Ali Farhadi, and Carlos Guestrin. Learning everything about anything: Webly-supervised visual concept learning. In CVPR, pp. 3270–3277, 2014.   
+Mark Everingham, Luc Van Gool, Christopher K. I. Williams, John M. Winn, and Andrew Zisserman. The pascal visual object classes (VOC) challenge. International Journal of Computer Vision, 88(2):303–338, 2010.   
+Rong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, Xiang-Rui Wang, and Chih-Jen Lin. LIBLINEAR: A library for large linear classification. JMLR, 9:1871–1874, 2008.   
+Ross Girshick, Ilija Radosavovic, Georgia Gkioxari, Piotr Dollar, and Kaiming He. Detectron. ´ https://github.com/facebookresearch/detectron, 2018.   
+Priya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra. Scaling and benchmarking selfsupervised visual representation learning. In ICCV, pp. 6391–6400, 2019.   
+Jean-Bastien Grill, Florian Strub, Florent Altche, Corentin Tallec, Pierre H. Richemond, Elena ´ Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, Bilal Piot, Koray Kavukcuoglu, Remi Munos, and Michal Valko. Bootstrap your own ´ latent: A new approach to self-supervised learning. arXiv preprint arXiv:2006.07733, 2020.   
+Sheng Guo, Weilin Huang, Haozhi Zhang, Chenfan Zhuang, Dengke Dong, Matthew R. Scott, and Dinglong Huang. Curriculumnet: Weakly supervised learning from large-scale web images. In ECCV, pp. 139–154, 2018.
+
+Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor W. Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In NeurIPS, pp. 8536–8546, 2018.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, pp. 770–778, 2016.
+
+Kaiming He, Georgia Gkioxari, Piotr Dollar, and Ross B. Girshick. Mask R-CNN. In ´ ICCV, pp. 2980–2988, 2017.
+
+Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. arXiv preprint arXiv:1911.05722, 2019.
+
+Dan Hendrycks, Kevin Zhao, Steven Basart, Jacob Steinhardt, and Dawn Song. Natural adversarial examples. arXiv preprint arXiv:1907.07174, 2019.
+
+Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, et al. The many faces of robustness: A critical analysis of out-of-distribution generalization. arXiv preprint arXiv:2006.16241, 2020.
+
+Lu Jiang, Zhengyuan Zhou, Thomas Leung, Li-Jia Li, and Li Fei-Fei. Mentornet: Learning datadriven curriculum for very deep neural networks on corrupted labels. In ICML, pp. 2309–2318, 2018.
+
+Lu Jiang, Di Huang, Mason Liu, and Weilong Yang. Beyond synthetic noise: Deep learning on controlled noisy labels. In ICML, 2020.
+
+Armand Joulin, Laurens van der Maaten, Allan Jabri, and Nicolas Vasilache. Learning visual features from large weakly supervised data. In Bastian Leibe, Jiri Matas, Nicu Sebe, and Max Welling (eds.), ECCV, 2016.
+
+Bingyi Kang, Saining Xie, Marcus Rohrbach, Zhicheng Yan, Albert Gordo, Jiashi Feng, and Yannis Kalantidis. Decoupling representation and classifier for long-tailed recognition. In ICLR, 2020.
+
+Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Joan Puigcerver, Jessica Yung, Sylvain Gelly, and Neil Houlsby. Large scale learning of general visual representations for transfer. In ECCV, 2020.
+
+Ananya Kumar, Percy Liang, and Tengyu Ma. Verified uncertainty calibration. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alche-Buc, Emily B. Fox, and Roman ´ Garnett (eds.), NeurIPS, pp. 3787–3798, 2019.
+
+Kuang-Huei Lee, Xiaodong He, Lei Zhang, and Linjun Yang. Cleannet: Transfer learning for scalable image classifier training with label noise. In CVPR, pp. 5447–5456, 2018.
+
+Junnan Li, Yongkang Wong, Qi Zhao, and Mohan S. Kankanhalli. Learning to learn from noisy labeled data. In CVPR, pp. 5051–5059, 2019.
+
+Junnan Li, Richard Socher, and Steven C.H. Hoi. Dividemix: Learning with noisy labels as semisupervised learning. In ICLR, 2020a.
+
+Junnan Li, Pan Zhou, Caiming Xiong, Richard Socher, and Steven C.H. Hoi. Prototypical contrastive learning of unsupervised representations. arXiv preprint arXiv:2005.04966, 2020b.
+
+Wen Li, Limin Wang, Wei Li, Eirikur Agustsson, and Luc Van Gool. Webvision database: Visual learning and understanding from web data. arXiv preprint arXiv:1708.02862, 2017.
+
+Tsung-Yi Lin, Michael Maire, Serge J. Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollar, and C. Lawrence Zitnick. Microsoft COCO: common objects in context. In ´ ECCV, pp. 740–755, 2014.
+
+Tsung-Yi Lin, Piotr Dollar, Ross B. Girshick, Kaiming He, Bharath Hariharan, and Serge J. Be-´ longie. Feature pyramid networks for object detection. In CVPR, pp. 936–944, 2017.
+
+Xingjun Ma, Yisen Wang, Michael E. Houle, Shuo Zhou, Sarah M. Erfani, Shu-Tao Xia, Sudanthi N. R. Wijewickrema, and James Bailey. Dimensionality-driven learning with noisy labels. In ICML, pp. 3361–3370, 2018.   
+Dhruv Mahajan, Ross B. Girshick, Vignesh Ramanathan, Kaiming He, Manohar Paluri, Yixuan Li, Ashwin Bharambe, and Laurens van der Maaten. Exploring the limits of weakly supervised pretraining. In ECCV, pp. 185–201, 2018.   
+Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018.   
+Scott E. Reed, Honglak Lee, Dragomir Anguelov, Christian Szegedy, Dumitru Erhan, and Andrew Rabinovich. Training deep neural networks on noisy labels with bootstrapping. In ICLR, 2015.   
+Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. In ICCV, pp. 843–852, 2017.   
+Daiki Tanaka, Daiki Ikami, Toshihiko Yamasaki, and Kiyoharu Aizawa. Joint optimization framework for learning with noisy labels. In CVPR, pp. 5552–5560, 2018.   
+Yi Tu, Li Niu, Dawei Cheng, and Liqing Zhang. Protonet: Learning from web data with memory. In CVPR, 2020.   
+Arash Vahdat. Toward robustness against label noise in training deep discriminative neural networks. In NIPS, pp. 5601–5610, 2017.   
+Andreas Veit, Neil Alldrin, Gal Chechik, Ivan Krasin, Abhinav Gupta, and Serge J. Belongie. Learning from noisy large-scale datasets with minimal supervision. In CVPR, pp. 6575–6583, 2017.   
+Yisen Wang, Weiyang Liu, Xingjun Ma, James Bailey, Hongyuan Zha, Le Song, and Shu-Tao Xia. Iterative learning with open-set noisy labels. In CVPR, pp. 8688–8696, 2018.   
+Zhirong Wu, Yuanjun Xiong, Stella X. Yu, and Dahua Lin. Unsupervised feature learning via nonparametric instance discrimination. In CVPR, pp. 3733–3742, 2018.   
+Tong Xiao, Tian Xia, Yi Yang, Chang Huang, and Xiaogang Wang. Learning from massive noisy labeled data for image classification. In CVPR, pp. 2691–2699, 2015.   
+Jingkang Yang, Litong Feng, Weirong Chen, Xiaopeng Yan, Huabin Zheng, Ping Luo, and Wayne Zhang. Webly supervised image classification with self-contained confidence. In ECCV, 2020.   
+Kun Yi and Jianxin Wu. Probabilistic end-to-end noise correction for learning with noisy labels. In CVPR, 2019.   
+Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. S4l: Self-supervised semisupervised learning. In ICCV, pp. 1476–1485, 2019.   
+Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017.   
+Weihe Zhang, Yali Wang, and Yu Qiao. Metacleaner: Learning to hallucinate clean representations for noisy-labeled visual recognition. In CVPR, 2019.   
+Zizhao Zhang, Han Zhang, Sercan Omer Arik, Honglak Lee, and Tomas Pfister. Distilling effective ¨ supervision from severe label noise. In CVPR, pp. 9291–9300, 2020.   
+Bolei Zhou, Agata Lapedriza, Jianxiong Xiao, Antonio Torralba, and Aude Oliva. Learning deep \` features for scene recognition using places database. In NIPS, pp. 487–495, 2014.
+
+# APPENDIX A NOISY SAMPLE VISUALIZATION
+
+In Figure 3, we show example images randomly chosen from the out-of-distribution samples filtered out by our method. In Figure 4, we show random examples where their pseudo-labels are different from the original training labels. By visual examination, we observe that our method can remove OOD samples and correct noisy labels at a high success rate.
+
+![](images/c371cc7a6aab2aade8f5011917c72d9e0c3d62d0338e457a7a654999320c671b.jpg)  
+Figure 3: Examples of randomly selected out-of-distribution samples filtered out by our method. The original training labels are shown below the images.
+
+![](images/7864b0659767aad1402685a6c680cc0068f4f7b997ffc69b896ef1cab2052ffb.jpg)  
+Figure 4: Examples of randomly selected samples with noisy labels corrected by our method. The original training labels are shown in red and corrected pseudo-labels are shown in green.
+
+# APPENDIX B PSEUDO-CODE OF MOPRO
+
+Algorithm 1 summarizes the proposed method.
+
+Algorithm 1: MoPro’s main algorithm.
+
+1 Input: number of classes $K$ , temperature $\tau$ , threshold $T$ , momentum $m$ , encoder network $f ( \cdot )$ , projection network $g ( \cdot )$ , classifier $h ( \cdot )$ , momentum encoder $g ^ { \prime } ( f ^ { \prime } ( \cdot ) )$ .
+
+2 for $\bar { \{ ( x _ { i } , y _ { i } ) \} } _ { i = 1 } ^ { b }$ in loader do // load a minibatch of noisy training data   
+3 for $i \in \{ 1 , . . . , b \}$ do   
+4 $\tilde { \mathbf { x } } _ { i } = \mathrm { w e a k . a u g } ( \mathbf { \mathbf { x } } _ { i } )$ // weak augmentation   
+5 $\tilde { \pmb { x } } _ { i } ^ { \prime } = \mathrm { s t r o n g . a u g } ( \pmb { x } _ { i } )$ // strong augmentation   
+6 vi = f (x˜i) // representation   
+7 zi = g(vi) // normalized low-dimensional embedding   
+8 zi = g 0 (f 0 (x˜ 0i )) // momentum embedding   
+10 9 si = {ski }Kk=1 , ski = pi = h(vi) P exp(zi·ck/τ)Kk=1 exp(zi·ck/τ) // prototypical score // class prediction   
+// noise correction   
+11 $\pmb { q } _ { i } = ( \pmb { p } _ { i } + \pmb { s } _ { i } ) / 2$ // soft pseudo-label   
+12 if maxk $q _ { i } ^ { k } > T$ then   
+13 $\hat { y } _ { i } = \arg \operatorname* { m a x } _ { k } q _ { i } ^ { k }$   
+14 else if $q _ { i } ^ { y _ { i } } > 1 / K$ then   
+15 $\hat { y } _ { i } = y _ { i }$   
+16 else   
+17 $\mathbf { \Pi } _ { \mathbf { e n d } } ^ { | \mathbf { \Pi } _ { \hat { y } _ { i } } = \operatorname { O O D } }$   
+18   
+// calculate losses   
+19 $\begin{array} { r } { \mathcal { L } _ { \mathrm { i n s } } ^ { i } = - \log \frac { \exp ( z _ { i } \cdot z _ { i } ^ { \prime } / \tau ) } { \sum _ { r = 0 } ^ { R } \exp ( z _ { i } \cdot z _ { r } ^ { \prime } / \tau ) } } \end{array}$ // instance contrastive loss   
+20 if $\hat { y } _ { i }$ is not OOD then   
+21 $\begin{array} { r l } & { \dot { \mathcal { L } } _ { \mathrm { p r o } } ^ { i } = - \log \frac { \exp ( z _ { i } \cdot c _ { \hat { y } _ { i } } / \tau ) } { \sum _ { k = 1 } ^ { K } \exp ( z _ { i } \cdot c _ { k } / \tau ) } } \\ & { \dot { \mathcal { L } } _ { \mathrm { c e } } ^ { i } = - \log ( p _ { i } ^ { \hat { y } _ { i } } ) } \end{array}$ // prototypical contrastive loss   
+22 // cross entropy loss   
+23 else   
+24 Lipr o = L ice = 0   
+25 end   
+/ update momentum prototypes   
+26 $\pmb { c } _ { \hat { y } _ { i } } \gets \mathrm { N o r m a l i z e } ( m \pmb { c } _ { \hat { y } _ { i } } + ( 1 - m ) \pmb { z } _ { i } )$   
+27 end   
+28 $\begin{array} { r } { \mathcal { L } = \sum _ { i = 1 } ^ { b } ( \mathcal { L } _ { \mathrm { c e } } ^ { i } + \mathcal { L } _ { \mathrm { p r o } } ^ { i } + \mathcal { L } _ { \mathrm { i n s } } ^ { i } ) } \end{array}$ // total loss   
+29 update networks $f , g , h$ to minimize $\mathcal { L }$ .   
+30 end
+
+# APPENDIX C TRANSFER LEARNING IMPLEMENTATION DETAILS
+
+For low-shot image classification on Places and VOC, we follow the procedure in Li et al. (2020b) and train linear SVMs on the global average pooling features of ResNet-50. We preprocess all images by resizing to 256 pixels along the shorter side and taking a $2 2 4 \times 2 2 4$ center crop. The SVMs are implemented in the LIBLINEAR (Fan et al., 2008) package.
+
+For low-resource finetuning on ImageNet, we adopt different finetuning strategy for different versions of WebVision pretrained models. For WebVision V0.5 and V1.0, since they contain the same 1000 classes as ImageNet, we finetune the entire model including the classification layer. We train with SGD, using a batch size of 256, a momentum of 0.9, a weight decay of 0, and a learning rate of 0.005. We train for 40 epochs, and drop the learning rate by 0.2 at 15 and 30 epochs. For WebVision 2.0, since it contains 5000 classes, we randomly initialize a new classification layer with 1000 output dimension, and finetune the model end-to-end. We train for 50 epochs, using a learning rate of 0.01, which is dropped by 0.1 at 20 and 40 epochs.
+
+For object detection and instance segmentation on COCO, we adopt the same setup in MoCo (He et al., 2019), using Detectron2 (Girshick et al., 2018) codebase. The image scale is in [640, 800] pixels during training and is 800 at inference. We fine-tune all layers end-to-end. We finetune on the train2017 set $\mathord { \sim } 1 1 8 \mathrm { k }$ images) and evaluate on val2017.
+
+# APPENDIX D STANDARD DEVIATION FOR LOW-SHOT CLASSIFICATION
+
+Table 7 reports the standard deviation for the low-shot image classification experiment in Section 5.1.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Pretrain dataset</td><td colspan="4">VOC07</td><td colspan="4">Places205</td></tr><tr><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td></tr><tr><td>CE(Sup.)]</td><td>）ImageNet</td><td>[54.3±4.8 67.8±4.4 73.9±0.9 79.6±0.8|</td><td></td><td></td><td></td><td></td><td>14.9±1.3 21.0±0.3 26.9±0.6 32.1±0.4</td><td></td><td></td></tr><tr><td>MoPro</td><td>WebVision-V1.0</td><td></td><td>59.5±5.2 71.3±2.2</td><td>76.5±1.18</td><td>181.4±0.6</td><td></td><td>16.9±1.3 23.2±0.31</td><td>29.2±0.6 34.5±0.3</td><td></td></tr><tr><td>MoPro</td><td>WebVision-V2.0</td><td></td><td>64.8±6.7 74.8±2.6 79.9±1.4 83.9±1.0</td><td></td><td></td><td></td><td>22.2±1.329.2±0.5</td><td>35.6±0.7 40.9±0.3</td><td></td></tr></table>
+
+Table 7: Low-shot image classification experiments. Mean and standard deviation are calculated across 5 runs.

parse/train/0-EYBhgw80y/0-EYBhgw80y_content_list.json

@@ -0,0 +1,1467 @@
+[
+    {
+        "type": "text",
+        "text": "MOPRO: WEBLY SUPERVISED LEARNING WITHMOMENTUM PROTOTYPES",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            743,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Junnan Li, Caiming Xiong, Steven C.H. Hoi Salesforce Research {junnan.li,cxiong,shoi}@salesforce.com ",
+        "bbox": [
+            183,
+            170,
+            553,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
+            544,
+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We propose a webly-supervised representation learning method that does not suffer from the annotation unscalability of supervised learning, nor the computation unscalability of self-supervised learning. Most existing works on weblysupervised representation learning adopt a vanilla supervised learning method without accounting for the prevalent noise in the training data, whereas most prior methods in learning with label noise are less effective for real-world large-scale noisy data. We propose momentum prototypes (MoPro), a simple contrastive learning method that achieves online label noise correction, out-of-distribution sample removal, and representation learning. MoPro achieves state-of-the-art performance on WebVision, a weakly-labeled noisy dataset. MoPro also shows superior performance when the pretrained model is transferred to down-stream image classification and detection tasks. It outperforms the ImageNet supervised pretrained model by $+ 1 0 . 5$ on 1-shot classification on VOC, and outperforms the best self-supervised pretrained model by $+ 1 7 . 3$ when finetuned on $1 \\%$ of ImageNet labeled samples. Furthermore, MoPro is more robust to distribution shifts. Code and pretrained models are available at https://github.com/ salesforce/MoPro. ",
+        "bbox": [
+            233,
+            281,
+            764,
+            516
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            544,
+            336,
+            560
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large-scale datasets with human-annotated labels have revolutionized computer vision. Supervised pretraining on ImageNet (Deng et al., 2009) has been the de facto formula of success for almost all state-of-the-art visual perception models. However, it is extremely labor intensive to manually annotate millions of images, which makes it a non-scalable solution. One alternative to reduce annotation cost is self-supervised representation learning, which leverages unlabeled data. However, self-supervised learning methods (Goyal et al., 2019; He et al., 2019; Chen et al., 2020a; Li et al., 2020b) have yet consistently shown superior performance compared to supervised learning, especially when transferred to downstream tasks with limited labels. ",
+        "bbox": [
+            174,
+            575,
+            825,
+            686
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the help of commercial search engines, photo-sharing websites, and social media platforms, there is near-infinite amount of weakly-labeled images available on the web. Several works have exploited the scalable source of web images and demonstrated promising results with weblysupervised representation learning (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). However, there exists two competing claims on whether weakly-labeled noisy datasets lead to worse generalization performance. One claim argues that the effect of noise can be overpowered by the scale of data, and simply applies standard supervised learning method on web datasets (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). The other claim argues that deep models can easily memorize noisy labels, resulting in worse generalization (Zhang et al., 2017; Ma et al., 2018). In this paper, we show that both claims are partially true. While increasing the size of data does improve the model’s robustness to noise, our method can substantially boost the representation learning performance by addressing noise. ",
+        "bbox": [
+            174,
+            694,
+            825,
+            861
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There exists a large body of literature on learning with label noise (Jiang et al., 2018; Han et al., 2018; Guo et al., 2018; Tanaka et al., 2018; Arazo et al., 2019; Li et al., 2020a). However, existing methods have several limitations that make them less effective for webly-supervised representation learning. First, most methods do not consider out-of-distribution (OOD) samples, which is a major source of noise in real-world web datasets. Second, many methods perform computation-heavy procedures for noise cleaning (Jiang et al., 2018; Li et al., 2019; 2020a), or require access to a set of samples with clean labels (Vahdat, 2017; Veit et al., 2017; Lee et al., 2018), which limit their scalability in practice. ",
+        "bbox": [
+            176,
+            867,
+            823,
+            922
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7ecbcd588a47f787db2184fc5789e2871d9c82a7936417547c95e4d0aa45ea1f.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of the normalized embedding space learned with MoPro. Samples from the same class gather around their class prototype, whereas OOD samples are separated from in-distribution samples. Label correction and OOD removal are achieved based on a sample’s distance with the prototypes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            246,
+            103,
+            797,
+            304
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            390,
+            825,
+            445
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We propose a new method for efficient representation learning from weakly-labeled web images. Our method is inspired by recent developments in contrastive learning for self-supervised learning (He et al., 2019; Chen et al., 2020a; Li et al., 2020b) We introduce Momentum Prototypes (MoPro), a simple component which is effective in label noise correction, OOD sample removal, and representation learning. A visual explanation of our method is shown in Figure 1. We use a deep network to project images into normalized low-dimensional embeddings, and calculate the prototype for a class as the moving-average embedding for clean samples in that class. We train the network such that embeddings are pulled closer to their corresponding prototypes, while pushed away from other prototypes. Images with corrupted labels are corrected either as another class or as an OOD sample based on their distance to the momentum prototypes. ",
+        "bbox": [
+            173,
+            453,
+            825,
+            592
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We experimentally show that: ",
+        "bbox": [
+            176,
+            598,
+            370,
+            613
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• MoPro achieves state-of-the-art performance on the upstream weakly-supervised learning task. • MoPro substantially improves representation learning performance when the pretrained model is transferred to downstream image classification and object detection tasks. For the first time, we show that weakly-supervised representation learning achieves similar performance as supervised representation learning, under the same data and computation budget. With a larger web dataset, MoPro outperforms ImageNet supervised learning by a large margin. • MoPro learns a more robust and calibrated model that generalizes better to distribution variations. ",
+        "bbox": [
+            174,
+            619,
+            825,
+            727
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            751,
+            341,
+            766
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 WEBLY-SUPERVISED REPRESENTATION LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            785,
+            562,
+            799
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A number of prior works exploit large web datasets for visual representation learning (Divvala et al., 2014; Chen & Gupta, 2015; Joulin et al., 2016; Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017; Kolesnikov et al., 2020). These datasets contain a considerable amount of noise. Approximately $20 \\%$ of the labels in the JMT-300M dataset (Sun et al., 2017) are noisy, whereas $34 \\%$ of images in the WebVision dataset (Li et al., 2017) are considered outliers. Surprisingly, most prior works have chosen to ignore the noise and applied vanilla supervised method, with the claim that the scale of data can overpower the noise (Mahajan et al., 2018; Sun et al., 2017; Li et al., 2017). However, we show that supervised method cannot fully harvest the power of large-scale weakly-labeled datasets. ",
+        "bbox": [
+            174,
+            811,
+            825,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our method achieves substantial improvement by addressing noise, and advances the potential of webly-supervised representation learning. ",
+        "bbox": [
+            174,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 LEARNING WITH LABEL NOISE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            150,
+            428,
+            164
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Learning with label noise has been widely studied. Some methods require access to a small set of clean samples (Xiao et al., 2015; Vahdat, 2017; Veit et al., 2017; Lee et al., 2018; Zhang et al., 2020), and other methods assume that no clean labels are available. There exist two major types of approaches. The first type performs label correction using predictions from the network (Reed et al., 2015; Ma et al., 2018; Tanaka et al., 2018; Yi & Wu, 2019; Yang et al., 2020). The second type separates clean samples from corrupted samples, and trains the model on clean samples (Han et al., 2018; Arazo et al., 2019; Jiang et al., 2018; Wang et al., 2018; Chen et al., 2019; Li et al., 2020a). However, existing methods have yet shown promising results for large-scale weakly-supervised representation learning. The main reasons include: (1) most methods do not consider OOD samples, which commonly occur in real-world web datasets; (2) most methods are computational-heavy due to co-training (Han et al., 2018; Li et al., 2020a; Jiang et al., 2018; 2020), iterative training (Tanaka et al., 2018; Yi & Wu, 2019; Wang et al., 2018; Chen et al., 2019), or meta-learning (Li et al., 2019; Zhang et al., 2019). ",
+        "bbox": [
+            174,
+            178,
+            825,
+            357
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Different from existing methods, MoPro achieves both label correction and OOD sample removal on-the-fly with a single step, based on the similarity between an image embedding and the momentum prototypes. MoPro also leverages contrastive learning to learn a robust embedding space. ",
+        "bbox": [
+            176,
+            364,
+            821,
+            406
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 SELF-SUPERVISED REPRESENTATION LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            426,
+            545,
+            439
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised methods have been proposed for representation learning using unlabeled data. The recent developments in self-supervised representation learning can be attributed to contrastive learning. Most methods (He et al., 2019; Chen et al., 2020a; Oord et al., 2018; Wu et al., 2018) leverage the task of instance discrimination, where augmented crops from the same source image are enforced to have similar embeddings. Prototypical contrastive learning (PCL) (Li et al., 2020b) performs clustering to find prototypical embeddings, and enforces an image embedding to be similar to its assigned prototypes. Different from PCL, we update prototypes on-the-fly in a weakly-supervised setting, where the momentum prototype of a class is the moving average of clean samples’ embeddings. Furthermore, we jointly optimize two contrastive losses and a cross-entropy loss. ",
+        "bbox": [
+            174,
+            452,
+            825,
+            577
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Current self-supervised representation learning methods are limited in (1) inferior performance in low-shot task adaptation, (2) huge computation cost, and (3) inadequate to harvest larger datasets. We show that weakly-supervised learning with MoPro addresses these limitations. ",
+        "bbox": [
+            176,
+            584,
+            825,
+            626
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            647,
+            282,
+            664
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we delineate the details of our method. First, we introduce the components in our representation learning framework. Then, we describe the loss functions. Finally, we explain the noise correction procedure for label correction and OOD sample removal. A pseudo-code of MoPro is provided in appendix B. ",
+        "bbox": [
+            174,
+            680,
+            825,
+            736
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 REPRESENTATION LEARNING FRAMEWORK ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            755,
+            514,
+            768
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our proposed framework consists of the following components. Figure 2 gives an illustration. ",
+        "bbox": [
+            171,
+            781,
+            787,
+            796
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "• A noisy training dataset $\\{ ( \\pmb { x } _ { i } , y _ { i } ) \\} _ { i = 1 } ^ { n }$ , where $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ is an image and $y _ { i } \\in \\{ 1 , . . . , K \\}$ is its class label.   \n• A pseudo-label $\\hat { y } _ { i }$ for each image $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ , which is its corrected label. Details for generating the pseudo-label is explained in Sec 3.3.   \n• An encoder network, which maps an augmented image $\\tilde { \\mathbf { x } } _ { i }$ to a representation vector $\\pmb { v } _ { i } \\in \\mathbb { R } ^ { d _ { e } }$ . We experiment with ResNet-50 (He et al., 2016) as the encoder, where the activations of the final global pooling layer $\\langle d _ { e } = 2 0 4 8 \\rangle$ ) are used as the representation vector.   \n• A classifier (a fully-connected layer followed by softmax) which receives the representation ${ \\mathbf { } } v _ { i }$ as input and outputs class predictions $\\mathbf { \\nabla } p _ { i }$ . ",
+        "bbox": [
+            173,
+            803,
+            826,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/996d567d2a9b08e3b048509f78a32a9841e8e3c1a949bf71cfe1559f14de6277.jpg",
+        "image_caption": [
+            "Figure 2: Proposed weakly-supervised learning framework. We jointly optimize a prototypical contrastive loss using momentum prototypes, an instance contrastive loss using momentum embeddings, and a cross-entropy loss using pseudo-labels. The pseudo-label for a sample is generated based on its original training label, the model’s prediction, and the sample’s distance to the prototypes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            99,
+            818,
+            285
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "• A projection network, which maps the representation ${ \\mathbf { } } v _ { i }$ into a low-dimensional embedding $z _ { i } \\in$ $\\mathbb { R } ^ { \\hat { d } _ { p } }$ $\\bar { \\boldsymbol { d } } _ { p } = 1 2 8 )$ . $z _ { i }$ is always normalized to the unit sphere. Following SimCLR (Chen et al., 2020a), we use a MLP with one hidden layer as the projection network. • Momentum embeddings $ { \\boldsymbol { z } } _ { i } ^ { \\prime }$ generated by a momentum encoder. The momentum encoder has the same architecture as the encoder followed by the projection network, and its parameters are the moving-average of the encoder’s and the projection network’s parameters. Same as in MoCo (He et al., 2019), we maintain a queue of momentum embeddings of past samples. • Momentum prototypes $C \\in \\mathbb { R } ^ { d _ { p } \\times K }$ . The momentum prototype of the $k$ -th class, $\\scriptstyle c _ { k }$ , is the normalized moving-average embedding for samples with pseudo-label ${ \\hat { y } } _ { i } = k$ . ",
+        "bbox": [
+            173,
+            369,
+            826,
+            501
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 CONTRASTIVE LOSS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            517,
+            357,
+            531
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 1, we aim to learn an embedding space where samples from the same class gather around its class prototype, while samples from different classes are seperated. We achieve it with two contrastive losses: (1) a prototypical contrastive loss $\\mathcal { L } _ { \\mathrm { { p r o } } }$ which increases the similarity between an embedding and its corresponding class prototype, $( z _ { i } , c _ { \\hat { y } _ { i } } )$ , in contrast to other prototypes; (2) an instance contrastive loss ${ \\mathcal { L } } _ { \\mathrm { i n s } }$ which increases the similarity between two embeddings of the same source image, $( z _ { i } , z _ { i } ^ { \\prime } )$ , in contrast to embeddings of other images. Specifically, the contrastive losses are defined as: ",
+        "bbox": [
+            173,
+            542,
+            825,
+            640
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b5e1b1e280cf286701a7921ba7da5b22019dd739b89dd9c834a84e1b5ef26255.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { p r o } } ^ { i } = - \\log \\frac { \\exp ( z _ { i } \\cdot c _ { \\hat { y } _ { i } } / \\tau ) } { \\sum _ { k = 1 } ^ { K } \\exp ( z _ { i } \\cdot c _ { k } / \\tau ) } , ~ \\mathcal { L } _ { \\mathrm { i n s } } ^ { i } = - \\log \\frac { \\exp ( z _ { i } \\cdot z _ { i } ^ { \\prime } / \\tau ) } { \\sum _ { r = 0 } ^ { R } \\exp ( z _ { i } \\cdot z _ { r } ^ { \\prime } / \\tau ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            245,
+            642,
+            751,
+            681
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\tau$ is a temperature parameter, and $\\hat { y } _ { i }$ is the pseudo-label. We use $R$ negative momentum embeddings to construct the denominator of the instance contrastive loss. ",
+        "bbox": [
+            173,
+            691,
+            823,
+            720
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We train the classifier with cross-entropy loss, using pseudo-labels as targets. ",
+        "bbox": [
+            174,
+            727,
+            681,
+            742
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d73c5422f429797fa3d3a72476f9486f6838893606074bfa353d5b0a0150ad51.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { c e } } ^ { i } = - \\log ( p _ { i } ^ { \\hat { y } _ { i } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            439,
+            746,
+            560,
+            767
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We jointly optimize the contrastive losses and the classification loss. The training objective is: ",
+        "bbox": [
+            173,
+            777,
+            789,
+            794
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/941a7fb45d7067cd3647e67ad880c905c18f1796636540ab9aee8a7372132643.jpg",
+        "text": "$$\n{ \\mathcal { L } } = \\sum _ { i = 1 } ^ { n } ( { \\mathcal { L } } _ { \\mathrm { c e } } ^ { i } + \\lambda _ { \\mathrm { p r o } } { \\mathcal { L } } _ { \\mathrm { p r o } } ^ { i } + \\lambda _ { \\mathrm { i n s } } { \\mathcal { L } } _ { \\mathrm { i n s } } ^ { i } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            372,
+            797,
+            625,
+            839
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For simplicity, we set $\\lambda _ { \\mathrm { p r o } } = \\lambda _ { \\mathrm { i n s } } = 1$ for all experiments. ",
+        "bbox": [
+            176,
+            843,
+            562,
+            859
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 NOISE CORRECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            869,
+            357,
+            883
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We propose a simple yet effective method for online noise correction during training, which cleans label noise and removes OOD samples. For each sample, we generate a soft pseudo-label $\\pmb { q } _ { i }$ by ",
+        "bbox": [
+            174,
+            895,
+            825,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "combining the classifier’s output probability $\\mathbf { \\nabla } _ { \\mathbf { p } _ { i } }$ with $\\mathbf { \\boldsymbol { s } } _ { i }$ , a class probability distribution calculated using the sample’s similarity $w . r . t$ the momentum prototypes: ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/705faa7902d28f4342f570e2ce0f2271fb7e4577f6a0b13feff08f10e3844c97.jpg",
+        "text": "$$\n\\begin{array} { l } { q _ { i } = \\alpha { { p } _ { i } } + ( 1 - \\alpha ) { { s } _ { i } } , } \\\\ { s _ { i } ^ { k } = \\displaystyle \\frac { \\exp ( z _ { i } \\cdot { { c } _ { k } } / \\tau ) } { \\sum _ { k = 1 } ^ { K } \\exp ( z _ { i } \\cdot { { c } _ { k } } / \\tau ) } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            401,
+            137,
+            594,
+            195
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the combination weight is simply set as $\\alpha = 0 . 5$ in all experiments. ",
+        "bbox": [
+            173,
+            198,
+            658,
+            213
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We convert $\\pmb q _ { i }$ into a hard pseudo-label $\\hat { y } _ { i }$ based on the following rules: (1) if the highest score of $\\pmb q _ { i }$ is above certain threshold $T$ , use the class with the highest score as the pseudo-label; (2) otherwise, if the score for the original label $y _ { i }$ is higher than uniform probability, use $y _ { i }$ as the pseudo-label; (3) otherwise, label it as an OOD sample. ",
+        "bbox": [
+            174,
+            218,
+            825,
+            275
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7d85dc9cd6d7ccbd980c80ab7414afe1674687e63cc50911440307846c122825.jpg",
+        "text": "$$\n\\begin{array} { r } { \\hat { y } _ { i } = \\left\\{ \\begin{array} { l l } { \\mathrm { a r g } \\operatorname* { m a x } _ { k } q _ { i } ^ { k } } & { \\mathrm { i f } \\operatorname* { m a x } _ { k } q _ { i } ^ { k } > T , } \\\\ { y _ { i } } & { \\mathrm { e l s e i f } q _ { i } ^ { y _ { i } } > 1 / K , } \\\\ { \\mathrm { O O D } } & { \\mathrm { o t h e r w i s e } . } \\end{array} \\right. } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
+            291,
+            635,
+            344
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We remove OOD samples from both the cross-entropy loss and the prototypical contrastive loss so that they do not affect class-specific learning, but include them in the instance contrastive loss to further separate them from in-distribution samples. Examples of OOD images and corrected pseudo-labels are shown in the appendices. ",
+        "bbox": [
+            174,
+            354,
+            825,
+            411
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 MOMENTUM PROTOTYPES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            428,
+            398,
+            441
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For each class $k$ , we calculate its momentum prototype as a moving-average of the normalized embeddings for samples with pseudo-label $k$ . Specifically, we update $c _ { k }$ by: ",
+        "bbox": [
+            171,
+            453,
+            823,
+            482
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f6cc303c078fc19c4f693b38d93cf3b8d60488e19dff81d683aa8ec35e385f1b.jpg",
+        "text": "$$\n\\begin{array} { r } { \\boldsymbol { c } _ { k } \\gets \\mathrm { N o r m a l i z e } ( m \\boldsymbol { c } _ { k } + ( 1 - m ) \\boldsymbol { z } _ { i } ) , \\forall i \\in \\{ i \\mid \\hat { y } _ { i } = k \\} , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            487,
+            691,
+            503
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathrm { N o r m a l i z e } } ( c ) = c / \\left\\| c \\right\\| _ { 2 }$ . The momentum coefficient $m$ is set 0.999 in our experiments. ",
+        "bbox": [
+            173,
+            508,
+            794,
+            525
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            544,
+            326,
+            560
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 DATASET FOR UPSTREAM TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            575,
+            464,
+            589
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use the WebVision (Li et al., 2017) dataset as the noisy training data. It consists of images automatically crawled from Google and Flickr, using visual concepts from ImageNet as queries. We experiment with three versions of WebVision with different sizes: (1) WebVision-V1.0 contains $2 . 4 4 \\mathrm { m }$ images with the same classes as the ImageNet-1k (ILSVRC 2012) dataset; (2) WebVisionV0.5 is a randomly sampled subset of WebVision-V1.0, which contains the same number of images $( 1 . 2 8 \\mathrm { m } )$ as ImageNet-1k; (3) WebVision- $. \\mathrm { V } 2 . 0$ contains $1 6 \\mathrm m$ images with 5k classes. ",
+        "bbox": [
+            174,
+            599,
+            825,
+            685
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            702,
+            403,
+            715
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We follow standard settings for ImageNet training: batch size is 256; total number of epochs is 90; optimizer is SGD with a momentum of 0.9; initial learning rate is 0.1, decayed at 40 and 80 epochs; weight decay is 0.0001. We use ResNet-50 (He et al., 2016) as the encoder. For MoProspecific hyperparameters, we set $\\tau = 0 . 1 , \\alpha = 0 . 5 , T = 0 . 8$ $T = 0 . 6$ for WebVision-V2.0). The momentum for both the momentum encoder and momentum prototypes is set as 0.999. The queue to store momentum embeddings has a size of 8192. We apply standard data augmentation (crop and horizontal flip) to the encoder’s input, and stronger data augmentation (color changes in MoCo (He et al., 2019)) to the momentum encoder’s input. We warm-up the model for 10 epochs by training on all samples with original labels, before applying noise correction. ",
+        "bbox": [
+            174,
+            727,
+            825,
+            853
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3 UPSTREAM TASK PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            869,
+            442,
+            883
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Table 1, we compare MoPro with existing weakly-supervised learning methods trained on WebVision-V1.0, where MoPro achieves state-of-the-art performance. Since the training dataset has imbalanced number of samples per-class, inspired by Kang et al. (2020), we perform the following decoupled training steps to re-balance the classifier: (1) pretrain the model with MoPro; (2) perform noise correction on the training data using the pretrained model, following the method in Section 3.3; (3) keep the pretrained encoder fixed and finetune the classifier on the cleaned dataset, using square-root data sampling (Mahajan et al., 2018) which balances the classes. We retrain the classifier for 15 epochs, using a learning rate of 0.01 which is decayed at 5 and 10 epochs. Surprisingly, we also find that a vanilla cross-entropy method with decoupled classifier re-balancing can also achieve competitive performance, outperforming most existing baselines. ",
+        "bbox": [
+            174,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/f5ffd00595e61ed4629d13be9ea7f7fa0e2243d8dad16a7aa5c31501679c93d7.jpg",
+        "table_caption": [
+            "Table 1: Comparison with state-of-the-art methods on WebVision-V1.0. Numbers denote accuracy $( \\% )$ on the clean WebVision-V1.0 validation set and the ILSVRC 2012 validation set. CleanNet (Lee et al., 2018) and Distill (Zhang et al., 2020) require data with clean annotations. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Architecture</td><td colspan=\"2\">WebVision</td><td colspan=\"2\">ImageNet</td></tr><tr><td>top-1</td><td>top-5</td><td>top-1</td><td>top-5</td></tr><tr><td>Cross-Entropy (Tu et al., 2020)</td><td>ResNet-50</td><td>66.4</td><td>83.4</td><td>57.7</td><td>78.4</td></tr><tr><td>MentorNet (Jiang et al.,2018)</td><td>InceptionResNet-V2</td><td>70.8</td><td>88.0</td><td>62.5</td><td>83.0</td></tr><tr><td>CurriculumNet (Guo et al., 2018)</td><td>Inception-V2</td><td>72.1</td><td>89.1</td><td>64.8</td><td>84.9</td></tr><tr><td>CleanNet (Lee et al.,2018)</td><td>ResNet-50</td><td>70.3</td><td>87.8</td><td>63.4</td><td>84.6</td></tr><tr><td>CurriculumNet (Guo et al., 2018; Tu et al., 2020)</td><td>ResNet-50</td><td>70.7</td><td>88.6</td><td>62.7</td><td>83.4</td></tr><tr><td>SOM (Tu et al., 2020)</td><td>ResNet-50</td><td>72.2</td><td>89.5</td><td>65.0</td><td>85.1</td></tr><tr><td>Distill (Zhang et al.,2020)</td><td>ResNet-50</td><td>1</td><td>-</td><td>65.8</td><td>85.8</td></tr><tr><td>Cross-Entropy (decoupled)</td><td>ResNet-50</td><td>72.4</td><td>89.0</td><td>65.7</td><td>85.1</td></tr><tr><td>MoPro (ours)</td><td>ResNet-50</td><td>73.9</td><td>90.0</td><td>67.8</td><td>87.0</td></tr></table>",
+        "bbox": [
+            176,
+            101,
+            818,
+            267
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            324,
+            825,
+            436
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 TRANSFER LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            458,
+            388,
+            473
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we transfer weakly-supervised learned models to a variety of downstream tasks. We show that MoPro yields superior performance in image classification, object detection, instance segmentation, and obtains better robustness to domain shifts. Implementation details for the transfer learning experiments are described in appendix C. ",
+        "bbox": [
+            174,
+            481,
+            825,
+            537
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 LOW-SHOT IMAGE CLASSIFICATION ON FIXED REPRESENTATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            549,
+            655,
+            563
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "First, we transfer the learned representation to downstream tasks with few training samples. We perform low-shot classification on two datasets: PASCAL VOC2007 (Everingham et al., 2010) for object classification and Places205 (Zhou et al., 2014) for scene recognition. Following the setup by Goyal et al. (2019); Li et al. (2020b), we train linear SVMs using fixed representations from pretrained models. We vary the number $k$ of samples per-class and report the average result across 5 independent runs. Table 2 shows the results. When pretrained on weakly-labeled datasets, MoPro consistently outperforms the vanilla CE method. The improvement of MoPro becomes less significant when the number of web images increases from $2 . 4 \\mathrm { m }$ to $1 6 \\mathrm m$ , suggesting that increasing dataset size is a viable solution to combat noise. ",
+        "bbox": [
+            174,
+            570,
+            825,
+            641
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/cd6646b21a5aa93c8e70a341ab45b1f5ab550957843cdd6eb1f7c8995e512719.jpg",
+        "table_caption": [
+            "Table 2: Low-shot image classification on VOC07 and Places205 using linear SVMs trained on fixed representations. We vary the number of labeled examples per-class $( k )$ , and report the average mAP (for VOC) and accuracy (for Places) across 5 independent runs. WebVision-V0.5 has the same number of training samples as ImageNet. The self-supervised learning methods∗ are trained for 200 epochs, while other methods are trained for 90 epochs. MoPro outperforms vanilla CE pretrained on Web datasets, as well as self-supervised learning and supervised learning methods pretrained on ImageNet. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Pretrain dataset</td><td colspan=\"5\">vOC07</td><td colspan=\"5\">Places205</td></tr><tr><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=16|</td><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=16</td></tr><tr><td>MoCo v2* PCL v2*</td><td>ImageNet ImageNet</td><td>46.3 47.9</td><td>58.4 59.6</td><td>64.9 66.2</td><td>72.5 74.5</td><td>76.1 78.3</td><td>11.9 12.5</td><td>17.0 17.5</td><td>22.6 23.2</td><td>28.1 28.1</td><td>32.4 32.3</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>54.3</td><td>67.8</td><td>73.9</td><td>79.6</td><td>82.3</td><td>14.9</td><td>21.0</td><td>26.9</td><td>32.1</td><td>36.0</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V0.5</td><td>49.8 54.3</td><td>63.9 67.8</td><td>69.9</td><td>76.1</td><td>79.2</td><td>13.5</td><td>19.3</td><td>24.7</td><td>29.5</td><td>33.8</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V1.0</td><td>54.5</td><td>67.1</td><td>73.5 72.8</td><td>79.2 78.4</td><td>81.8 81.4</td><td>15.0 15.1</td><td>21.2 21.5</td><td>26.6 27.2</td><td>31.8 32.1</td><td>36.0 36.4</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V2.0</td><td>59.5 63.0 64.8 74.8</td><td>71.3 73.8 79.9</td><td>76.5 78.7</td><td>81.4 83.0</td><td>83.7 85.4</td><td>16.9 21.8 22.2</td><td>23.2 28.6</td><td>29.2 35.1</td><td>34.5 40.0</td><td>38.7 43.6</td></tr></table>",
+        "bbox": [
+            174,
+            654,
+            823,
+            832
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            823,
+            159
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "When compared with ImageNet pretrained models, MoPro substantially outperforms self-supervised learning (MoCo v2 (Chen et al., 2020b) and PCL v2 (Li et al., 2020b)), and achieves comparable performance with supervised learning when the same amount of web images (i.e. WebVision-V0.5) is used. Our results for the first time show that weakly-supervised representation learning can be as powerful as supervised representation learning under the same data and computation budget. ",
+        "bbox": [
+            174,
+            166,
+            825,
+            236
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2 LOW-RESOURCE TRANSFER WITH FINETUNING ",
+        "text_level": 1,
+        "bbox": [
+            179,
+            255,
+            534,
+            268
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we perform experiment to evaluate whether the pretrained model provides a good basis for finetuning when the downstream task has limited training data. Following the setup by Chen et al. (2020a), we finetune the pretrained model on $1 \\%$ or $1 0 \\%$ of ImageNet training samples. Table 3 shows the results. MoPro consistently outperforms CE when pretrained on Web datasets. Compared to self-supervised learning methods pretrained on ImageNet, weakly-supervised learning achieves significantly better performance with fewer number of epochs. ",
+        "bbox": [
+            173,
+            275,
+            825,
+            359
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Surprisingly, pretraining on the larger WebVision-V2 leads to worse performance compared to ${ \\mathrm { V } } 0 . 5$ and V1.0. This is because WebVision- $. \\mathrm { V } 0 . 5$ and $\\mathrm { V } 1 . 0$ contain the same 1k class as ImageNet, whereas V2 also contains $4 \\mathrm { k }$ extra classes. Hence, the representations learned from V2 are less task-specific and more difficult to adapt to ImageNet, especially with only $1 \\%$ of samples for finetuning. This suggests that if the classes for a downstream task are known a priori, it is more effective to curate a task-specific weakly-labeled dataset with the same classes. ",
+        "bbox": [
+            174,
+            364,
+            825,
+            449
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5ccea36413733e5764260c0b098ca6800c71733395eb2df26cb92ddcb98b603d.jpg",
+        "table_caption": [
+            "Table 3: Low-resource finetuning on ImageNet. A pretrained model is finetuned with $1 \\%$ or $10 \\%$ of ImageNet training data. Weakly-supervised learning with MoPro substantially outperforms self-supervised learning methods: PCL (Li et al., 2020b), SimCLR (Chen et al., 2020a), BYOL (Grill et al., 2020), and SwAV (Caron et al., 2020). Result for random init. is from Zhai et al. (2019). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Pretrain Method</td><td>Pretrain dataset</td><td>#Pretrain epochs</td><td>Top-1 1% 10%</td><td>Top-5 1%</td><td>10%</td></tr><tr><td>Random init.</td><td>None</td><td>None</td><td>None</td><td>25.4 56.4</td><td>48.4</td><td>80.4</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>PCL SimCLR</td><td>ImageNet</td><td>200 1000</td><td>48.8 48.3</td><td>62.9 75.3 65.6 75.5</td><td>85.6 87.8</td></tr><tr><td>BYOL</td><td></td><td>1000</td><td>53.2</td><td>68.8 78.4</td><td>89.0</td></tr><tr><td>SwAV</td><td></td><td>800</td><td>53.9</td><td>70.2 78.5</td><td>89.9</td></tr><tr><td rowspan=\"4\">Weakly-supervised</td><td>CE MoPro (ours)</td><td>WebVision-V0.5</td><td>90</td><td>65.9 69.3</td><td>72.4 73.3</td><td>87.0 90.9 91.7</td></tr><tr><td>CE MoPro (ours)</td><td>WebVision-V1.0</td><td>90</td><td>67.6 73.5</td><td>89.1 88.3</td><td>91.7</td></tr><tr><td>CE</td><td></td><td></td><td>71.2 74.8 62.1 72.9</td><td>90.5 86.9</td><td>92.4</td></tr><tr><td>MoPro (ours)</td><td>WebVision-V2.0</td><td>90</td><td>65.3 73.7</td><td>88.2</td><td>91.4 92.1</td></tr></table>",
+        "bbox": [
+            196,
+            458,
+            799,
+            650
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3 OBJECT DETECTION AND INSTANCE SEGMENTATION",
+        "text_level": 1,
+        "bbox": [
+            173,
+            726,
+            576,
+            738
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We further transfer the pretrained model to object detection and instance segmentation tasks on COCO (Lin et al., 2014). Following the setup by He et al. (2019), we use the pretrained ResNet-50 as the backbone for a Mask-RCNN (He et al., 2017) with FPN (Lin et al., 2017). We finetune all layers end-to-end, including BN. The schedule is the default $1 \\times$ or $2 \\times$ in Girshick et al. (2018) Table 4 shows the results. Weakly-supervised learning with MoPro outperforms both supervised learning on ImageNet and self-supervised learning on one billion Instagram images. ",
+        "bbox": [
+            174,
+            746,
+            825,
+            829
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4 ROBUSTNESS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            847,
+            308,
+            861
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It has been shown that deep models trained on ImageNet lack robustness to out-of-distribution samples, often falsely producing over-confident predictions. Hendricks et al. have curated two benchmark datasets to evaluate models’ robustness to real-world distribution variation: (1) ImageNetR (Hendrycks et al., 2020) which contains various artistic renditions of object classes from the original ImageNet dataset, and (2) ImageNet-A (Hendrycks et al., 2019) which contains natural images where ImageNet-pretrained models consistently fail due to variations in background elements, color, or texture. Both datasets contain 200 classes, a subset of ImageNet’s 1,000 classes. ",
+        "bbox": [
+            174,
+            868,
+            823,
+            922
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ad3ec65c1969e6faf07ae84a6bb7d34e51ae2f051f2a786b6949f26fc1fffccf.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "(a) $2 \\times$ schedule "
+        ],
+        "table_body": "<table><tr><td>Method</td><td>Pretrain dataset</td><td>Apbb AP</td><td>AP</td><td>Apmk</td><td>AP</td><td>AP</td></tr><tr><td>random</td><td>None</td><td>31.0 49.5</td><td>33.2</td><td>28.5</td><td>46.8</td><td>30.4</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>38.9 59.6</td><td>42.7</td><td>35.4</td><td>56.5</td><td>38.1</td></tr><tr><td>MoCo</td><td>Instagram-1B</td><td>38.9 59.4</td><td>42.3</td><td>35.4</td><td>56.5</td><td>37.9</td></tr><tr><td>CE</td><td>WebVision-V1.0</td><td>39.2 60.0</td><td>42.9</td><td>35.6</td><td>56.8</td><td>38.0</td></tr><tr><td>MoPro MoPro</td><td>WebVision-V2.0</td><td>39.7 (+0.8) 40.7 (+1.8)</td><td>60.9 (+1.3) 43.1 (+0.4)</td><td>36.1 (+0.7) 36.8 (+1.4)</td><td>57.5 (+1.0) 58.4 (+1.9)</td><td>38.6 (+0.5) ）39.6 (+1.5)</td></tr><tr><td colspan=\"7\">61.7 (+2.1) 44.5 (+1.8) (a) 1× schedule</td></tr><tr><td>Method</td><td>Pretrain dataset</td><td>Apbb AP</td><td>AP</td><td>Apmk</td><td></td><td></td></tr><tr><td>random</td><td>None</td><td>36.7</td><td>40.0</td><td>33.7</td><td>AP 53.8</td><td>AP 35.9</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>40.6</td><td>44.4</td><td>36.8</td><td>58.1</td><td>39.5</td></tr><tr><td>MoCo</td><td>Instagram-1B</td><td>41.1</td><td>45.1</td><td>37.4</td><td>59.1</td><td>40.2</td></tr><tr><td>CE MoPro</td><td>WebVision-V1.0</td><td>40.9</td><td>44.7</td><td>37.2</td><td>58.7</td><td>40.1</td></tr><tr><td>MoPro</td><td>WebVision-V2.0</td><td>41.2 (+0.6) 41.8 (+1.2)</td><td>62.2 (+0.9) 45.0 (+0.6) 62.6 (+1.3) 45.6 (+1.2)</td><td>37.4 (+0.6) 37.8 (+1.0)</td><td>58.9 (+0.8) 59.5 (+1.4)</td><td>40.3 (+0.8) 40.6 (+1.1)</td></tr></table>",
+        "bbox": [
+            171,
+            101,
+            821,
+            333
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1d6b94d1e930d7f07e6cfdf9625cb8ce8e339556ee9c8701b0673629daca2483.jpg",
+        "table_caption": [
+            "Table 4: Object detection and instance segmentation using Mask-RCNN with R50-FPN fine-tuned on COCO train2017. We evaluate bounding-box AP $( \\mathsf { A P } ^ { \\mathsf { b b } } )$ and mask AP $( \\mathbf { A P } ^ { \\mathrm { m k } } )$ on $\\mathtt { v a l } 2 0 1 7$ . Weaklysupervised learning with MoPro outperforms both supervised learning on ImageNet and self-supervised learning (MoCo (He et al., 2019)) on one billion Instagram images. ",
+            "Table 5: Evaluation of model robustness on images with artistic and natural distribution shifts. Weakly supervised learning with MoPro leads to a more robust and well-calibrated model. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Pretrain dataset</td><td colspan=\"2\">ImageNet-R</td><td colspan=\"2\">ImageNet-A</td></tr><tr><td>Accuracy (↑)</td><td>Calib. Error(↓）</td><td>Accuracy (↑)</td><td>Calib. Error (↓)</td></tr><tr><td>CE (Sup.)</td><td>ImageNet</td><td>36.14</td><td>19.66</td><td>0.03</td><td>62.50</td></tr><tr><td>CE</td><td rowspan=\"2\">WebVision-V1.0</td><td>49.56</td><td>10.05</td><td>10.24</td><td>37.84</td></tr><tr><td>MoPro</td><td> 54.87</td><td> 5.73</td><td>11.93</td><td>35.85</td></tr></table>",
+        "bbox": [
+            199,
+            416,
+            797,
+            502
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            566,
+            823,
+            608
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We evaluate weakly-supervised trained models on these two robustness benchmarks. We report both accuracy and the $\\ell _ { 2 }$ calibration error (Kumar et al., 2019). The calibration error measures the misalignment between a model’s confidence and its accuracy. Concretely, a well-calibrated classifier which give examples $80 \\%$ confidence should be correct $80 \\%$ of the time. Results are shown in Table 5. Webly-supervised learning show significantly higher accuracy and lower calibration error. The robustness to distribution shift could come from the higher diversity of samples in Web images. Compared to vanilla CE, MoPro further improves the model’s robustness on both datasets. Note that we made sure that the training data of WebVision does not overlap with the test data. ",
+        "bbox": [
+            174,
+            616,
+            825,
+            727
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            747,
+            357,
+            763
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We perform ablation study to verify the effectiveness of three important components in MoPro: (1) prototypical contrastive loss ${ \\mathcal { L } } _ { \\mathrm { p r o } }$ , (2) instance contrastive loss ${ \\mathcal { L } } _ { \\mathrm { i n s } }$ , (3) prototypical similarity $\\mathbf { \\boldsymbol { s } } _ { i }$ used for noise correction (equation 4). We choose low-resource finetuning on $1 \\%$ of ImageNet training data as the benchmark, and report the top-1 accuracy for models pretrained on WebVisionV0.5. As shown in Table 6, all of the three components contribute to the efficacy of MoPro. ",
+        "bbox": [
+            174,
+            773,
+            823,
+            843
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            863,
+            318,
+            880
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This paper introduces a new contrastive learning framework for webly-supervised representation learning. We propose momentum prototypes, a simple component that is effective in label noise ",
+        "bbox": [
+            173,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fc71a2de7fe75a3564bad93f1483eab0625b4e37b04706ebe7d06b12ded7b6c6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MoPro</td><td>w/oLpro</td><td></td><td></td><td>w/o Linst |w/o si (i.e.α =1) | w/o Lpro &amp; Linst &amp;si</td><td>CE</td></tr><tr><td>ImageNet acc.</td><td>69.3</td><td>68.0</td><td>68.2 一</td><td>68.4</td><td>一 66.9</td><td>65.9</td></tr></table>",
+        "bbox": [
+            184,
+            102,
+            813,
+            142
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Ablation study where different components are removed from MoPro. Models are pre-trained on WebVision-V0.5 and finetuned on $1 \\%$ of ImageNet data. ",
+        "bbox": [
+            173,
+            154,
+            823,
+            179
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "correction, OOD sample removal, and representation learning. MoPro achieves state-of-the-art performance on the upstream task of learning from real-world noisy data, and superior representation learning performance on multiple down-stream tasks. Webly-supervised learning with MoPro does not require the expensive annotation cost in supervised learning, nor the huge computation budget in self-supervised learning. For future work, MoPro could be extended to utilize other sources of free Web data, such as weakly-labeled videos, for representation learning in other domains. ",
+        "bbox": [
+            174,
+            202,
+            825,
+            286
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            306,
+            285,
+            321
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Eric Arazo, Diego Ortego, Paul Albert, Noel E. O’Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In ICML, pp. 312–321, 2019.   \nMathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. arXiv preprint arXiv:2006.09882, 2020.   \nPengfei Chen, Benben Liao, Guangyong Chen, and Shengyu Zhang. Understanding and utilizing deep neural networks trained with noisy labels. In ICML, pp. 1062–1070, 2019.   \nTing Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, 2020a.   \nXinlei Chen and Abhinav Gupta. Webly supervised learning of convolutional networks. In ICCV, pp. 1431–1439, 2015.   \nXinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He. Improved baselines with momentum contrastive learning. arXiv preprint arXiv:2003.04297, 2020b.   \nJia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Fei-Fei Li. Imagenet: A large-scale hierarchical image database. In CVPR, pp. 248–255, 2009.   \nSantosh Kumar Divvala, Ali Farhadi, and Carlos Guestrin. Learning everything about anything: Webly-supervised visual concept learning. In CVPR, pp. 3270–3277, 2014.   \nMark Everingham, Luc Van Gool, Christopher K. I. Williams, John M. Winn, and Andrew Zisserman. The pascal visual object classes (VOC) challenge. International Journal of Computer Vision, 88(2):303–338, 2010.   \nRong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, Xiang-Rui Wang, and Chih-Jen Lin. LIBLINEAR: A library for large linear classification. JMLR, 9:1871–1874, 2008.   \nRoss Girshick, Ilija Radosavovic, Georgia Gkioxari, Piotr Dollar, and Kaiming He. Detectron. ´ https://github.com/facebookresearch/detectron, 2018.   \nPriya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra. Scaling and benchmarking selfsupervised visual representation learning. In ICCV, pp. 6391–6400, 2019.   \nJean-Bastien Grill, Florian Strub, Florent Altche, Corentin Tallec, Pierre H. Richemond, Elena ´ Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, Bilal Piot, Koray Kavukcuoglu, Remi Munos, and Michal Valko. Bootstrap your own ´ latent: A new approach to self-supervised learning. arXiv preprint arXiv:2006.07733, 2020.   \nSheng Guo, Weilin Huang, Haozhi Zhang, Chenfan Zhuang, Dengke Dong, Matthew R. Scott, and Dinglong Huang. Curriculumnet: Weakly supervised learning from large-scale web images. In ECCV, pp. 139–154, 2018. ",
+        "bbox": [
+            171,
+            329,
+            826,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor W. Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In NeurIPS, pp. 8536–8546, 2018. ",
+        "bbox": [
+            176,
+            103,
+            821,
+            146
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, pp. 770–778, 2016. ",
+        "bbox": [
+            171,
+            155,
+            821,
+            185
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Georgia Gkioxari, Piotr Dollar, and Ross B. Girshick. Mask R-CNN. In ´ ICCV, pp. 2980–2988, 2017. ",
+        "bbox": [
+            173,
+            194,
+            821,
+            223
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. arXiv preprint arXiv:1911.05722, 2019. ",
+        "bbox": [
+            173,
+            232,
+            823,
+            262
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Dan Hendrycks, Kevin Zhao, Steven Basart, Jacob Steinhardt, and Dawn Song. Natural adversarial examples. arXiv preprint arXiv:1907.07174, 2019. ",
+        "bbox": [
+            173,
+            271,
+            823,
+            301
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, et al. The many faces of robustness: A critical analysis of out-of-distribution generalization. arXiv preprint arXiv:2006.16241, 2020. ",
+        "bbox": [
+            174,
+            309,
+            825,
+            353
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Lu Jiang, Zhengyuan Zhou, Thomas Leung, Li-Jia Li, and Li Fei-Fei. Mentornet: Learning datadriven curriculum for very deep neural networks on corrupted labels. In ICML, pp. 2309–2318, 2018. ",
+        "bbox": [
+            173,
+            362,
+            825,
+            405
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Lu Jiang, Di Huang, Mason Liu, and Weilong Yang. Beyond synthetic noise: Deep learning on controlled noisy labels. In ICML, 2020. ",
+        "bbox": [
+            169,
+            415,
+            823,
+            444
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Armand Joulin, Laurens van der Maaten, Allan Jabri, and Nicolas Vasilache. Learning visual features from large weakly supervised data. In Bastian Leibe, Jiri Matas, Nicu Sebe, and Max Welling (eds.), ECCV, 2016. ",
+        "bbox": [
+            173,
+            454,
+            823,
+            496
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Bingyi Kang, Saining Xie, Marcus Rohrbach, Zhicheng Yan, Albert Gordo, Jiashi Feng, and Yannis Kalantidis. Decoupling representation and classifier for long-tailed recognition. In ICLR, 2020. ",
+        "bbox": [
+            173,
+            506,
+            823,
+            536
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Joan Puigcerver, Jessica Yung, Sylvain Gelly, and Neil Houlsby. Large scale learning of general visual representations for transfer. In ECCV, 2020. ",
+        "bbox": [
+            174,
+            544,
+            823,
+            587
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ananya Kumar, Percy Liang, and Tengyu Ma. Verified uncertainty calibration. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alche-Buc, Emily B. Fox, and Roman ´ Garnett (eds.), NeurIPS, pp. 3787–3798, 2019. ",
+        "bbox": [
+            174,
+            597,
+            823,
+            640
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kuang-Huei Lee, Xiaodong He, Lei Zhang, and Linjun Yang. Cleannet: Transfer learning for scalable image classifier training with label noise. In CVPR, pp. 5447–5456, 2018. ",
+        "bbox": [
+            173,
+            648,
+            821,
+            679
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Junnan Li, Yongkang Wong, Qi Zhao, and Mohan S. Kankanhalli. Learning to learn from noisy labeled data. In CVPR, pp. 5051–5059, 2019. ",
+        "bbox": [
+            173,
+            688,
+            823,
+            717
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Junnan Li, Richard Socher, and Steven C.H. Hoi. Dividemix: Learning with noisy labels as semisupervised learning. In ICLR, 2020a. ",
+        "bbox": [
+            169,
+            727,
+            823,
+            756
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Junnan Li, Pan Zhou, Caiming Xiong, Richard Socher, and Steven C.H. Hoi. Prototypical contrastive learning of unsupervised representations. arXiv preprint arXiv:2005.04966, 2020b. ",
+        "bbox": [
+            171,
+            765,
+            823,
+            795
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Wen Li, Limin Wang, Wei Li, Eirikur Agustsson, and Luc Van Gool. Webvision database: Visual learning and understanding from web data. arXiv preprint arXiv:1708.02862, 2017. ",
+        "bbox": [
+            169,
+            804,
+            823,
+            833
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Tsung-Yi Lin, Michael Maire, Serge J. Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollar, and C. Lawrence Zitnick. Microsoft COCO: common objects in context. In ´ ECCV, pp. 740–755, 2014. ",
+        "bbox": [
+            173,
+            843,
+            823,
+            886
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Tsung-Yi Lin, Piotr Dollar, Ross B. Girshick, Kaiming He, Bharath Hariharan, and Serge J. Be-´ longie. Feature pyramid networks for object detection. In CVPR, pp. 936–944, 2017. ",
+        "bbox": [
+            173,
+            895,
+            820,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Xingjun Ma, Yisen Wang, Michael E. Houle, Shuo Zhou, Sarah M. Erfani, Shu-Tao Xia, Sudanthi N. R. Wijewickrema, and James Bailey. Dimensionality-driven learning with noisy labels. In ICML, pp. 3361–3370, 2018.   \nDhruv Mahajan, Ross B. Girshick, Vignesh Ramanathan, Kaiming He, Manohar Paluri, Yixuan Li, Ashwin Bharambe, and Laurens van der Maaten. Exploring the limits of weakly supervised pretraining. In ECCV, pp. 185–201, 2018.   \nAaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv preprint arXiv:1807.03748, 2018.   \nScott E. Reed, Honglak Lee, Dragomir Anguelov, Christian Szegedy, Dumitru Erhan, and Andrew Rabinovich. Training deep neural networks on noisy labels with bootstrapping. In ICLR, 2015.   \nChen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. In ICCV, pp. 843–852, 2017.   \nDaiki Tanaka, Daiki Ikami, Toshihiko Yamasaki, and Kiyoharu Aizawa. Joint optimization framework for learning with noisy labels. In CVPR, pp. 5552–5560, 2018.   \nYi Tu, Li Niu, Dawei Cheng, and Liqing Zhang. Protonet: Learning from web data with memory. In CVPR, 2020.   \nArash Vahdat. Toward robustness against label noise in training deep discriminative neural networks. In NIPS, pp. 5601–5610, 2017.   \nAndreas Veit, Neil Alldrin, Gal Chechik, Ivan Krasin, Abhinav Gupta, and Serge J. Belongie. Learning from noisy large-scale datasets with minimal supervision. In CVPR, pp. 6575–6583, 2017.   \nYisen Wang, Weiyang Liu, Xingjun Ma, James Bailey, Hongyuan Zha, Le Song, and Shu-Tao Xia. Iterative learning with open-set noisy labels. In CVPR, pp. 8688–8696, 2018.   \nZhirong Wu, Yuanjun Xiong, Stella X. Yu, and Dahua Lin. Unsupervised feature learning via nonparametric instance discrimination. In CVPR, pp. 3733–3742, 2018.   \nTong Xiao, Tian Xia, Yi Yang, Chang Huang, and Xiaogang Wang. Learning from massive noisy labeled data for image classification. In CVPR, pp. 2691–2699, 2015.   \nJingkang Yang, Litong Feng, Weirong Chen, Xiaopeng Yan, Huabin Zheng, Ping Luo, and Wayne Zhang. Webly supervised image classification with self-contained confidence. In ECCV, 2020.   \nKun Yi and Jianxin Wu. Probabilistic end-to-end noise correction for learning with noisy labels. In CVPR, 2019.   \nXiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. S4l: Self-supervised semisupervised learning. In ICCV, pp. 1476–1485, 2019.   \nChiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017.   \nWeihe Zhang, Yali Wang, and Yu Qiao. Metacleaner: Learning to hallucinate clean representations for noisy-labeled visual recognition. In CVPR, 2019.   \nZizhao Zhang, Han Zhang, Sercan Omer Arik, Honglak Lee, and Tomas Pfister. Distilling effective ¨ supervision from severe label noise. In CVPR, pp. 9291–9300, 2020.   \nBolei Zhou, Agata Lapedriza, Jianxiong Xiao, Antonio Torralba, and Aude Oliva. Learning deep \\` features for scene recognition using places database. In NIPS, pp. 487–495, 2014. ",
+        "bbox": [
+            171,
+            12,
+            826,
+            842
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX A NOISY SAMPLE VISUALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            566,
+            118
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In Figure 3, we show example images randomly chosen from the out-of-distribution samples filtered out by our method. In Figure 4, we show random examples where their pseudo-labels are different from the original training labels. By visual examination, we observe that our method can remove OOD samples and correct noisy labels at a high success rate. ",
+        "bbox": [
+            173,
+            142,
+            825,
+            199
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/c371cc7a6aab2aade8f5011917c72d9e0c3d62d0338e457a7a654999320c671b.jpg",
+        "image_caption": [
+            "Figure 3: Examples of randomly selected out-of-distribution samples filtered out by our method. The original training labels are shown below the images. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            219,
+            825,
+            838
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/7864b0659767aad1402685a6c680cc0068f4f7b997ffc69b896ef1cab2052ffb.jpg",
+        "image_caption": [
+            "Figure 4: Examples of randomly selected samples with noisy labels corrected by our method. The original training labels are shown in red and corrected pseudo-labels are shown in green. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            92,
+            821,
+            815
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX B PSEUDO-CODE OF MOPRO ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            522,
+            118
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 summarizes the proposed method. ",
+        "bbox": [
+            174,
+            135,
+            482,
+            148
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1: MoPro’s main algorithm. ",
+        "bbox": [
+            174,
+            170,
+            418,
+            184
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "1 Input: number of classes $K$ , temperature $\\tau$ , threshold $T$ , momentum $m$ , encoder network $f ( \\cdot )$ , projection network $g ( \\cdot )$ , classifier $h ( \\cdot )$ , momentum encoder $g ^ { \\prime } ( f ^ { \\prime } ( \\cdot ) )$ . ",
+        "bbox": [
+            160,
+            188,
+            800,
+            215
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "2 for $\\bar { \\{ ( x _ { i } , y _ { i } ) \\} } _ { i = 1 } ^ { b }$ in loader do // load a minibatch of noisy training data   \n3 for $i \\in \\{ 1 , . . . , b \\}$ do   \n4 $\\tilde { \\mathbf { x } } _ { i } = \\mathrm { w e a k . a u g } ( \\mathbf { \\mathbf { x } } _ { i } )$ // weak augmentation   \n5 $\\tilde { \\pmb { x } } _ { i } ^ { \\prime } = \\mathrm { s t r o n g . a u g } ( \\pmb { x } _ { i } )$ // strong augmentation   \n6 vi = f (x˜i) // representation   \n7 zi = g(vi) // normalized low-dimensional embedding   \n8 zi = g 0 (f 0 (x˜ 0i )) // momentum embedding   \n10 9 si = {ski }Kk=1 , ski = pi = h(vi) P exp(zi·ck/τ)Kk=1 exp(zi·ck/τ) // prototypical score // class prediction   \n// noise correction   \n11 $\\pmb { q } _ { i } = ( \\pmb { p } _ { i } + \\pmb { s } _ { i } ) / 2$ // soft pseudo-label   \n12 if maxk $q _ { i } ^ { k } > T$ then   \n13 $\\hat { y } _ { i } = \\arg \\operatorname* { m a x } _ { k } q _ { i } ^ { k }$   \n14 else if $q _ { i } ^ { y _ { i } } > 1 / K$ then   \n15 $\\hat { y } _ { i } = y _ { i }$   \n16 else   \n17 $\\mathbf { \\Pi } _ { \\mathbf { e n d } } ^ { | \\mathbf { \\Pi } _ { \\hat { y } _ { i } } = \\operatorname { O O D } }$   \n18   \n// calculate losses   \n19 $\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { i n s } } ^ { i } = - \\log \\frac { \\exp ( z _ { i } \\cdot z _ { i } ^ { \\prime } / \\tau ) } { \\sum _ { r = 0 } ^ { R } \\exp ( z _ { i } \\cdot z _ { r } ^ { \\prime } / \\tau ) } } \\end{array}$ // instance contrastive loss   \n20 if $\\hat { y } _ { i }$ is not OOD then   \n21 $\\begin{array} { r l } & { \\dot { \\mathcal { L } } _ { \\mathrm { p r o } } ^ { i } = - \\log \\frac { \\exp ( z _ { i } \\cdot c _ { \\hat { y } _ { i } } / \\tau ) } { \\sum _ { k = 1 } ^ { K } \\exp ( z _ { i } \\cdot c _ { k } / \\tau ) } } \\\\ & { \\dot { \\mathcal { L } } _ { \\mathrm { c e } } ^ { i } = - \\log ( p _ { i } ^ { \\hat { y } _ { i } } ) } \\end{array}$ // prototypical contrastive loss   \n22 // cross entropy loss   \n23 else   \n24 Lipr o = L ice = 0   \n25 end   \n/ update momentum prototypes   \n26 $\\pmb { c } _ { \\hat { y } _ { i } } \\gets \\mathrm { N o r m a l i z e } ( m \\pmb { c } _ { \\hat { y } _ { i } } + ( 1 - m ) \\pmb { z } _ { i } )$   \n27 end   \n28 $\\begin{array} { r } { \\mathcal { L } = \\sum _ { i = 1 } ^ { b } ( \\mathcal { L } _ { \\mathrm { c e } } ^ { i } + \\mathcal { L } _ { \\mathrm { p r o } } ^ { i } + \\mathcal { L } _ { \\mathrm { i n s } } ^ { i } ) } \\end{array}$ // total loss   \n29 update networks $f , g , h$ to minimize $\\mathcal { L }$ .   \n30 end ",
+        "bbox": [
+            153,
+            198,
+            805,
+            708
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX C TRANSFER LEARNING IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            746,
+            714,
+            761
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For low-shot image classification on Places and VOC, we follow the procedure in Li et al. (2020b) and train linear SVMs on the global average pooling features of ResNet-50. We preprocess all images by resizing to 256 pixels along the shorter side and taking a $2 2 4 \\times 2 2 4$ center crop. The SVMs are implemented in the LIBLINEAR (Fan et al., 2008) package. ",
+        "bbox": [
+            174,
+            776,
+            825,
+            833
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For low-resource finetuning on ImageNet, we adopt different finetuning strategy for different versions of WebVision pretrained models. For WebVision V0.5 and V1.0, since they contain the same 1000 classes as ImageNet, we finetune the entire model including the classification layer. We train with SGD, using a batch size of 256, a momentum of 0.9, a weight decay of 0, and a learning rate of 0.005. We train for 40 epochs, and drop the learning rate by 0.2 at 15 and 30 epochs. For WebVision 2.0, since it contains 5000 classes, we randomly initialize a new classification layer with 1000 output dimension, and finetune the model end-to-end. We train for 50 epochs, using a learning rate of 0.01, which is dropped by 0.1 at 20 and 40 epochs. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "For object detection and instance segmentation on COCO, we adopt the same setup in MoCo (He et al., 2019), using Detectron2 (Girshick et al., 2018) codebase. The image scale is in [640, 800] pixels during training and is 800 at inference. We fine-tune all layers end-to-end. We finetune on the train2017 set $\\mathord { \\sim } 1 1 8 \\mathrm { k }$ images) and evaluate on val2017. ",
+        "bbox": [
+            174,
+            138,
+            825,
+            195
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX D STANDARD DEVIATION FOR LOW-SHOT CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            215,
+            767,
+            232
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/1d413b15c90892ff6267d66c0b0588f4f4e69c3ee04b9c752a46fd462206efbc.jpg",
+        "table_caption": [
+            "Table 7 reports the standard deviation for the low-shot image classification experiment in Section 5.1. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Pretrain dataset</td><td colspan=\"4\">VOC07</td><td colspan=\"4\">Places205</td></tr><tr><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td><td>k=1</td><td>k=2</td><td>k=4</td><td>k=8</td></tr><tr><td>CE(Sup.)]</td><td>）ImageNet</td><td>[54.3±4.8 67.8±4.4 73.9±0.9 79.6±0.8|</td><td></td><td></td><td></td><td></td><td>14.9±1.3 21.0±0.3 26.9±0.6 32.1±0.4</td><td></td><td></td></tr><tr><td>MoPro</td><td>WebVision-V1.0</td><td></td><td>59.5±5.2 71.3±2.2</td><td>76.5±1.18</td><td>181.4±0.6</td><td></td><td>16.9±1.3 23.2±0.31</td><td>29.2±0.6 34.5±0.3</td><td></td></tr><tr><td>MoPro</td><td>WebVision-V2.0</td><td></td><td>64.8±6.7 74.8±2.6 79.9±1.4 83.9±1.0</td><td></td><td></td><td></td><td>22.2±1.329.2±0.5</td><td>35.6±0.7 40.9±0.3</td><td></td></tr></table>",
+        "bbox": [
+            176,
+            273,
+            821,
+            349
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Table 7: Low-shot image classification experiments. Mean and standard deviation are calculated across 5 runs. ",
+        "bbox": [
+            171,
+            361,
+            821,
+            375
+        ],
+        "page_idx": 14
+    }
+]

parse/train/AAes_3W-2z/AAes_3W-2z.md

@@ -0,0 +1,487 @@
+# WASSERSTEIN EMBEDDING FOR GRAPH LEARNING
+
+Soheil Kolouri∗ †, Navid Naderializadeh∗†, Gustavo K. Rohde‡, & Heiko Hoffmann†
+
+{skolouri,nnaderializadeh,hhoffmann}@hrl.com, gustavo@virginia.edu
+
+# ABSTRACT
+
+We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.
+
+# 1 INTRODUCTION
+
+Many exciting and practical machine learning applications involve learning from graph-structured data. While images, videos, and temporal signals (e.g., audio or biometrics) are instances of data that are supported on grid-like structures, data in social networks, cyber-physical systems, communication networks, chemistry, and bioinformatics often live on irregular structures (Backstrom & Leskovec, 2011; Sadreazami et al., 2017; Jin et al., 2017; Agrawal et al., 2018; Naderializadeh et al., 2020). One can represent such data as (attributed) graphs, which are universal data structures. Efficient and generalizable learning from graph-structured data opens the door to a vast number of applications, which were beyond the reach of classic machine learning (ML) and, more specifically, deep learning (DL) algorithms.
+
+Analyzing graph-structured data has received significant attention from the ML, network science, and signal processing communities over the past few years. On the one hand, there has been a rush toward extending the success of deep neural networks to graph-structured data, which has led to a variety of graph neural network (GNN) architectures. On the other hand, the research on kernel approaches (Gärtner et al., 2003), perhaps most notably the random walk kernel (Kashima et al., 2003) and the Weisfeiler-Lehman (WL) kernel (Shervashidze et al., 2011; Rieck et al., 2019; Morris et al., 2019; 2020), remains an active field of study and the methods developed therein provide competitive performance in various graph representation tasks (see the recent survey by Kriege et al. (2020)).
+
+To learn graph representations, GNN-based frameworks make use of three generic modules, which provide i) feature aggregation, ii) graph pooling (i.e., readout), and iii) classification $\mathrm { H u ^ { * } }$ et al., 2020). The feature aggregator provides a vector representation for each node of the graph, referred to as a node embedding. The graph pooling module creates a representation for the graph from its node embeddings, whose dimensionality is fixed regardless of the underlying graph size, and which can then be analyzed using a downstream classifier of choice. On the graph kernel side, one leverages a kernel to measure the similarities between pairs of graphs, and uses conventional kernel methods to perform learning on a set of graphs (Hofmann et al., 2008). A recent example of such methods is the framework provided by Togninalli et al. (2019), in which the authors propose a novel node embedding inspired by the WL kernel, and combine the resulting node embeddings with the
+
+Wasserstein distance (Villani, 2008; Kolouri et al., 2017) to measure the dissimilarity between two graphs. Afterwards, they leverage conventional kernel methods based on the pairwise-measured dissimilarities to perform learning on graphs.
+
+Considering the ever-increasing scale of graph datasets, which may contain tens of thousands of graphs or millions to billions of nodes per graph, the issue of scalability and algorithmic efficiency becomes of vital importance for graph learning methods (Hernandez & Brown, 2020; Hu et al., 2020). However, both of the aforementioned paradigms of GNNs and kernel methods suffer in this sense. On the GNN side, acceleration of the training procedure is challenging and scales poorly as the graph size grows (Bojchevski et al., 2019). On the graph kernel side, the need for calculating the matrix of all pairwise similarities can be a burden in datasets with a large number of graphs, especially if calculating the similarity between each pair of graphs is computationally expensive. For instance, in the method proposed in (Togninalli et al., 2019), the computational complexity of each calculation of the Wasserstein distance is cubic in the number of nodes (or linearithmic for the entropy-regularized distance).
+
+To overcome these issues, inspired by the linear optimal transport framework of (Wang et al., 2013), we propose a linear Wasserstein Embedding for Graph Learning, which we refer to as WEGL. Our proposed approach embeds a graph into a Hilbert space, where the $\ell _ { 2 }$ distance between two embedded graphs provides a true metric between the graphs that approximates their 2-Wasserstein distance. For a set of $M$ graphs, the proposed method provides:
+
+1. Reduced computational complexity of estimating the graph Wasserstein distance (Togninalli et al., 2019) for a dataset of $M$ graphs from a quadratic complexity in the number of graphs, i.e., M(M−1)2 calculations, to linear complexity, i.e., M calculations of the Wasserstein distance; and 2. An explicit Hilbertian embedding for graphs, which is not restricted to kernel methods, and therefore can be used in conjunction with any downstream classification framework.
+
+We show that compared to multiple GNN and graph kernel baselines, WEGL achieves either stateof-the-art or competitive results on benchmark graph-level classification tasks, including classical graph classification datasets (Kersting et al., 2020) and the recent molecular property-prediction benchmarks (Hu et al., 2020). We also compare the algorithmic efficiency of WEGL with two baseline GNN and graph kernel methods and demonstrate that it is much more computationally efficient relative to those algorithms.
+
+# 2 BACKGROUND AND RELATED WORK
+
+In this section, we provide a brief background on different methods for deriving representations for graphs and an overview on Wasserstein distances by reviewing the related work in the literature.
+
+# 2.1 GRAPH REPRESENTATION METHODS
+
+Let $G = ( \nu , \mathcal { E } )$ denote a graph, comprising a set of nodes $\nu$ and a set of edges $\mathcal { E } \subseteq \mathcal { V } ^ { 2 }$ , where two nodes $u , v \in \mathcal { V }$ are connected to each other if and only if $( u , v ) \in \mathcal { E }$ .1 For each node $v \in \mathcal V$ , we define its set of neighbors as $\mathcal { N } _ { v } \triangleq \{ u \in \mathcal { V } : ( u , v ) \in \mathcal { E } \}$ . The nodes of the graph $G$ may have categorical labels and/or continuous attribute vectors. We use a unified notation of $\mathbf { \bar { \boldsymbol { x } } } _ { v } \in \mathbb { R } ^ { F }$ to denote the label and/or attribute vector of node $v \in \mathcal V$ , where $F$ denotes the node feature dimensionality. Moreover, we use $w _ { u v } \in \mathbb { R } ^ { E }$ to denote the edge feature vector for any edge $( u , v ) \in \mathcal { E }$ , where $E$ denotes the edge feature dimensionality. Node and edge features may be present depending on the graph dataset under consideration.
+
+To learn graph properties from the graph structure and its node/edge features, one can use a function $\psi : \mathcal { G }  \mathcal { H }$ to map any graph $G$ in the space of all possible graphs $\mathcal { G }$ to an embedding $\psi ( G )$ in a Hilbert space $\mathcal { H }$ . Kernel methods have been among the most popular ways of creating such graph embeddings. A graph kernel is defined as a function $k : \mathcal { G } ^ { 2 }  \mathbb { R }$ , where for two graphs $G$ and $G ^ { \prime }$ , $k ( G , G ^ { \prime } )$ represents the inner product of the embeddings $\psi ( G )$ and $\psi ( G ^ { \prime } )$ over the Hilbert space $\mathcal { H }$ . The mapping $\psi$ could be explicit, as in graph convolutional neural networks, or implicit as in the case of the kernel similarity function $k ( \cdot , \cdot )$ (i.e., the kernel trick). Kriege et al. (2014) provide a thorough discussion on explicit and implicit embeddings for learning from graphs.
+
+Kashima et al. (2003) introduced graph kernels based on random walks on labeled graphs. Subsequently, shortest-path kernels were introduced in (Borgwardt & Kriegel, 2005). These works have been followed by graphlet and Weisfeiler-Lehman subtree kernel methods (Shervashidze et al., 2009; 2011; Morris et al., 2017). More recently, kernel methods using spectral approaches (Kondor & Pan, 2016), assignment-based approaches (Kriege et al., 2016; Nikolentzos et al., 2017), and graph decomposition algorithms (Nikolentzos et al., 2018) have also been proposed in the literature.
+
+Despite being successful for many years, kernel methods often fail to leverage the explicit continuous features that are provided for the graph nodes and/or edges, making them less adaptable to the underlying data distribution. To alleviate these issues, and thanks in part to the prominent success of deep learning in many domains, including computer vision and natural language processing, techniques based on graph neural networks (GNNs) have emerged as an alternative paradigm for learning representations from graph-based data. In general, a GNN comprises multiple hidden layers, where at each layer, each node combines the features of its neighboring nodes in the graph to derive a new feature vector. At the GNN output, the feature vectors of all nodes are aggregated using a readout function (such as global average pooling), resulting in the final graph embedding $\psi ( G )$ . More details on the combining and readout mechanisms of GNNs are provided in Appendix A.4.
+
+Kipf and Welling (Kipf & Welling, 2016) proposed a GNN architecture based on a graph convolutional network (GCN) framework. This work, alongside other notable works on geometric deep learning (Defferrard et al., 2016), initiated a surge of interest in GNN architectures, which has led to several architectures, including the Graph Attention network (GAT) (Velickovi ˇ c et al., 2017), ´ Graph SAmple and aggreGatE (GraphSAGE) (Hamilton et al., 2017), and the Graph Isomorphism Network (GIN) (Xu et al., 2019). Each of these architectures modifies the GNN combining and readout functions and demonstrates state-of-the-art performance in a variety of graph representation learning tasks.
+
+# 2.2 WASSERSTEIN DISTANCES
+
+Let $\mu _ { i }$ denote a Borel probability measure with finite $p ^ { \mathrm { t h } }$ moment defined on $\mathcal { Z } \subseteq \mathbb { R } ^ { d }$ , with corresponding probability density function $p _ { i }$ , i.e., $d \mu _ { i } ( z ) = p _ { i } ( z ) d z$ . The 2-Wasserstein distance between $\mu _ { i }$ and $\mu _ { j }$ defined on $\mathcal { Z } , \mathcal { Z } ^ { j } \subseteq \mathbb { R } ^ { d }$ is the solution to the optimal mass transportation problem with $\ell _ { 2 }$ transport cost (Villani, 2008):
+
+$$
+\mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } ) = \binom { \operatorname* { i n f } _ { } } { \gamma \in \Gamma ( \mu _ { i } , \mu _ { j } ) } \int _ { \mathcal { Z } \times \mathcal { Z } ^ { \prime } } \| z - z ^ { \prime } \| ^ { 2 } d \gamma ( z , z ^ { \prime } ) \bigg ) ^ { \frac { 1 } { 2 } } ,
+$$
+
+where $\Gamma ( \mu _ { i } , \mu _ { j } )$ is the set of all transportation plans $\gamma \in \Gamma ( \mu _ { i } , \mu _ { j } )$ such that $\gamma ( A \times \mathcal { Z } ^ { \prime } ) = \mu _ { i } ( A )$ and $\gamma ( \mathcal { Z } \times B ) = \mu _ { j } ( B )$ for any Borel subsets $A \subseteq { \mathcal { Z } }$ and $B \subseteq { \mathcal { Z } } ^ { \prime }$ . Due to Brenier’s theorem (Brenier, 1991), for absolutely continuous probability measures $\mu _ { i }$ and $\mu _ { j }$ (with respect to the Lebesgue measure), the 2-Wasserstein distance can be equivalently obtained from
+
+$$
+{ \mathcal W } _ { 2 } ( \mu _ { i } , \mu _ { j } ) = \bigg ( \operatorname* { i n f } _ { f \in M P ( \mu _ { i } , \mu _ { j } ) } \int _ { \mathcal Z } \| z - f ( z ) \| ^ { 2 } d \mu _ { i } ( z ) \bigg ) ^ { \frac { 1 } { 2 } } ,
+$$
+
+where $M P ( \mu _ { i } , \mu _ { j } ) = \{ f : \mathcal { Z } \to \mathcal { Z } ^ { \prime } | f _ { \# } \mu _ { i } = \mu _ { j } \}$ and $f _ { \# } \mu _ { i }$ represents the pushforward of measure $\mu _ { i }$ , characterized as
+
+$$
+\int _ { B } d \mu _ { j } ( z ^ { \prime } ) = \int _ { f ^ { - 1 } ( B ) } d \mu _ { i } ( z ) \quad \mathrm { f o r a n y B o r e l s u b s e t } B \subseteq { \mathcal { Z } } ^ { \prime } .
+$$
+
+The mapping $f$ is referred to as a transport map (Kolouri et al., 2017), and the optimal transport map is called the Monge map. For absolutely continuous measures, the differential form of the above equation takes the following form, $d e t ( \tilde { D f } ( z ) ) p _ { j } ( f ( z ) ) = p _ { i } ( z )$ , which is referred to as the Jacobian equation. For discrete probability measures, when the transport plan $\gamma$ is a deterministic optimal coupling, such a transport plan is referred to as a Monge coupling (Villani, 2008).
+
+Recently, Wasserstein distances have been used for representation learning on graphs and images (Togninalli et al., 2019; Zhang et al., 2020; Bécigneul et al., 2020). In particular, (Togninalli et al., 2019) proposed a Wasserstein kernel for graphs that involves pairwise calculation of the Wasserstein distance between graph representations. Pairwise calculation of the Wasserstein distance, however, could be expensive, especially for large graph datasets. In what follows, we apply the linear optimal transportation framework (Wang et al., 2013) to define a Hilbertian embedding, in which the $\ell _ { 2 }$ distance provides a true metric between the probability measures that approximates $\mathcal { W } _ { 2 }$ . We show that in a dataset containing $M$ graphs, this framework reduces the computational complexity from calculating $\frac { M ( M - 1 ) } { 2 }$ linear programs to $M$ .
+
+# 3 LINEAR WASSERSTEIN EMBEDDING
+
+Wang et al. (2013) and the follow-up works (Seguy & Cuturi, 2015; Kolouri et al., 2016; Courty et al., 2018) describe frameworks for isometric Hilbertian embedding of probability measures such that the Euclidean distance between the embedded images approximates $\mathcal { W } _ { 2 }$ . We leverage the prior work and introduce the concept of linear Wasserstein embedding for learning graph embeddings.
+
+# 3.1 THEORETICAL FOUNDATION
+
+We adhere to the definition of the linear Wasserstein embedding for continuous measures. However, all derivations hold for discrete measures as well. More precisely, let $\mu _ { 0 }$ be a reference probability measure defined on $\mathcal { Z } \subseteq \mathbb { R } ^ { d }$ , with a positive probability density function $p _ { 0 }$ , s.t. $d \mu _ { 0 } ( z ) = p _ { 0 } ( z ) d z$ and $p _ { 0 } ( z ) > 0$ for $\forall z \in { \mathcal { Z } }$ . Let $f _ { i }$ denote the Monge map that pushes $\mu _ { 0 }$ into $\mu _ { i }$ , i.e.,
+
+![](images/22195713a537f15e56f81ca8b9d73d9c4103132190c954fe59635f9dfc03e701.jpg)  
+Figure 1: Graphical representation of the linear Wasserstein embedding framework, where the probability distributions are mapped to the tangent space with respect to a fixed reference distribution. The figure is adapted from Kolouri et al. (2017).
+
+$$
+f _ { i } = \mathrm { a r g m i n } _ { f \in M P ( \mu _ { 0 } , \mu _ { i } ) } \int _ { \mathcal Z } \| z - f ( z ) \| ^ { 2 } d \mu _ { 0 } ( z ) .
+$$
+
+Define $\phi ( \mu _ { i } ) \triangleq ( f _ { i } - i d ) \sqrt { p _ { 0 } }$ , where $i d ( z ) = z , \forall z \in \mathcal { Z }$ is the identity function. In cartography, such a mapping is known as the equidistant azimuthal projection, while in differential geometry, it is called the logarithmic map. The mapping $\phi ( \cdot )$ has the following characteristics (partially illustrated in Figure 1):
+
+1. $\phi ( \cdot )$ provides an isometric embedding for probability measures, i.e., using the Jacobian equation pi = det(Df −1i )p0(f −1i ), where fi = φ(µi)√p .
+
+2. $\phi ( \mu _ { 0 } ) = 0$ , i.e., the reference is mapped to zero.
+
+3. $\| \phi ( \mu _ { i } ) - \phi ( \mu _ { 0 } ) \| _ { 2 } = \| \phi ( \mu _ { i } ) \| _ { 2 } = \mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { 0 } )$ , i.e., the mapping preserves distances to $\mu _ { 0 }$
+
+4. $\lVert \phi ( \mu _ { i } ) - \phi ( \mu _ { j } ) \rVert _ { 2 } \approx \mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } )$ , i.e., the $\ell _ { 2 }$ distance between $\phi ( \mu _ { i } )$ and $\phi ( \mu _ { j } )$ , while being a true metric between $\mu _ { i }$ and $\mu _ { j }$ , is an approximation of $\mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } )$ .
+
+Embedding probability measures $\{ \mu _ { i } \} _ { i = 1 } ^ { M }$ via $\phi ( \cdot )$ requires calculating $M$ Monge maps. The fourth characteristic above states that $\phi ( \cdot )$ provides a linear embedding for the probability measures. Therefore, we call it the linear Wasserstein embedding. The mapping $\phi ( \mu _ { i } )$ could be thought as the Reproducing Kernel Hilbert Space (RKHS) embedding of the measure, $\mu _ { i }$ (Muandet et al., 2017). In practice, for discrete distributions, the Monge coupling is used, which could be approximated from the Kantorovich plan (i.e., the transport plan) via the so-called barycenteric projection (Wang et al., 2013). We here acknowledge the concurrent work by Mialon et al. (2021), where the authors use a similar idea to the linear Wasserstein embedding as a pooling operator for learning from sets of features. The authors demonstrate the relationship between their proposed optimal transport-based pooling operation and the widespread attention pooling methods in the literature. A detailed description of the capabilities of the linear Wasserstein embedding framework is included in Appendix A.1. We next provide the numerical details of the barycenteric projection (Ambrosio et al., 2008; Wang et al., 2013).
+
+# 3.2 NUMERICAL DETAILS
+
+Consider a set of probability distributions $\{ p _ { i } \} _ { i = 1 } ^ { M }$ , and let $Z _ { i } = \left[ z _ { 1 } ^ { i } , \ldots , z _ { N _ { i } } ^ { i } \right] ^ { T } \in \mathbb { R } ^ { N _ { i } \times d }$ be an array containing $N _ { i }$ i.i.d. samples from distribution $p _ { i }$ , i.e., $z _ { k } ^ { i } \in \mathbb { R } ^ { d } \sim p _ { i } , \forall k \in \{ 1 , \dots , N _ { i } \} .$ . Let us define $p _ { 0 }$ to be a reference distribution, with $\boldsymbol { Z } _ { 0 } = \left[ z _ { 1 } ^ { 0 } , \ldots , z _ { N } ^ { 0 } \right] ^ { T } \in \mathbb { R } ^ { N \times d }$ , where $\begin{array} { r } { N = \lfloor \frac { 1 } { M } \sum _ { i = 1 } ^ { M } N _ { i } \rfloor } \end{array}$ and $z _ { j } ^ { 0 } \in \mathbb { R } ^ { d } \sim p _ { 0 } , \forall j \in \{ 1 , \dots , N \}$ . The optimal transport plan between $p _ { i }$ and $p _ { 0 }$ , denoted by $\pi _ { i } ^ { * } \in \mathbb { R } ^ { N \times N _ { i } }$ , is the solution to the following linear program,
+
+$$
+\begin{array} { r } { \pi _ { i } ^ { * } = \underset { \ b { \pi } \in \Pi _ { i } } { \operatorname { a r g m i n } } \sum _ { \ b { \pi } \in \Pi _ { i } } ^ { N } \displaystyle \sum _ { j = 1 } ^ { N _ { i } } \sum _ { k = 1 } ^ { N _ { i } } \pi _ { j k } \lVert z _ { j } ^ { 0 } - z _ { k } ^ { i } \rVert ^ { 2 } , } \end{array}
+$$
+
+where $\Pi _ { i } \triangleq \Big \{ \pi \in \mathbb { R } ^ { N \times N _ { i } } \big | N _ { i } \sum _ { j = 1 } ^ { N } \pi _ { j k } = N \sum _ { k = 1 } ^ { N _ { i } } \pi _ { j k } = 1 , \forall k \in \{ 1 , \dots , N _ { i } \} , \forall j \in \{ 1 , \dots , N \} \Big \} .$ The Monge map is then approximated from the optimal transport plan by barycentric projection via
+
+$$
+F _ { i } = N ( \pi _ { i } ^ { * } Z _ { i } ) \in \mathbb { R } ^ { N \times d } .
+$$
+
+Note that the transport plan $\pi _ { i }$ could split the mass in $z _ { j } ^ { 0 } \in Z _ { 0 }$ and distribute it on $z _ { k } ^ { i } \mathrm { s }$ . The barycentric projection calculates the center of mass of the transportation locations for $z _ { j } ^ { 0 }$ to ensure that no mass splitting is happening (see Figure 5), and hence it approximates a Monge coupling. Finally, the√ embedding can be calculated by $\phi ( Z _ { i } ) = ( F _ { i } - Z _ { 0 } ) / \sqrt { N } \in \mathbb { R } ^ { N \times d }$ . With a slight abuse of notation, we use $\phi ( p _ { i } )$ and $\phi ( Z _ { i } )$ interchangeably throughout the paper. Due to the barycenteric projection, here, $\phi ( \cdot )$ is only pseudo-invertible.
+
+# 4 WEGL: A LINEAR WASSERSTEIN EMBEDDING FOR GRAPHS
+
+The application of the optimal transport problem to graphs is multifaceted. For instance, some works focus on solving the “structured” optimal transport concerning an optimal probability flow, where the transport cost comes from distances on an often unchanging underlying graph (Léonard et al., 2016; Essid & Solomon, 2018; Titouan et al., 2019). Here, we are interested in applying optimal transport to measure the dissimilarity between two graphs (Maretic et al., 2019; Togninalli et al., 2019; Dong & Sawin, 2020). Our work significantly differs from (Maretic et al., 2019; Dong & Sawin, 2020), which measure the dissimilarity between non-attributed graphs based on distributions defined by their Laplacian spectra and is closer to (Togninalli et al., 2019).
+
+Our proposed graph embedding framework, termed Wasserstein Embedding for Graph Learning (WEGL), combines node embedding methods for graphs with the linear Wasserstein embedding explained in Section 3. More precisely, let $\{ G _ { i } = ( \breve { \mathcal { V } } _ { i } , \dot { \mathcal { E } } _ { i } ) \} _ { i = 1 } ^ { M }$ denote a set of $M$ individual graphs, each with a set of possible node features $\{ x _ { v } \} _ { v \in \mathcal { V } _ { i } }$ and a set of possible edge features $\{ w _ { u v } \} _ { ( u , v ) \in \mathcal { E } _ { i } }$ . Let $h ( \cdot )$ be an arbitrary node embedding process, where $h ( G _ { i } ) = Z _ { i } = \left[ z _ { 1 } , \ldots , z _ { | \mathcal { V } _ { i } | } \right] ^ { T } \in \mathbb { R } ^ { | \mathcal { V } _ { i } | \times d }$ . Having the node embeddings $\{ Z _ { i } \} _ { i = 1 } ^ { M }$ , we can then calculate a reference node embedding $Z _ { 0 }$ (see Section 4.2 for details), which leads to the linear Wasserstein embedding $\phi ( Z _ { i } )$ with respect to $Z _ { 0 }$ , as described in Section 3. Therefore, the entire embedding for each graph $G _ { i } , i \in \{ 1 , \dots , M \}$ , is obtained by composing $\phi ( \cdot )$ and $h ( \cdot )$ , i.e., $\psi ( G _ { i } ) = \phi { \left( h ( G _ { i } ) \right) }$ . Figure 2 visualizes this process.
+
+# 4.1 NODE EMBEDDING
+
+There are many choices for node embedding methods (Chami et al., 2020). These methods in general could be parametric or non-parametric, e.g., as in propagation/diffusion-based embeddings. Parametric embeddings are often implemented via a GNN encoder. The encoder can capture different graph properties depending on the type of supervision (e.g., supervised or unsupervised). Selfsupervised embedding methods have also been recently shown to be promising $\mathrm { H u ^ { * } }$ et al., 2020).
+
+In this paper, for our node embedding process $h ( \cdot )$ , we follow a similar non-parametric propagation/diffusion-based encoder as in (Togninalli et al., 2019). One of the appealing advantages of this framework is its simplicity, as there are no trainable parameters involved. In short, given a graph $G = ( \nu , \mathcal { E } )$ with node features $\{ x _ { v } \} _ { v \in \mathcal { V } }$ and scalar edge features $\{ w _ { u v } \} _ { ( u , v ) \in \mathcal { E } }$ , we use the following instantiation of equation 12 to define the combining function as
+
+![](images/477c7e7f9c34eee92deae36b603a73ab39b15d39fbb4169ee9450945ae3174cf.jpg)  
+Figure 2: Our proposed graph embedding framework, WEGL, combines node embedding methods with the linear Wasserstein embedding framework described in Section 3. Given a graph $G _ { i } = ( \nu _ { i } , \bar { \mathcal { E } } _ { i } )$ , we first embed the graph nodes into a $d$ -dimensional Hilbert space and obtain an array of node embeddings, denoted by $h ( G _ { i } ) = Z _ { i } \in \mathbb { R } ^ { | V _ { i } | \times d }$ . We then calculate the linear Wasserstein embedding of $Z _ { i }$ with respect to a reference $Z _ { 0 }$ , i.e., $\phi ( Z _ { i } )$ , to derive the final graph embedding.
+
+$$
+x _ { v } ^ { ( l ) } = \sum _ { u \in { \mathcal { N } } _ { v } \cup \{ v \} } \frac { w _ { u v } } { \sqrt { { \mathsf { d e g } } ( u ) { \mathsf { d e g } } ( v ) } } \cdot x _ { u } ^ { ( l - 1 ) } , \forall l \in \{ 1 , \ldots , L \} , \forall v \in \mathcal { V } ,
+$$
+
+where for any node $v \in \mathcal V$ , its degree ${ \mathsf { d e g } } ( v )$ is defined as its number of neighbors in $G$ augmented with self-connections, i.e., $\deg ( v ) \triangleq 1 + | \mathcal { N } _ { v } |$ . Note that the normalization of the messages between graph nodes by the (square root of) the two end-point degrees in equation 7 have also been used in other architectures, including GCN (Kipf & Welling, 2016). For the cases where the edge weights are not available, including self-connection weights $\{ w _ { v v } \} _ { v \in \mathcal { V } }$ , we set them to one. In Appendix A.5, we show how we use an extension of equation 7 to treat graphs with multiple edge features/labels. Finally, we let $z _ { v } = g \left( \{ x _ { v } ^ { ( l ) } \} _ { l = 0 } ^ { L } \right)$ represent the resultant embedding for each node $v \in \mathcal V$ , where $g ( \cdot )$ is a local pooling process on a single node (not a global pooling), e.g., concatenation or averaging.
+
+# 4.2 CALCULATION OF THE REFERENCE DISTRIBUTION
+
+To calculate the reference distribution, we use the $k$ -means clustering algorithm on $\textstyle \bigcup _ { i = 1 } ^ { M } Z _ { i }$ with $\begin{array} { r } { N = \left\lfloor { \frac { 1 } { M } } \sum _ { i = 1 } ^ { M } N _ { i } \right\rfloor } \end{array}$ centroids. Alternatively, one can calculate the Wasserstein barycenter (Cuturi & Doucet, 2014) of the node embeddings or simply use $N$ samples from a normal distribution. While approximation of the 2-Wasserstein distance in the tangent space depends on the reference distribution choice, surprisingly, we see a stable performance of WEGL for different references. In Appendix A.2, we compare the performance of WEGL with respect to different references.
+
+# 5 EXPERIMENTAL EVALUATION
+
+In this section, we discuss the evaluation results of our proposed algorithm on multiple benchmark graph classification datasets. We use the PyTorch Geometric framework (Fey & Lenssen, 2019) for implementing WEGL. In all experiments, we use scikit-learn for the implementation of our downstream classifiers on the embedded graphs (Buitinck et al., 2013).
+
+# 5.1 MOLECULAR PROPERTY PREDICTION ON THE OPEN GRAPH BENCHMARK
+
+We first evaluate our algorithm on the molecular property prediction task on the ogbg-molhiv dataset. This dataset is part of the Open Graph Benchmark (Hu et al., 2020), which involves node-level, link-level, and graph-level learning and prediction tasks on multiple datasets spanning diverse problem domains. The ogbg-molhiv dataset, in particular, is a molecular tree-like dataset, consisting of 41, 127 graphs, with an average number of 25.5 nodes and 27.5 edges per graph. Each graph is a molecule, with nodes representing atoms and edges representing bonds between them, and
+
+<table><tr><td rowspan=10 colspan=1>NNO</td><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=1>Validation ROC-AUC(%) Test ROC-AUC (%)</td></tr><tr><td rowspan=1 colspan=1>GCN (Kipf &amp; Welling,2016)</td><td rowspan=1 colspan=1>83.8±0.9           76.0 ±1.2</td></tr><tr><td rowspan=1 colspan=1>GIN + Virtual Node (Xu et al., 2019)</td><td rowspan=1 colspan=1>84.8 ± 0.7           77.1 ± 1.5</td></tr><tr><td rowspan=1 colspan=1>DeeperGCN (Li et al.,2020)</td><td rowspan=1 colspan=1>84.3±0.6           78.6 ± 1.2</td></tr><tr><td rowspan=1 colspan=1>HIMP (Fey et al., 2020)</td><td rowspan=1 colspan=1>78.8 ± 0.8</td></tr><tr><td rowspan=1 colspan=1>GCN + GraphNorm (Cai et al., 2020)</td><td rowspan=1 colspan=1>79.0 ± 1.1           78.8±1.0</td></tr><tr><td rowspan=1 colspan=1>WEGL+Random Forest</td><td rowspan=1 colspan=1>79.2 ± 2.2           75.5 ± 1.5</td></tr><tr><td rowspan=1 colspan=1>WEGL + Virtual Node + Random Forest</td><td rowspan=1 colspan=1>81.9 ± 1.3           76.5 ± 1.8</td></tr><tr><td rowspan=1 colspan=1>WEGL + Virtual Node + AutoML</td><td rowspan=1 colspan=1>81.6± 0.6           79.1 ± 0.3</td></tr><tr><td rowspan=1 colspan=1>GAP + Virtual Node +Random Forest</td><td rowspan=1 colspan=1>74.9 ± 2.4           72.1 ± 1.7</td></tr></table>
+
+Table 1: Graph classification results on the ogbg-molhiv dataset. The results for GCN and GIN are reported from (Hu et al., 2020). The best validation and test results are shown in bold.
+
+it includes both node and edge attributes, characterizing the atom and bond features. The goal is to predict a binary label indicating whether or not a molecule inhibits HIV replication.
+
+To train and evaluate our proposed method, we use the scaffold split provided by the dataset, and report the mean and standard deviation of the results across 10 different random seeds. We perform a grid search over a set of hyperparameters and report the configuration that leads to the best validation performance. We also report a virtual node variant of the graphs in our evaluations, where each graph is augmented with an additional node that is connected to all the original nodes in the graph. This node serves as a shortcut for message passing among the graph nodes, bringing any pair of nodes within at most two hops of each other. The complete implementation details can be found in Appendix A.5.
+
+Table 1 shows the evaluation results of WEGL on the ogbg-molhiv dataset in terms of the ROC-AUC (i.e., Receiver Operating Characteristic Area Under the Curve), alongside multiple GNNbased baseline algorithms. Specifically, we show the results using two classifiers: A random forest classifier (Breiman, 2001) and an automated machine learning (AutoML) classifier using the AutoSklearn 2.0 library (Feurer et al., 2020). As the table demonstrates, while WEGL embeddings combined with random forest achieve a decent performance level, using AutoML further enhances the performance and achieves state-of-the-art test results on this dataset, showing the high expressive power of WEGL in large-scale graph datasets, without the need for end-to-end training.
+
+Moreover, as an ablation study, we report the evaluation results on the ogbg-molhiv dataset using a random forest classifier, where the Wasserstein embedding module after the node embedding process is replaced with global average pooling (GAP) among the output node embeddings of each graph to derive the graph-level embedding. As the table demonstrates, there is a significant performance drop when using GAP graph embedding, which indicates the benefit of our proposed graph embedding method as opposed to average readout.
+
+# 5.2 TUD BENCHMARK DATASETS
+
+We also consider a set of social network, bioinformatics and molecule graph datasets (Kersting et al., 2020). The social network datasets (IMDB-BINARY, IMDB-MULTI, COLLAB, REDDIT-BINARY, and REDDIT-MULTI-5K) lack both node and edge features. Therefore, in these datasets we use a one-hot representation of the node degrees as their initial feature vectors, as also used in prior work, e.g., (Xu et al., 2019). To handle the large scale of the REDDIT-BINARY and REDDIT-MULTI-5K and datasets, we clip the node degrees at 500.
+
+Moreover, for the molecule (PTC-MR) and bioinformatics (ENZYMES and PROTEINS) datasets, we use the readily-provided node labels in (Kersting et al., 2020) as the initial node feature vectors. Besides, for PTC-MR which has edge labels, as explained in Appendix A.5, we use an extension of equation 7 to use the one-hot encoded edge features in the diffusion process. To evaluate the performance of WEGL, we follow the methodology used in (Yanardag & Vishwanathan, 2015; Niepert et al., 2016; Xu et al., 2019), where for each dataset, we perform 10-fold cross-validation with random splitting on the entire dataset, conducting a grid search over the desired set of hyperparameters as mentioned in Appendix A.5, and we then report the mean and standard deviation of the validation accuracies achieved during cross-validation. For this experiment, we use two ensemble classifiers, namely Random Forest and Gradient Boosted Decision Tree (GBDT), together with kernel-SVM with an RBF kernel (SVM-RBF). Given that the Euclidean distance in the embedding space approximates the 2-Wasserstein distance, the SVM-RBF classification results are comparable with those reported by Togninalli et al. (2019).
+
+Table 2: Graph classification accuracy $( \% )$ of our method and comparison with the state-of-the-art GNNs and graph kernels (GKs) on various TUD graph classification tasks. The results for DGCNN are reported from (Errica et al., 2020). The top-three performers on each dataset are shown in bold.   
+
+<table><tr><td rowspan="5">NNO</td><td>Method</td><td>IMDB-B</td><td>IMDB-M</td><td>COLLAB</td><td>RE-B</td><td>RE-M5K PTC-MR</td><td>ENZYMES</td><td>PROTEINS</td></tr><tr><td>DGCNN (Zhang et al.,2018a)</td><td>69.2±3.0</td><td>45.6±3.4 71.2±1.9</td><td>87.8±2.5</td><td>49.2±1.2</td><td>58.6</td><td>38.9±5.7</td><td>72.9±3.5</td></tr><tr><td>GraphSAGE (Hamilton et al.,2017)</td><td>68.8±4.5 47.6±3.5 73.9±1.7 84.3±1.9 50.0±1.3 63.9±7.7</td><td></td><td></td><td></td><td></td><td></td><td>75.9±3.2</td></tr><tr><td>GIN (Xu et al., 2019)</td><td>75.1±5.1</td><td>2.3±2.8</td><td>80.2±1.9</td><td>92.4±2.5 57.5±1.5</td><td>564.6±7.0</td><td></td><td>76.2±2.8</td></tr><tr><td>GNTK (Du et al., 2019)</td><td></td><td>76.9±3.6 52.8±4.6 83.6±1.0</td><td></td><td></td><td>67.9±6.9</td><td></td><td>75.6±4.2</td></tr><tr><td rowspan="5"></td><td>CapsGNN (Xinyi &amp; Chen,2019)</td><td>73.1±4.8</td><td>50.3±2.6 79.6±0.9</td><td></td><td>52.9±1.5</td><td></td><td>54.7±5.7</td><td>76.3±3.6</td></tr><tr><td>GraphNorm (Cai et al.,2020)</td><td>76.0±3.7</td><td></td><td>80.2±1.0 93.5±2.1</td><td></td><td>64.9±7.5</td><td></td><td> 77.4±4.9</td></tr><tr><td>DGK(Yanardag &amp; Vishwanathan,2015)</td><td></td><td></td><td></td><td></td><td>67.0±0.6 44.6±0.5 73.1±0.3 78.0±0.4 41.3±0.2 57.3±1.1</td><td>27.1±0.8</td><td>71.7±0.5</td></tr><tr><td>WL (Shervashidze et al.,2011)</td><td>73.8±3.9 49.8±0.5 74.8±0.2 68.2±0.2 51.2±0.3 57.0±2.0</td><td></td><td></td><td></td><td></td><td>53.2±1.1</td><td>72.9±0.6</td></tr><tr><td>RetGK (Zhang et al., 2018b)</td><td></td><td></td><td></td><td></td><td>71.0±0.6 46.7±0.6 73.6±0.3 90.8±0.2 54.2±0.3 67.9±1.4 59.1±1.1</td><td></td><td>75.2±0.3</td></tr><tr><td rowspan="4">3</td><td>AWE (Ivanov &amp; Burnaev,2018)</td><td></td><td>74.5±5.8 51.5±3.6 73.9±1.9 87.9±2.5 50.5±1.9</td><td></td><td></td><td></td><td>35.8±5.9</td><td></td></tr><tr><td>WWL(Togninalli et al., 2019)</td><td>74.4±0.8</td><td></td><td></td><td></td><td>66.3±1.2</td><td>59.1±0.8</td><td>74.3±0.6</td></tr><tr><td>WEGL +SVM-RBF</td><td></td><td></td><td></td><td></td><td>73.4±2.5 51.7±3.1 78.6±1.0 92.1±1.9 56.1±2.3 63.4±5.3</td><td>57.3±4.2</td><td>76.0±4.4</td></tr><tr><td>WEGL + Random Forest</td><td></td><td></td><td></td><td>75.4±5.0 52.0±4.1 79.8±1.5 92.0±0.8 55.1±2.5</td><td></td><td>67.5±7.7 60.5±5.9</td><td>76.5±4.2</td></tr><tr><td>s.InO</td><td>WEGL + GBDT</td><td>75.2±5.0</td><td>52.3±2.9</td><td>80.6±2.0 92.9±1.9</td><td>55.4±1.6</td><td>66.2±6.9</td><td>60.0±6.3</td><td>76.3±3.9</td></tr></table>
+
+Table 2 shows the classification accuracies achieved by WEGL on the aforementioned datasets as compared with several GNN and graph kernel baselines, whose results are extracted from the corresponding original papers. As the table demonstrates, our proposed algorithm achieves either state-of-the-art or competitive results across all the datasets, and in particular, it is among the top-three performers in all of them. This shows the effectiveness of the proposed linear Wasserstein embedding for learning graph-level properties across different domains.
+
+# 5.3 COMPUTATION TIME
+
+As mentioned before, one of the most important advantages of WEGL as compared to other graph representation learning methods is its algorithmic efficiency. To evaluate that, we compare the wall-clock training and inference times of WEGL with those of GIN and the Wasserstein Weisfeiler-Lehman (WWL) graph kernel on five different TUD datasets (IMDB-B, MUTAG, PTC-MR, PROTEINS, and $\mathrm { { N C I 1 } } ) ^ { 2 }$ . For WEGL and WWL, we use the exact linear programming solver (as opposed to the entropy-regularized version). We carry out our experiments for WEGL and WWL on a $2 . 3 \ : \mathrm { G H z }$ Intel
+
+Figure 3 shows how the training and inference run-times of WEGL, WWL and GIN scale with the number of graphs in the dataset, the average number of nodes per graph, and the average number of edges per graph. As the figure illustrates, while having similar or even better performance, training WEGL is several orders of magnitude faster than WWL and GIN, especially for datasets with larger numbers of graphs. Note that training WWL becomes very inefficient as the number of graphs in the dataset increases due to the pairwise distance calculation between all the graphs.
+
+During inference, WEGL is slightly slower than GIN, when implemented on a GPU. However, on most datasets, WEGL is considerably faster in inference as compared to GIN implemented on a CPU. Moreover, both algorithms are significantly faster than WWL. Using GPU-accelerated implementations of the diffusion process in equation 7 and the entropy-regularized transport problem could potentially further enhance the computational efficiency of WEGL during inference.
+
+![](images/591c2668336dfb73566a7d2cead85eb10fad140965c98313c86bf6cfcb9d280e.jpg)  
+Figure 3: Average wall-clock time comparison of our proposed method, WEGL with WWL (Togninalli et al., 2019) and GIN (Xu et al., 2019). WEGL and WWL were implemented on a 2.3 GHz Intel
+
+# 6 CONCLUSION
+
+We considered the problem of graph property prediction and introduced the linear Wasserstein Embedding for Graph Learning, which we denoted as WEGL. Similar to (Togninalli et al., 2019), our approach also relies on measuring the Wasserstein distances between the node embeddings of graphs. Unlike (Togninalli et al., 2019), however, we further embed the node embeddings of graphs into a Hilbert space, in which their Euclidean distance approximates their 2-Wasserstein distance. WEGL provides two significant benefits: i) it has linear complexity in the number of graphs (as opposed to the quadratic complexity of (Togninalli et al., 2019)), and ii) it enables the application of any ML algorithm of choice, such as random forest, gradient boosted decision tree, or even AutoML. We demonstrated WEGL’s superior performance and highly efficient training on a wide range of benchmark datasets, including the ogbg-molhiv dataset and the TUD graph classification tasks.
+
+# ACKNOWLEDGEMENT
+
+We gratefully acknowledge funding by the United States Air Force under Contract No. FA8750-19- C-0098. Gustavo K. Rohde also acknowledges funding by NIH grant GM130825. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force and DARPA.
+
+# REFERENCES
+
+Monica Agrawal, Marinka Zitnik, and Jure Leskovec. Large-scale analysis of disease pathways in the human interactome. In PSB, pp. 111–122. World Scientific, 2018.
+
+Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré. Gradient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2008.
+
+Lars Backstrom and Jure Leskovec. Supervised random walks: predicting and recommending links in social networks. In Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, pp. 635–644, 2011.
+
+Gary Bécigneul, Octavian-Eugen Ganea, Benson Chen, Regina Barzilay, and Tommi Jaakkola. Optimal transport graph neural networks. arXiv preprint arXiv:2006.04804, 2020.
+
+Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Martin Blais, Amol Kapoor, Michal Lukasik, and Stephan Günnemann. Is pagerank all you need for scalable graph neural networks? In Proceedings of the $1 5 ^ { t h }$ International Workshop on Mining and Learning with Graphs (MLG), 2019.
+
+Karsten M Borgwardt and Hans-Peter Kriegel. Shortest-path kernels on graphs. In Fifth IEEE International Conference on Data Mining (ICDM’05). IEEE, 2005.
+
+Leo Breiman. Random forests. Machine learning, 45(1):5–32, 2001.
+
+Yann Brenier. Polar factorization and monotone rearrangement of vector-valued functions. Communications on pure and applied mathematics, 44(4):375–417, 1991.
+
+Lars Buitinck, Gilles Louppe, Mathieu Blondel, Fabian Pedregosa, Andreas Mueller, Olivier Grisel, Vlad Niculae, Peter Prettenhofer, Alexandre Gramfort, Jaques Grobler, Robert Layton, Jake VanderPlas, Arnaud Joly, Brian Holt, and Gaël Varoquaux. API design for machine learning software: Experiences from the scikit-learn project. In ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pp. 108–122, 2013.
+
+Tianle Cai, Shengjie Luo, Keyulu Xu, Di He, Tie-yan Liu, and Liwei Wang. Graphnorm: A principled approach to accelerating graph neural network training. arXiv preprint arXiv:2009.03294, 2020.
+
+Ines Chami, Sami Abu-El-Haija, Bryan Perozzi, Christopher Ré, and Kevin Murphy. Machine learning on graphs: A model and comprehensive taxonomy. arXiv preprint arXiv:2005.03675, 2020.
+
+Nicolas Courty, Rémi Flamary, and Mélanie Ducoffe. Learning wasserstein embeddings. In International Conference on Learning Representations, 2018.
+
+Marco Cuturi and Arnaud Doucet. Fast computation of Wasserstein barycenters. In Proceedings of the 31st International Conference on Machine Learning, Proceedings of Machine Learning Research, pp. 685–693. PMLR, 2014. URL http://proceedings.mlr.press/v32/cuturi14. html.
+
+Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems, pp. 3844–3852, 2016.
+
+Yihe Dong and Will Sawin. COPT: Coordinated optimal transport on graphs. arXiv preprint arXiv:2003.03892, 2020.
+
+Simon S Du, Kangcheng Hou, Russ R Salakhutdinov, Barnabas Poczos, Ruosong Wang, and Keyulu Xu. Graph neural tangent kernel: Fusing graph neural networks with graph kernels. In Advances in Neural Information Processing Systems, pp. 5724–5734, 2019.
+
+P Dvurechensky, A Gasnikov, and A Kroshnin. Computational optimal transport: Complexity by accelerated gradient descent is better than by sinkhorn’s algorithm. In 35th International Conference on Machine Learning, ICML 2018, pp. 2196–2220, 2018.
+
+Federico Errica, Marco Podda, Davide Bacciu, and Alessio Micheli. A fair comparison of graph neural networks for graph classification. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id $=$ HygDF6NFPB.
+
+Montacer Essid and Justin Solomon. Quadratically regularized optimal transport on graphs. SIAM Journal on Scientific Computing, 40(4):A1961–A1986, 2018.
+
+Matthias Feurer, Katharina Eggensperger, Stefan Falkner, Marius Lindauer, and Frank Hutter. Autosklearn 2.0: The next generation. arXiv preprint arXiv:2007.04074, 2020.
+
+Matthias Fey and Jan E. Lenssen. Fast graph representation learning with PyTorch Geometric. In ICLR Workshop on Representation Learning on Graphs and Manifolds, 2019.
+
+Matthias Fey, Jan-Gin Yuen, and Frank Weichert. Hierarchical inter-message passing for learning on molecular graphs. arXiv preprint arXiv:2006.12179, 2020.
+
+R’emi Flamary and Nicolas Courty. Pot python optimal transport library, 2017. URL https: //pythonot.github.io/.
+
+Thomas Gärtner, Peter Flach, and Stefan Wrobel. On graph kernels: Hardness results and efficient alternatives. In Learning Theory and Kernel Machines, pp. 129–143. Springer, 2003.
+
+Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems, pp. 1024–1034, 2017.
+
+Danny Hernandez and Tom B Brown. Measuring the algorithmic efficiency of neural networks. arXiv preprint arXiv:2005.04305, 2020.
+
+Thomas Hofmann, Bernhard Schölkopf, and Alexander J Smola. Kernel methods in machine learning. The Annals of Statistics, pp. 1171–1220, 2008.
+
+Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. arXiv preprint arXiv:2005.00687, 2020.
+
+Weihua $\mathrm { H u ^ { * } }$ , Bowen Liu\*, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, and Jure Leskovec. Strategies for pre-training graph neural networks. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } }$ HJlWWJSFDH.
+
+Sergey Ivanov and Evgeny Burnaev. Anonymous walk embeddings. In International Conference on Machine Learning, pp. 2186–2195, 2018.
+
+Wengong Jin, Connor Coley, Regina Barzilay, and Tommi Jaakkola. Predicting organic reaction outcomes with Weisfeiler-Lehman network. In Advances in Neural Information Processing Systems, pp. 2607–2616, 2017.
+
+Hisashi Kashima, Koji Tsuda, and Akihiro Inokuchi. Marginalized kernels between labeled graphs. In Proceedings of the $2 { \cal O } ^ { t h }$ International Conference on Machine Learning (ICML-03), pp. 321–328, 2003.
+
+Kristian Kersting, Nils M. Kriege, Christopher Morris, Petra Mutzel, and Marion Neumann. Benchmark data sets for graph kernels, 2020. URL http://www.graphlearning.io/.
+
+Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907, 2016.
+
+Soheil Kolouri, Akif B Tosun, John A Ozolek, and Gustavo K Rohde. A continuous linear optimal transport approach for pattern analysis in image datasets. Pattern Recognition, 51:453–462, 2016.
+
+Soheil Kolouri, Se Rim Park, Matthew Thorpe, Dejan Slepcev, and Gustavo K Rohde. Optimal mass transport: Signal processing and machine-learning applications. IEEE Signal Processing Magazine, 34(4):43–59, 2017.
+
+Risi Kondor and Horace Pan. The multiscale Laplacian graph kernel. In Advances in Neural Information Processing Systems, pp. 2990–2998, 2016.
+
+Nils Kriege, Marion Neumann, Kristian Kersting, and Petra Mutzel. Explicit versus implicit graph feature maps: A computational phase transition for walk kernels. In 2014 IEEE international conference on data mining, pp. 881–886. IEEE, 2014.
+
+Nils M Kriege, Pierre-Louis Giscard, and Richard Wilson. On valid optimal assignment kernels and applications to graph classification. In Advances in Neural Information Processing Systems, pp. 1623–1631, 2016.
+
+Nils M Kriege, Fredrik D Johansson, and Christopher Morris. A survey on graph kernels. Applied Network Science, 5(1):1–42, 2020.
+
+Christian Léonard et al. Lazy random walks and optimal transport on graphs. The Annals of Probability, 44(3):1864–1915, 2016.
+
+Guohao Li, Chenxin Xiong, Ali Thabet, and Bernard Ghanem. Deepergcn: All you need to train deeper gcns. arXiv preprint arXiv:2006.07739, 2020.
+
+Hermina Petric Maretic, Mireille El Gheche, Giovanni Chierchia, and Pascal Frossard. GOT: An optimal transport framework for graph comparison. In Advances in Neural Information Processing Systems, pp. 13876–13887, 2019.
+
+Grégoire Mialon, Dexiong Chen, Alexandre d’Aspremont, and Julien Mairal. A trainable optimal transport embedding for feature aggregation and its relationship to attention. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum? id $=$ ZK6vTvb84s.
+
+Caroline Moosmüller and Alexander Cloninger. Linear optimal transport embedding: Provable fast wasserstein distance computation and classification for nonlinear problems. arXiv preprint arXiv:2008.09165, 2020.
+
+Christopher Morris, Kristian Kersting, and Petra Mutzel. Glocalized Weisfeiler-Lehman graph kernels: Global-local feature maps of graphs. In 2017 IEEE International Conference on Data Mining (ICDM), pp. 327–336. IEEE, 2017.
+
+Christopher Morris, Martin Ritzert, Matthias Fey, William L Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe. Weisfeiler and leman go neural: Higher-order graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 4602–4609, 2019.
+
+Christopher Morris, Gaurav Rattan, and Petra Mutzel. Weisfeiler and leman go sparse: Towards scalable higher-order graph embeddings. Advances in Neural Information Processing Systems, 33, 2020.
+
+K Muandet, K Fukumizu, B Sriperumbudur, and B Schölkopf. Kernel mean embedding of distributions: A review and beyond. Foundations and Trends in Machine Learning, 10(1-2):1–144, 2017.
+
+Navid Naderializadeh, Mark Eisen, and Alejandro Ribeiro. Wireless power control via counterfactual optimization of graph neural networks. arXiv preprint arXiv:2002.07631, 2020.
+
+Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. Learning convolutional neural networks for graphs. In International Conference on Machine Learning, pp. 2014–2023, 2016.
+
+Giannis Nikolentzos, Polykarpos Meladianos, and Michalis Vazirgiannis. Matching node embeddings for graph similarity. In Thirty-First AAAI Conference on Artificial Intelligence, 2017.
+
+Giannis Nikolentzos, Polykarpos Meladianos, Stratis Limnios, and Michalis Vazirgiannis. A degeneracy framework for graph similarity. In IJCAI, pp. 2595–2601, 2018.
+
+Bastian Rieck, Christian Bock, and Karsten Borgwardt. A persistent weisfeiler-lehman procedure for graph classification. In International Conference on Machine Learning, pp. 5448–5458, 2019.
+
+Hamidreza Sadreazami, Arash Mohammadi, Amir Asif, and Konstantinos N Plataniotis. Distributedgraph-based statistical approach for intrusion detection in cyber-physical systems. IEEE Transactions on Signal and Information Processing over Networks, 4(1):137–147, 2017.
+
+Vivien Seguy and Marco Cuturi. Principal geodesic analysis for probability measures under the optimal transport metric. In Advances in Neural Information Processing Systems, pp. 3312–3320, 2015.
+
+Nino Shervashidze, SVN Vishwanathan, Tobias Petri, Kurt Mehlhorn, and Karsten Borgwardt. Efficient graphlet kernels for large graph comparison. In Artificial Intelligence and Statistics, pp. 488–495, 2009.
+
+Nino Shervashidze, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, and Karsten M Borgwardt. Weisfeiler-Lehman graph kernels. Journal of Machine Learning Research, 12(77): 2539–2561, 2011.
+
+Vayer Titouan, Nicolas Courty, Romain Tavenard, Chapel Laetitia, and Rémi Flamary. Optimal transport for structured data with application on graphs. In Proceedings of the $3 6 ^ { t h }$ International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 6275–6284, Long Beach, California, USA, 09–15 Jun 2019. PMLR. URL http://proceedings.mlr.press/v97/titouan19a.html.
+
+Matteo Togninalli, Elisabetta Ghisu, Felipe Llinares-López, Bastian Rieck, and Karsten Borgwardt. Wasserstein Weisfeiler-Lehman graph kernels. In Advances in Neural Information Processing Systems, pp. 6436–6446, 2019.
+
+Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua ´ Bengio. Graph attention networks. arXiv preprint arXiv:1710.10903, 2017.
+
+Cédric Villani. Optimal transport: Old and new, volume 338. Springer Science & Business Media, 2008.
+
+Wei Wang, Dejan Slepcev, Saurav Basu, John A Ozolek, and Gustavo K Rohde. A linear optimal ˇ transportation framework for quantifying and visualizing variations in sets of images. International Journal of Computer Vision, 101(2):254–269, 2013.
+
+Zhang Xinyi and Lihui Chen. Capsule graph neural network. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } } =$ Byl8BnRcYm.
+
+Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations, 2019. URL https: //openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } } =$ ryGs6iA5Km.
+
+Pinar Yanardag and SVN Vishwanathan. Deep graph kernels. In Proceedings of the $2 { { I } ^ { s t } }$ ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1365–1374, 2015.
+
+Chi Zhang, Yujun Cai, Guosheng Lin, and Chunhua Shen. Deepemd: Few-shot image classification with differentiable earth mover’s distance and structured classifiers. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.
+
+Muhan Zhang, Zhicheng Cui, Marion Neumann, and Yixin Chen. An end-to-end deep learning architecture for graph classification. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018a.
+
+Zhen Zhang, Mianzhi Wang, Yijian Xiang, Yan Huang, and Arye Nehorai. RetGK: Graph kernels based on return probabilities of random walks. In Advances in Neural Information Processing Systems, pp. 3964–3974, 2018b.
+
+# A APPENDIX
+
+Here we provide further details on the theoretical aspect of WEGL, our implementation details, and the sensitivity of the results to the choice of reference distribution. We also share our implementation code on the ogbg-molhiv dataset to help with the review process.
+
+# A.1 DETAILED DISCUSSION ON LINEAR WASSERSTEIN EMBEDDING
+
+The linear Wasserstein embedding used in WEGL is based on the Linear Optimal Transport (LOT) framework introduced in (Wang et al., 2013). The main idea is to compute the “projection” of the manifold of probability measures to the tangent space at a fixed reference measure. In particular, the tangent space at measure $\mu _ { 0 }$ is the set of vector fields $\begin{array} { r } { \mathcal { V } _ { \mu _ { 0 } } = \{ v : \mathcal { Z } \to \mathbb { R } ^ { d } \mid \int _ { \mathcal { Z } } \vert v ( z ) \vert ^ { 2 } \hat { d } \mu _ { 0 } ( z ) < \infty \} } \end{array}$ such that the inner product is the weighted $\ell _ { 2 }$ :
+
+$$
+\langle v _ { i } , v _ { j } \rangle _ { \mu _ { 0 } } = \int _ { \mathcal Z } v _ { i } ( z ) \cdot v _ { j } ( z ) d \mu _ { 0 } ( z ) .
+$$
+
+We can then define $v _ { i } ( \cdot ) \triangleq f ( \cdot ) - i d ( \cdot )$ , where $f ( \cdot )$ is the optimal transport map from $\mu _ { 0 }$ to $\mu _ { i }$ . Note that $v _ { i } \in \mathcal { V } _ { \mu _ { 0 } }$ , $v _ { 0 } = 0$ , and
+
+$$
+\lVert v _ { i } - v _ { 0 } \rVert _ { \mu _ { 0 } } ^ { 2 } = \lVert v _ { i } \rVert _ { \mu _ { 0 } } ^ { 2 } = \langle v _ { i } , v _ { i } \rangle _ { \mu _ { 0 } } = \int _ { \mathcal { Z } } \lVert f ( z ) - z \rVert ^ { 2 } d \mu _ { 0 } ( z ) = \mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { 0 } ) .
+$$
+
+In the paper, we use $\phi ( \mu _ { i } ) = v _ { i } \sqrt { p _ { 0 } }$ to turn the weighted- $\ell _ { 2 }$ into $\ell _ { 2 }$ .
+
+The discussion above assumes an absolutely continuous reference measure $\mu _ { 0 }$ . A more interesting treatment of the problem is via the generalized geodesics defined in (Ambrosio et al., 2008), connecting $\mu _ { i }$ and $\mu _ { j }$ and enabling us to use discrete reference measures. Following the notation in (Ambrosio et al., 2008), given the reference measure $\mu _ { 0 }$ , let $\Gamma ( \mu _ { i } , \mu _ { 0 } )$ be the set of transport plans between $\mu _ { i }$ and $\mu _ { 0 }$ , and let $\Gamma ( \mu _ { i } , \mu _ { j } , \mu _ { 0 } )$ be the set of all measures on the product space ${ \mathcal { Z } } \times { \mathcal { Z } } \times { \mathcal { Z } }$ such that the marginals over $\mu _ { i }$ and $\mu _ { j }$ are $\Gamma ( \mu _ { j } , \mu _ { 0 } )$ and $\Gamma ( \mu _ { i } , \mu _ { 0 } )$ , respectively. Then the linearized optimal transport distance is defined as
+
+$$
+d _ { \mathrm { L O T } , \mu _ { 0 } } ^ { 2 } ( \mu _ { i } , \mu _ { j } ) = \operatorname* { i n f } _ { \gamma \in \Gamma ( \mu _ { i } , \mu _ { j } , \mu _ { 0 } ) } \int _ { \mathcal { Z } \times \mathcal { Z } \times \mathcal { Z } } \| z - z ^ { \prime } \| ^ { 2 } d \gamma ( z , z ^ { \prime } , z ^ { \prime \prime } ) .
+$$
+
+In a discrete setting, where $\begin{array} { r } { \mu _ { i } = \frac { 1 } { N _ { i } } \displaystyle \sum _ { n = 1 } ^ { N _ { i } } \delta _ { z _ { n } } , \mu _ { j } = \frac { 1 } { N _ { j } } \displaystyle \sum _ { m = 1 } ^ { N _ { j } } \delta _ { z _ { m } ^ { \prime } } } \end{array}$ , and $\mu _ { 0 } = \frac { 1 } { N } \sum _ { l = 1 } ^ { N } \delta _ { z _ { l } ^ { \prime \prime } }$ , we have
+
+$$
+d _ { \mathrm { L O T } , \mu _ { 0 } } ^ { 2 } ( \mu _ { i } , \mu _ { j } ) = \operatorname* { m i n } _ { \gamma \in \Gamma ( \mu _ { i } , \mu _ { j } , \mu _ { 0 } ) } \frac { 1 } { N _ { i } N _ { j } N } \sum _ { n = 1 } ^ { N _ { i } } \sum _ { m = 1 } ^ { N _ { j } } \sum _ { l = 1 } ^ { N } \gamma _ { n m l } \lVert z _ { n } - z _ { m } ^ { \prime } \rVert ^ { 2 } .
+$$
+
+See Figure 4a for a depiction of Equation equation 11’s meaning. Finally, the idea of barycenteric projection used to approximate Monge couplings and provide a fixed-size representation is shown in Figure 4b.
+
+![](images/22b3b5b8f9ec209ef8f43aff5446d5d200137f87ce9a2f6399d1d57ea538fb3e.jpg)  
+Figure 4: Illustration of (a) the meaning behind $\gamma _ { n m l }$ used in the LOT distance in equation 11, and (b) the idea of the barycenteric projection, which provides a fixed-size representation (i.e., of size $N$ ).
+
+![](images/ca6999dd65de4210d34bbfb7e5d18432ad25ecf2894353179c166a8285638bf4.jpg)  
+Figure 5: An experiment demonstrating the capability of the linear Wasserstein embedding. (a) A simple dataset consisting of shifted and scaled noisy ring distributions $\{ p _ { i } \} _ { i = 1 } ^ { M }$ , where we only observe samples Zi = [zik ∼ pi]Nii=1 from each distribution, together with the process of obtaining the linear Wasserstein embedding with respect to a reference distribution. In short, for each distribution $p _ { i }$ , the embedding approximates the Monge-map (i.e., a vector field) from the reference samples $Z _ { 0 }$ to the target samples $Z _ { i }$ by a barycentric projection of the optimal transport plan. Adding samples in the embedding space corresponds to adding their vector fields, which can be used to calculate (b) the mean distribution in the embedding space, i.e., $\begin{array} { r } { \phi ^ { - 1 } \big ( \frac { 1 } { M } \sum _ { i = 1 } ^ { M } \phi ( p _ { i } ) \big ) } \end{array}$ and (c)-(d) the Euclidean geodesics in this space, i.e., $\phi ^ { - 1 } ( \alpha \phi ( p _ { i } ) + ( 1 - \alpha ) \phi ( p _ { j } ) )$ for $\alpha \in [ 0 , 1 ]$ . As can be seen, the calculated mean is the Wasserstein barycenter of the dataset, and the Euclidean geodesics in the embedding space follow the Wasserstein geodesics in the original space.
+
+Next, to demonstrate the capability of the linear Wasserstein embedding, we present the following experiment. Consider a set of distributions $\{ p _ { i } \} _ { i = 1 } ^ { M }$ , where each $p _ { i }$ is a translated and dilated ring distribution in $\mathbb { R } ^ { 2 }$ , and $N _ { i }$ samples are observed from $p _ { i }$ , where $N _ { i }$ and $N _ { j }$ could be different for $i \neq j$ . We then consider a normal distribution as the reference distribution and calculate the linear Wasserstein embedding with respect to the reference (See Figure 5a). Given the pseudo-invertible nature of the embedding, to demonstrate the modeling capability of the framework, we calculate the mean in the embedding space (i.e., on the vector fields), and invert it to obtain the mean distribution $\bar { p }$ . Figure 5b shows the calculated mean, indicating that the linear Wasserstein embedding framework has successfully retrieved a ring distribution as the mean. Finally, we calculate Euclidean geodesics in the embedding space (i.e., the convex combination of the vector fields) between $p _ { i }$ and $p _ { 0 }$ , as well as between $p _ { i }$ and $p _ { j }$ , and show the inverted geodesics in Figures 5c and 5d, respectively. As the figures demonstrate, the calculated geodesics follow the Wasserstein geodesics.
+
+# APPROXIMATION ERROR OF THE EMBEDDING
+
+Given the Euclidean distance in the embedding space is a transport-based distance (i.e., the socalled LOT distance) that approximates the Wasserstein distance, a natural question arises about the approximation error. Here we point the reader to the recent work of Moosmüller $\&$ Cloninger (2020) in which the authors provide bounds on how well the Euclidean distance in the embedding space approximates the 2-Wasserstein distance. In particular, the authors show that:
+
+$$
+\mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } ) \le \| \phi ( \mu _ { i } ) - \phi ( \mu _ { j } ) \| _ { 2 } \le \mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } ) + \| f _ { \mu _ { i } } ^ { \mu _ { j } } - f _ { \mu _ { 0 } } ^ { \mu _ { j } } \circ f _ { \mu _ { i } } ^ { \mu _ { 0 } } \| _ { \mu _ { i } } ,
+$$
+
+where $f _ { \mu _ { i } } ^ { \mu _ { j } }$ is the optimal transport map from $\mu _ { i }$ to $\mu _ { j }$ . This inequality simply indicates that the approximation error is caused by conditioning the transport map to be obtained by composition of the optimal transport maps from $\mu _ { i }$ to $\mu _ { 0 }$ , and then from $\mu _ { 0 }$ to $\mu _ { j }$ . More importantly, it can be shown that if $\mu _ { i }$ and $\mu _ { j }$ are shifted and scaled versions of the reference measure, $\mu _ { 0 }$ , then the embedding is isometric (See Figure 1 and 2 in Moosmüller $\&$ Cloninger (2020)).
+
+Maybe a less interesting upper bound can also be obtained by the triangle inequality:
+
+$$
+\mathcal { W } _ { 2 } ( \mu _ { i } , \mu _ { j } ) \le \| \phi ( \mu _ { i } ) - \phi ( \mu _ { j } ) \| _ { 2 } \le \mathcal { W } _ { 2 } ( \mu _ { i } , \sigma ) + \mathcal { W } _ { 2 } ( \sigma , \mu _ { j } ) ,
+$$
+
+which ensures some regularity of the embedding.
+
+# REGULARITY OF THE EMBEDDING
+
+A good question was raised during the feedback period, about the regularity of the proposed embedding. The regularity of the graph embedding will depend on both the regularity of node-embedding and the Wasserstein embedding. In the following, we avoid the discussion on regularity of the nodeembedding (as it is not the main focus of our work), and focus on the regularity of the Wasserstein embedding. To that end, we first point out several regularity characteristics pointed out in Appendix A of Moosmüller & Cloninger (2020). Most notably Theorem 4.2 in their paper, shows an almost isometric property when the distortions are within an $\epsilon$ -tube around the set of shifts and scalings. In short, let $\varepsilon _ { 2 } ( \mathcal { Z } ) , R > 0 , \epsilon > 0 , \mathcal { E }$ be the set of all shifts and scalings, and
+
+$$
+\mathcal { E } _ { \mu , R } = \{ h \in \mathcal { E } : \| h \| _ { \mu } \leq R \} ,
+$$
+
+and let
+
+$$
+\mathcal G _ { \mu , R , \epsilon } = \{ g \in L ^ { 2 } ( \mathcal Z , \mu ) : \exists h \in \mathcal E _ { \mu , R } : \| g - h \| _ { \mu } \leq \epsilon \} ,
+$$
+
+which is the $\epsilon$ -tube around set of shifts and scalings. Now, assume $\mu _ { 0 } \in P _ { 2 } ( \mathcal { Z } )$ is the reference measure and both $\mu$ and $\mu _ { 0 }$ satisfy Caffarelli’s regularity theorem. Then for $g _ { 1 } , g _ { 2 } \in \mathcal { G } _ { \mu , R , \epsilon }$ we have
+
+$$
+0 \leq \| \phi ( g _ { 1 \# } \mu ) - \phi ( g _ { 2 \# } \mu ) \| _ { 2 } - \mathcal { W } _ { 2 } ( g _ { 1 \# } \mu , g _ { 2 \# } \mu ) \leq C _ { \mu _ { 0 } , \mu , R } \epsilon + \bar { C } _ { \mu _ { 0 } , \mu , R } \epsilon ^ { 2 } ,
+$$
+
+where $C _ { \mu _ { 0 } , \mu , R }$ and $\bar { C } _ { \mu _ { 0 } , \mu , R }$ are constants depending on $\mu _ { 0 } , \mu$ , and $R$
+
+The results shown above can be used to derive regularity results for the linear Wasserstein embedding with respect to additive noise. We know that the addition of two random variables leads to a new random variable with its PDF being the convolution of the original PDFs. Therefore, for features $Z _ { i } = [ z _ { 1 } , . . . , z _ { N _ { i } } ] ^ { T }$ , let $\hat { Z } _ { i } = \underbrace { [ z _ { 1 } + \bar { e } _ { 1 } } _ { \hat { z } _ { 1 } } , . . . , \underbrace { z _ { N _ { i } } + e _ { N _ { i } } } _ { \hat { z } _ { N _ { i } } } ] ^ { T }$ denote the noisy samples for $e _ { i } \sim \eta$ , where $\eta$ is the noise distribution. Then the noisy samples, $\hat { z } _ { i }$ , will be distributed according to $\hat { \mu } _ { i } = \mu _ { i } * \eta$ . For instance, for the Gaussian additive noise, $\hat { \mu } _ { i }$ is the smoothed version of $\mu _ { i }$ . Therefore, there exists a transport map in $g \in \mathcal { G } _ { \mu _ { i } , R , \epsilon }$ for which, $\hat { \mu } _ { i } = g _ { \# } \mu _ { i }$ and $\Vert g - i d \Vert _ { \mu _ { i } } = \mathcal { W } _ { 2 } ( \hat { \mu } _ { i } , \mu _ { i } ) \leq \epsilon$ , and we have:
+
+$$
+0 \leq \| \phi ( \mu _ { i } ) - \phi ( \hat { \mu } _ { i } ) \| _ { 2 } \leq ( C _ { \mu _ { 0 } , \mu _ { i } , R } + 1 ) \epsilon + \bar { C } _ { \mu _ { 0 } , \mu _ { i } , R } \epsilon ^ { 2 }
+$$
+
+# A.2 SENSITIVITY TO THE CHOICE OF REFERENCE DISTRIBUTION
+
+To measure the dependency of WEGL on the reference distribution choice, we changed the reference to a normal distribution (i.e., data-independent). We compared the results of WEGL using the new reference distribution to that using a reference distribution calculated via $k$ -means on the training set. We used the ogbg-molhiv dataset with initial node embedding of size 300 and 4 diffusion layers. We ran the experiment with 100 different random seeds, and measured the test ROC-AUC of WEGL calculated with the two aforementioned reference distributions. Figure 6 shows the results of this experiment, indicating that the choice of reference distribution is statistically insignificant.
+
+![](images/421dd9059f3a6e5d0b1bbe94d97b5f76a8ad74d3785fd3dcbf8642848a975a8a.jpg)  
+Figure 6: ROC-AUC $( \% )$ results on ogbg-molhiv dataset, when the reference distribution is calculated by $k$ -means (Section 4.2) on the training dataset (denoted as $k$ -means), compared to when it is fixed to be a normal distribution (denoted as Normal). With a $p$ -value $= 0 . 0 5$ , the choice of the template is statistically insignificant.
+
+![](images/c06b0e927f9c7cdd4d1630ea44df2b94211f2ec47b385828426087ec619b5100.jpg)  
+Figure 7: Comparing the performance of the linear programming (LP) solver with the Sinkhorn algorithm (on entropy regularized OT problem) on the ogbg-molhiv dataset for various regularization parameters.
+
+A.3 LINEAR PROGRAMMING VS. ENTROPY REGULARIZATION
+
+In this paper, we used the Python Optimal Transport (Flamary & Courty, 2017) for the calculation of the optimal transport plans. During the feedback period, a point came up regarding the entropyregularized version of the OT problem (Cuturi & Doucet, 2014), which reduces the complexity of the linear programming problem from being cubic, in the number of nodes, to being quadratic, using the Sinkhorn algorithm. Given the Sinkhorn algorithm’s iterative nature, the computational gain of the method is prominent when calculating the transportation problem between graphs with a large number of nodes (e.g., larger than $1 0 ^ { 3 }$ ). However, the graph datasets used in this paper often have a small number of nodes (e.g., $< 5 0$ ). In these settings, linear programming is efficient. To obtain any computational gain using the Sinkhorn algorithm, one would need to use a large regularization coefficient, which reduces the Sinkhorn algorithm’s precision.
+
+Here we ran an experiment on the ogbg-molhiv dataset. We obtain the transport plans between the node embeddings and the reference distribution using the linear programming solver (using ot.emd2 from (Flamary & Courty, 2017)) and the Sinkhorn algorithm for the entropy-regularized problem (using ot.sinkhorn2 from (Flamary & Courty, 2017)). We measure the calculation time as well as the calculated distances for both algorithms. For the Sinkhorn algorithm, we used four different regularization values. We report the mean and standard deviation of calculation time ratio, i.e., tSinkhorntLP and the relative error of calculating the 2-Wasserstein distance, i.e., $| \frac { \mathcal { W } _ { 2 , S i n k h o r n } - \mathcal { W } _ { 2 , L P } } { \mathcal { W } _ { 2 , L P } } |$ in Figure 7. As the figure shows, due to the small graph size, the LP solver is efficient and little to no gain can be obtained using the Sinkhorn algorithm. Nevertheless, in the case of dealing with larger graph sizes, the entropy regularized formulation should be the definite choice. Finally, for the entropy-regularized OT problem, more efficient solvers have been proposed that outperform the Sinkhorn algorithm (Dvurechensky et al., 2018). However, given the acceptable performance of the linear programming solver (at least for the graph datasets in this paper), we did not find it necessary to seek more efficient solvers.
+
+# A.4 INNER WORKING OF GNNS
+
+In its most general form, a GNN consists of $L$ hidden layers, where at the $l ^ { \mathrm { t h } }$ layer, each node $v \in \mathcal V$ aggregates and combines messages from its 1-hop neighboring nodes $\mathcal { N } _ { v }$ , resulting in the feature vector
+
+$$
+x _ { v } ^ { ( l ) } = \Psi _ { \mathrm { c o m b i n e } } \left( x _ { v } ^ { ( l - 1 ) } , \left\{ ( x _ { u } ^ { ( l - 1 ) } , w _ { u v } ) \right\} _ { u \in \mathcal { N } _ { v } } \right) , \forall l \in \left\{ 1 , \ldots , L \right\} , \forall v \in \mathcal { V } ,
+$$
+
+where $\Psi _ { \mathsf { c o m b i n e } } ( \cdot )$ denotes a parametrized and differentiable combining function.
+
+At the input layer, each node $v \in \mathcal V$ starts with its initial feature vector $x _ { v } ^ { 0 } = x _ { v } \in \mathbb { R } ^ { F }$ , and the $\{ x _ { v } ^ { ( l ) } \} _ { l = 1 } ^ { L }$ l application of GN. At the GNN output,.e., readout) function s in equation 12, computes intermediate feature vectorse vectors of all nodes from all layers go through a global, resulting in the final graph embedding $\Psi _ { \mathrm { r e a d o u t } } ( \cdot )$
+
+$$
+\psi ( G ) = \Psi _ { \sf r e a d o u t } \left( \left\{ x _ { v } ^ { ( l ) } \right\} _ { v \in \mathcal { V } , l \in \{ 0 , \dots , L \} } \right) .
+$$
+
+# A.5 IMPLEMENTATION DETAILS
+
+To derive the node embeddings, we use the diffusion process in equation 7 for the datasets without edge features/labels, i.e., all the social network datasets (IMDB-BINARY, IMDB-MULTI, COLLAB, REDDIT-BINARY, REDDIT-MULTI-5K, and REDDIT-MULTI-12K) and four of the molecule and bioinformatics datasets (ENZYMES, PROTEINS, D&D, and NCI1). We specifically set $w _ { u v } = 1$ for any $( u , v ) \in \mathcal { E }$ and also for all self-connections, i.e., $w _ { v v } = 1$ , $\forall v \in \nu$ .
+
+The remaining datasets contain edge labels that cannot be directly used with equation 7. Specifically, each edge in the MUTAG and PTC-MR datasets has a categorical label, encoded as a one-hot vector of dimension four. Moreover, in the ogbg-molhiv dataset, each edge has three categorical features indicating bond type (five categories), bond stereochemistry (six categories) and whether the bond is conjugated (two categories). We first convert each categorical feature to its one-hot representation, and then concatenate them together, resulting in a binary 13-dimensional feature vector for each edge.
+
+In each of the three aforementioned datasets, for any edge $( u , v ) \in \mathcal { E }$ , let us denote its binary feature vector by $w _ { u v } \in \{ 0 , 1 \} ^ { E }$ , where $E$ is equal to 4, 4, and 13 for MUTAG, PTC-MR, and ogbg-molhiv, respectively. We then use the following extension of the diffusion process in equation 7,
+
+$$
+x _ { v } ^ { ( l ) } = \sum _ { u \in \mathcal { V } } \left( \sum _ { e = 1 } ^ { E } \frac { w _ { u v , e } } { \sqrt { \deg _ { e } ( u ) \deg _ { e } ( v ) } } \right) x _ { u } ^ { ( l - 1 ) } , \forall l \in \{ 1 , \ldots , L \} , \forall v \in \mathcal { V } ,
+$$
+
+where for any $e \in \{ 1 , \ldots , E \}$ , $w _ { u v , e }$ denotes the $e ^ { \mathrm { t h } }$ element of $w _ { u v }$ , and for any node $v \in \nu$ , we define ${ \mathsf { d e g } } _ { e } ( v )$ as its degree over the $e ^ { \mathrm { t h } }$ elements of the edge features; i.e., $\begin{array} { r } { \mathsf { d e g } _ { e } ( v ) \triangleq \sum _ { u \in \mathcal { V } } w _ { u v , e } } \end{array}$ We assign vectors of all-one features to the self-connections in the graph; i.e., $w _ { v v , e } = 1$ , $\forall v \in$ $\mathcal { V } , \forall e \in \mathsf { \bar { \{ 1 , \dots , E \} } }$ . Note that the formulation of the diffusion process in equation 14 can be seen as an extension of equation 7, where the underlying graph with multi-dimensional edge features is broken into $E$ parallel graphs with non-negative single-dimensional edge features, and the parallel graphs perform message passing at each round/layer of the diffusion process.
+
+For the ogbg-molhiv experiments in which virtual nodes were appended to the original molecule graphs, we set the initial feature vectors of all virtual nodes to all-zero vectors. Moreover, for any graph $G _ { i }$ in the dataset with $| \nu _ { i } |$ nodes, we set the edge features for the edge between the virtual node $v _ { \mathsf { v i r t u a l } }$ and each of the original graph nodes $u \in \mathcal { V } _ { i }$ as $\begin{array} { r } { w _ { u v _ { \mathrm { v i r t u a l } } , e } = \frac { 1 } { | \mathcal { V } _ { i } | } , \mathsf { \bar { v } } e \in \{ 1 , \dots , E \} } \end{array}$ . The normalization by the number of graph nodes is included so as to regulate the degree of the virtual node used in equation 14. We also include the resultant embedding of the virtual node at the end of the diffusion process in the calculation of the graph embedding $\psi ( G _ { i } )$ .
+
+In the experiments conducted on each dataset, once the node embeddings are derived from the diffusion process, we standardize them by subtracting the mean embedding and dividing by the standard deviation of the embeddings, where the statistics are calculated based on all the graphs in the dataset. Moreover, to reduce the computational complexity of estimating the graph embeddings for the ogbg-molhiv dataset, we further apply a 20-dimensional PCA on the node embeddings.
+
+# HYPERPARAMETERS
+
+We use the following set of hyperparameters to perform a grid search over in each of the experiments:
+
+• Random Forest: min_samples_leaf $\in \quad \{ 1 , 2 , 5 \}$ , min_samples_split $\in$ $\{ 2 , 5 , 1 0 \}$ , and n_estimators $\in \{ 2 5 , 5 0 , 1 0 0 , 1 \dot { 5 } 0 , 2 0 \dot { 0 } \}$ .   
+• Gradient Boosted Decision Tree (GBDT): min_samples_leaf $\in \quad \{ 1 , 2 , 5 \}$ , min_samples_split $\in \ \{ 2 , 5 , 1 0 \}$ , n_estimators $\in \{ 2 5 , 5 0 , 1 0 0 , 1 5 0 , 2 0 0 \}$ , and max_depth $\in \{ 1 , 3 , 5 \}$ .   
+• SVM-Linear and SVM-RBF: $C \in \{ 1 0 ^ { - 2 } , . . . , 1 0 ^ { 5 } \}$ .   
+• Multi-Layer Perceptron (MLP): $\mathrm { h i d d e n \_ l a y e r \_ s i z e s } \in \{ ( 1 2 8 ) , ( 2 5 6 ) , ( 1 2 8 , 6 4 ) , ( 2 5 6 , 1 2 8 ) \} .$   
+• Auto-ML: Auto-Sklearn 2.0 searches over a space of 42 hyperparameters using Bayesian optimization techniques, as mentioned in Feurer et al. (2020).   
+• Number of Diffusion Layers in equation 7 and equation 14: $L \in \{ 3 , \ldots , 8 \}$ .
+
+• Initial Node Feature Dimensionality (for ogbg-molhiv only): $\{ 1 0 0 , 3 0 0 , 5 0 0 \}$ • Node Embedding Type: For a graph with $F$ -dimensional initial node features, we consider using the following three types of node embedding:
+
+– Concat: $z _ { v } = \Big [ x _ { v } ^ { ( 0 ) } \big \| \ x _ { v } ^ { ( 1 ) } \big \| \ . . . \big \| \ x _ { v } ^ { ( L ) } \Big ] \in \mathbb { R } ^ { ( L + 1 ) F }$ , where $\parallel$ denotes concatenation.   
+– Average: $\begin{array} { r } { z _ { v } = \frac { 1 } { L + 1 } \sum _ { l = 0 } ^ { L } x _ { v } ^ { ( l ) } \in \mathbb { R } ^ { F } } \end{array}$ .   
+– Final: $z _ { v } = x _ { v } ^ { ( L ) } \in \mathbb { R } ^ { F }$ .
+
+# A.6 TUD BENCHMARK — COMPLETE RESULTS
+
+Here, we report the comprehensive set of classification results of our proposed method, WEGL, for each of the node embedding types mentioned in Section A.5, using five different classifiers: Linear SVM, Kernel-SVM (SVM-RBF), Gradient Boosted Decision Trees (GBDT), Multi-Layer Perceptron (MLP), and Random Forest (RF). The results are shown in Table 3.
+
+<table><tr><td rowspan=1 colspan=3>7.16.815.33 5.55 5.24,1</td><td rowspan=1 colspan=3>1&#x27;78&#x27;2917 1597659</td><td rowspan=1 colspan=3>914846778414.95</td><td rowspan=10 colspan=4>9.45198&#x27;0干 0.09533 6.6779 07858干07869干6.18111441845238.14935555535729  7090&#x27;2干 1&#x27;19£&#x27;9 干9&#x27;19</td><td rowspan=25 colspan=2>L&#x27;1F8&#x27;9L 1&#x27;1干9&#x27;9,333581 8.1557867951155559555.557.451.946.755556.9F189S.157.354,/F9.49 L&#x27;L干S&#x27;L95953.955 3.53330555.118&#x27;0F0&#x27;76 0&#x27;£+8.505 4&#x27;1-8&#x27;81&#x27;[干8&#x27;6L5.558.01 3.454.11 5£9F6.451.1441.155.15</td></tr><tr><td rowspan=1 colspan=3>7.16.815.33 5.55 5.24,1</td><td rowspan=2 colspan=3>1&#x27;78&#x27;2917 15976599L干0&#x27;48 583038 648</td><td rowspan=3 colspan=3>914846778499干ε687&#x27;9 干8&#x27;280&#x27;01 7&#x27;28633595L6S187651</td></tr><tr><td rowspan=1 colspan=3>569984/08 51614</td></tr><tr><td rowspan=1 colspan=3>士士土</td><td rowspan=1 colspan=3>士土土</td></tr><tr><td rowspan=1 colspan=3>11441247517：11</td><td rowspan=1 colspan=3>440.94 4444</td><td rowspan=1 colspan=3>633595L6S1</td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2>土土</td><td rowspan=1 colspan=3>士士土</td><td rowspan=1 colspan=3></td></tr><tr><td rowspan=1 colspan=1>3.030.05</td><td rowspan=1 colspan=2>32：3623 133</td><td rowspan=1 colspan=3>7:33405F 8:05</td><td rowspan=1 colspan=3>£&#x27;9干009555 585</td></tr><tr><td rowspan=1 colspan=3>584960</td><td rowspan=2 colspan=3>32355578879</td><td rowspan=2 colspan=3>0&#x27;9 干 7&#x27;5969干799</td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2>土土</td></tr><tr><td rowspan=1 colspan=1>60</td><td rowspan=1 colspan=2>99  779</td><td rowspan=1 colspan=3>56488</td><td rowspan=1 colspan=3>646262</td><td rowspan=1 colspan=2>9  709</td></tr><tr><td rowspan=1 colspan=3>25</td><td rowspan=3 colspan=3></td><td rowspan=3 colspan=3>1</td><td rowspan=3 colspan=4>9.53511</td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=3>1926</td><td rowspan=2 colspan=3>61干8&#x27;88</td><td rowspan=1 colspan=1></td><td rowspan=3 colspan=3></td><td rowspan=4 colspan=1>8&#x27;0F0&#x27;765</td><td rowspan=6 colspan=1>0&#x27;£+8.504&#x27;1-8&#x27;81</td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>61干8&#x27;88</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>B</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>26</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>20</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>24</td><td rowspan=1 colspan=3></td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>，</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>，</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>土</td><td rowspan=2 colspan=3></td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>&#x27;[干8&#x27;6L</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=2>3463</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>28</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=2>38</td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2>土土</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>43</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>395115</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>313111</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3></td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>55</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>24</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=2>5020</td><td rowspan=1 colspan=1>5</td><td rowspan=2 colspan=3></td></tr><tr><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=1>土</td><td rowspan=1 colspan=2>土土</td><td rowspan=1 colspan=1>土</td></tr><tr><td rowspan=1 colspan=3>1 </td><td rowspan=1 colspan=3>17415</td><td rowspan=1 colspan=3>744144</td><td rowspan=1 colspan=4>12575</td></tr><tr><td rowspan=1 colspan=1>Ceoer</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[u</td><td rowspan=1 colspan=1>Coocer</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>[rng</td><td rowspan=1 colspan=1>Cooeea</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>[eu</td><td rowspan=1 colspan=1>Coeee</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>Ceoeea</td><td rowspan=1 colspan=1> </td></tr><tr><td rowspan=1 colspan=3> JIITrr - iit</td><td rowspan=1 colspan=3>SUY - IKH</td><td rowspan=1 colspan=3>GERI</td><td rowspan=1 colspan=4>JTN</td><td rowspan=1 colspan=2>F</td></tr></table>

parse/train/B14rPj0qY7/B14rPj0qY7.md

@@ -0,0 +1,206 @@
+# RETHINKING SELF-DRIVING: MULTI-TASK KNOWLEDGE FOR BETTER GENERALIZATION AND ACCIDENT EXPLANATION ABILITY
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Current end-to-end deep learning driving models have two problems: (1) Poor generalization ability of unobserved driving environment when diversity of training driving dataset is limited (2) Lack of accident explanation ability when driving models don’t work as expected. To tackle these two problems, rooted on the believe that knowledge of associated easy task is benificial for addressing difficult task, we proposed a new driving model which is composed of perception module for see and think and driving module for behave, and trained it with multi-task perception-related basic knowledge and driving knowledge stepwisely. Specifically segmentation map and depth map (pixel level understanding of images) were considered as what & where and how far knowledge for tackling easier drivingrelated perception problems before generating final control commands for difficult driving task. The results of experiments demonstrated the effectiveness of multitask perception knowledge for better generalization and accident explanation ability. With our method the average sucess rate of finishing most difficult navigation tasks in untrained city of CoRL test surpassed current benchmark method for 15 percent in trained weather and 20 percent in untrained weathers.
+
+# 1 INTRODUCTION
+
+Observing progressive improvement in various fields of pattern recognition with end-to-end deep learning based methods(Krizhevsky et al., 2012; Girshick, 2015), self-driving researchers try to revolutionize autonomous car field with the help of end-to-end deep learning techniques(Bojarski et al., 2016b; Chen et al., 2015; Codevilla et al., 2017). Impressive results have been acquired by mapping camera images directly to driving control commands(Bojarski et al., 2016b) with simple structure similar to ones for image classfication task(Simonyan & Zisserman, 2014). Further researches were conducted to improve the performance of deep learning based autonomous driving system, for example, Conditional Imitation Learning(Codevilla et al., 2017) approach has been proposed to solve the ambigious action problem.
+
+However, two crutial problems failed to be spotted: (1) Poor generalization ability of unobserved driving environment given limited diversity of training scenerios. For example, though Dosovitskiy et al. (2017) addressed the driving direction selection problem, it showed poor generalization ability in unseen test town which has different map and building structure than training town’s. This generalization problem is extremely important since collected driving dataset always has limitation of diversity (2) Current end-to-end autonomous approaches lack of accident explanation ability when these models behave unexpectedly. Although saliency map based visualization methods(Smilkov et al., 2017; Sundararajan et al., 2017; Springenberg et al., 2014; Bojarski et al., 2016a) have been proposed to dig into the ’black box’, the only information these methods could bring is the possible attention of the model instead of the perception process of the model.
+
+We proposed a new driving approach to solve the two aforementioned problems by using multi-task basic perception knowledge. We argue that when end-to-end model is trained to address a specific difficult task, it’s better to train the model with some basic knowledge to solve relevant easier tasks before(Pan et al., 2010). An analogy for this can be observed when human beings learn a difficult knowledge. For example, to solve a complex integration problem, compared with students without basic math knowledge, students who know about basic knowledge of math are able to learn the core of intergration more quickly and solve other similar integration problems instead of memorizing the solution of the specific problem.
+
+Our proposed model consists of two modules: perception module and driving module as in Fig. 1. The perception module is used for learning easier driving-related perception knowledge, which we refer as ability of pixel level understanding of input including what & where and how far knowledge. We trained perception module with segmentation map and depth map first, while the former serves as what & where knowledge and the latter serves as how far knowledge. By visualizing inferenced segmentation and depth results whether perception process works well or not could be inferred. After the perception module was trained to have ability of pixel level understanding of its image input, we freezed the perception module weights and trained driving module with driving dataset. This decomposition of end-to-end driving network strucuture is considered to be mediated perception approach(Ullman, 1980). With our proposed driving structure and stepwise training strategy, the generalization and accident explanation problems were addressed to a certain extent.
+
+# 2 RELATED WORK
+
+Depending on whether mediated perception knowledge are generated, self-driving models are categorized into mediated perception approach(Ullman, 1980) and behavior reflex approach.
+
+For mediated perception approaches, there are several well-behaved deep learning methods, for example, Deep-Driving method(Chen et al., 2015) fisrtly converts input RGB images to some key perception indicators related to final driving controls. They designed a very simple driving controller based on predicted perception indicators. Problem of this approach is that key perception indicators have limitation of describing unseen scenerios and are difficult to collect in reality. Except for inferencing for final driving controls, there are approaches which focus on inferencing intermediate description of driving situation only. For separate scene understanding task, car detection(Lenz et al., 2011) and lane detection(Aly, 2008) are two main topics in this area.
+
+Instead of inferencing one perception task at most, multi-task learning method aims at tackling several relevant tasks simultaneously. Teichmann et al. (2016) uses input image to solve both object detection and road segmentation tasks. Branched E-Net(Neven et al., 2017) not only infers for segmentation map, but also depth map of current driving scenarios. These multi-task learning methods shows better result when sharing the encoder of different perception tasks together, but they haven’t really tried to make the car drive either in simulator or reality.
+
+As for behavior reflex approach which is also called ’end-to-end learning’, NVIDIA firstly proposed a model for mapping input image pixels directly to final driving control output(steer only)(Bojarski et al., 2016b). Some other approaches further atempted to create more robust models, for example, long short-term memory (LSTM) was utilized to make driving models store a memory of past(Chi & Mu, 2017).
+
+One problem is that aforementioned methods were tested in dissimlar driving scenerios using different driving dataset, thus it’s hard to determine if model itself is the source of the better driving behavior instead of effectiveness of data(Sun et al., 2017).
+
+Codevilla et al. (2017) was tested in a public urban driving simulator Dosovitskiy et al. (2017) and sucessed to tackle the ambigous action problem which refers as optimal driving action can’t be inferred from perceptual input alone. Benefit from CoRL test in Dosovitskiy et al. (2017), fair comparision could be conducted using same driving dataset. Codevilla et al. (2017) showed limitation of generalization ability problem in test town different from train town(Dosovitskiy et al., 2017) as in CoRL test training dataset could be only collected from single train town.
+
+When the end-to-end driving method behaves badly and causes accidents, accident explanation ability is required. Though saliency-map based visualization methods(Bojarski et al., 2016a; Smilkov et al., 2017) help understand the influence of input on final driving control, it’s extremely hard to derive which module of the model fails when driving problems happen — If the model percepts incorrectly or the driving inference processes wrongly based on good perception information. Driving system was enabled to give quantitative explanation by visualizing inferenced multi-task basic knowledge to solve this problem.
+
+# 3 FRAMEWORK OF PROPOSED SYSTEM
+
+Basic strucure of the proposed model is shown in Fig. 1. The proposed model has two parts: (1) Multi-task basic knowledge perception module (2) Driving decision branch module. The perception module is used to percept the world by inferencing dpeth map and segmentation map, which is composed of one shared encoder and two decoders for two different basic perception knowledge: (1) Segmentation decoder for generating ’what & where’ information by predicting segmentation maps; (2) Depth decoder for predicting ’how far’ the objects in vision are by inferencing depth maps. The perception module is aimed at extracting encoded feature map containing pixel level understanding information for driving module and qualitative explanation when proposed model doesn’t work as expected by visualizing the predicted segmentation and depth maps to determine if the driving problem is caused by percept process or driving process.
+
+The driving module enbales the model to generate driving decisions for different direction following guidances. We categorized the real world driving guidance into four types: (1) Following lane (2) Turning left (3) Going straight (4) Turning right as done in Codevilla et al. (2017). For each driving guidance direction, there is a driving branch(which predicts the value of driving controls) corresponding to it, therefore there are four driving guidance branches totally. The output of second last layer in perception module is inputted to the driving module, therefore the training of which could benefit from the multi-knowledge extracted by the perception module. Instead of linear layers, convolution layers are utilized for inferencing final driving controls for each direction, which helps keeping the spatial relation of information and reducing number of parameters as non-negligible quantity of direction branches.
+
+# 3.1 MULTI-TASK BASIC KNOWLEDGE PERCEPTION MODULE
+
+The perception module is built with residual block proposed in (He et al., 2016) which solves gradient vanishing and ’degradation problem’, and it has a structure similar to Segnet(Badrinarayanan et al., 2015) prosposed for efficient image segmentation task. Huge difference is that in our proposed method there are two different decoders for inferencing both segmentation and depth maps simultaneously instead of segmentation map only. Besides, we constraint the total strides in encoder to 8 for keeping resolution of feature map, as large total stride has negative influence on feature map size reconstuction. Hybrid Dilated Convolution Wang et al. (2017) is adapted as last part of the encoder as it enlarges the receptive field and avoids theoretical issue of gridding problem. Groupout(Park) is also adapted to avoid overfitting problem in the convolution network.
+
+# 3.2 DRIVING DECISION BRANCH MODULE
+
+The driving module is built with residual block and has a general form as Codevilla et al. (2017) in last output layer for several direction outputs. It is all based on convolutional layers in order to keep the spatial information and reduce parameters motivated by Springenberg et al. (2014). Four different high level driving guidance such as ”turning right” are utilized for selecting which direction branch’s output is supposed to be considered as final driving outputs. Driving outputs contain steering and acceleration/brake, both of them range from -1 to 1. Since there are 4 output branches corresponding to 4 high level driving guidances, 8 feature map size convolution kernels are set in the last layer for output scalar value, in which each two are regarded as driving controls for one driving guidance. To determine the limitation of RGB image, no other information such as current speed or steering angle were used as input. Instead we atempted to predict the current speed based on current RGB image to keep the driving smoothly as done in (Codevilla et al., 2017). The input of the driving module is not from the last layer’s output of the encoder part in the perception module, but the second last layer’s output of the encoder part due to empirically selection for best generalization.
+
+![](images/6dc827fdcb69b3a1fa85c7f890f6534bb34f1abd9ff10df5c2beca34f9569196.jpg)  
+Figure 1: Basic structure of proposed self-driving system. The components which lie in the red bounding box are refered as parts of perception module. The components which lie in the blue bounding box forms the driving module. In order to see the limiation of RGB image, only current RGB image and driving guidance are used as inputs seperatedly for perception module and driving module.
+
+# 4 EXPERIMENTS
+
+# 4.1 SYSTEM SETUP
+
+The training dataset is collected in CARLA simulator(Dosovitskiy et al., 2017). CARLA simulator is a self-driving simulator developed by Intel Co. for collecting self-driving related information and evaluating driving model with a standard testing environment named CoRL test. CoRL test is composed of 4 tasks of increasing difficulty: (1) Straight: the goal is straight ahead of the starting position. (2) One turn: getting to the goal takes one turn, left or right. (3) Navigation: navigation with an arbitrary number of turns. (4) Navigation with dynamic obstacles: same as previous task, but with other vehicles and pedestrians(Dosovitskiy et al., 2017).
+
+The main metric for quantitatively evaluating is the average success rate of finishing seperate tasks in CoRL test. CoRL test contains tests both in trained town and untrained town under both trained and untrained weathers. Test trained town and untrained town are constructed with different maps and different building texture.
+
+# 4.2 DATASET
+
+Dataset for training our model could be categorized into 2 items: (1) Perception module training dataset (2) Driving module training dataset. For perception module, we trained it with 35,000 pairs of RGB images, segmentation and depth maps and evaluated with 5,000 pairs. As for driving module, we trained with 455,000 dataset, and evaluated on 62,000 evaluation dataset. Before training our proposed model, two vital data processing methods were used: balancing dataset and data augmentation.
+
+Table 1: Quantitive evaluation of methods in the goal-directed navigation tasks in CoRL test. The table reports the percentage of success rate of finishing corresponding task in different condition. Higher means better performance.   
+
+<table><tr><td></td><td colspan="4">Training conditions</td><td colspan="4">New town</td><td colspan="4">New weather</td><td colspan="4">New town&amp;weather</td></tr><tr><td>Task</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td></tr><tr><td>Straight</td><td>98</td><td>95</td><td>89</td><td>98</td><td>92</td><td>97</td><td>74</td><td>100</td><td>100</td><td>98</td><td>86</td><td>100</td><td>50</td><td>80</td><td>68</td><td>96</td></tr><tr><td>One turn</td><td>82</td><td>89</td><td>34</td><td>87</td><td>61</td><td>59</td><td>12</td><td>81</td><td>95</td><td>90</td><td>16</td><td>88</td><td>50</td><td>48</td><td>20</td><td>82</td></tr><tr><td>Navigation</td><td>80</td><td>86</td><td>14</td><td>81</td><td>24</td><td>40</td><td>3</td><td>72</td><td>94</td><td>84</td><td>2</td><td>88</td><td>47</td><td>44</td><td>6</td><td>78</td></tr><tr><td>Nav. dynamic</td><td>77</td><td>83</td><td>7</td><td>81</td><td>24</td><td>38</td><td>2</td><td>53</td><td>89</td><td>82</td><td>2</td><td>80</td><td>44</td><td>42</td><td>4</td><td>62</td></tr></table>
+
+For fair comparison, we use same driving dataset published by Conditional Imitation Learning(Codevilla et al., 2017) except that we collected extra segmentation and depth maps in train town for training our proposed perception module.
+
+# 4.2.1 DATA BALANCING
+
+Dataset balancing contributed to better generalization of both perception module and driving module in our experiments as it enables each mini-batch to be a microcosm of the whole dataset. For perception module, dataset were balanced to ensure that each mini-batch contains all different training weathers and an equal amount of going straight and turning situations. For driving module, we balance each training mini-batch to ensure equally distribution of different driving direction guidance, and reorganized large steer(absolute value larger than 0.4) data accounts for 1/3 in each mini-batch, brake situation data acounts for $1 / 3$ , noise steer situation for 1/10.
+
+# 4.2.2 DATA AUGMENTATION
+
+We add guassian noise, coarse dropout, contrast normalization, Guassian blur to both training dataset for perception and driving module for enlarging training dataset distribution.
+
+# 4.3 TRAINING DETAILS
+
+We trained the whole system using a step-wise training method which is firstly we trained the perception module with multi-task basic perception knowledge, then we freezed the weights of perception module and train driving module with driving dataset. For training the perception module, we used mini-batch size 24 and set ratio of segmentation loss and depth loss to be 1.5:1. Softmax categorical crossentropy is used for segmentation loss, binary crossentropy is used for depth loss. Adam of 0.001, which is multiplied by a factor of 0.2 of previous learning rate if validation loss does’t drop for 1 epoch is used as optmizer. L2 weight decay and early stopping are also used for avoid overfitting. As for training the driving module, we consider MSE loss and use Adam with starting learning rate of 0.002 which exponentially decay of 0.9 every epoch. Early stopping and L2 decay are used for regularization.
+
+# 5 EXPERIMENTS & RESULTS
+
+# 5.1 GENERALIZATION ABILITY TEST
+
+We compare the results of driving performance between our proposal and other methods tested in CoRL test via success rate of finishing each task. The details of results are shown in Table. 1
+
+From Table. 1, though our proposal finished slightly less in training conditions comparing with other methods, our proposal achieved much higher success rate in untrained town environments, which demonstrates our model has much better generalization ability of adapting to untrain town than other methods tested in the CoRL test when trained with limited diversity of training conditions. One important notice is that we use the almost the same driving dataset for training as the method Codevilla et al. (2017) showed in the Table. ??.
+
+We could also visualize the perception process when the model works. One example of test in untrained town and untrained weather is shown in Fig. 2.
+
+![](images/38c6d27d6247d2c234bb0cc042e4068451b217e86c064e62c146d63476c9de47.jpg)  
+Figure 2: Screenshots of captured single RGB image and our proposal’s inference results which consists of predicted segmentation map and depth map during test in untrained town under untrained weather. Obviously from the inferenced segmentation and depth maps we get information that the driving model knows a car is passing by the left side.
+
+# 5.2 ORIGIN OF BETTER GERNERALIZATION ABILITY
+
+Since we observed our training model has better generalization ability in unseen town comparing with other methods when almost the same driving dataset were used to train (except that we collected extra depth maps and segmentation maps in same training environments), we want to investigate the origin of the better generalization ability. There are two possible reasons why our training model has better generalization ability in unseen town: (1) Basic knowledge (segmentation map and depth map) (2) Network structure. Therefore we conduct experiments by comparing performance of two methods:
+
+• Our original proposal: Firstly train perception module with basic knowledge, after training perception module, freeze its weights and train driving module with driving dataset Compared method: Train the encoder of perception module and driving module together with driving dataset. No basic perception knowledge is used for training model.
+
+Since tests in CoRL cost much time, we limited our evaluation to the most difficult untrained town under untrained weathers test. Results are shown in Table. 2. From the results it’s obvious that multibasic knowledge we use in the training phase is the origin of our proposal’s good generalization ability of untrained town instead of the network structure. Moreover, the network structure could be improved to achieve better performance in the furture.
+
+# 5.3 QUALITATIVE CAUSE EXPLANATION ABILITY OF DRIVING PROBLEMS
+
+Besides basic knowledge leads to better generalization ability, it could also be used to give a qualitative explanation of driving problems. Basic knowledge of segmentation map and depth map are output from the perception module during test phase, therefore how the driving module percepts the current scenario could be known by simply visualizing the outputs of segmentation and depth from perception module. Depending on the predicted pixel understanding of the situation, cause of driving problem could be inferred.
+
+Table 2: Quantitive evaluation of original proposal which uses segmentataion and depth maps in training phase and compared method which doesn’t use. Results shows that when multi-knowldge is not used for training, the success rate drops hugely in the testing town under untained weathers. It indicates that multi-basic knowledge is the main origin of the good generalization ability in our proposal.   
+New town&weather test   
+
+<table><tr><td>Task</td><td>COMPARED</td><td>ORIGINAL</td></tr><tr><td>Straight</td><td>91</td><td>96</td></tr><tr><td>One turn</td><td>52</td><td>82</td></tr><tr><td>Navigation</td><td>20</td><td>78</td></tr><tr><td>Nav. dynamic</td><td>16</td><td>62</td></tr></table>
+
+One example is shown in Fig. 3. For a failed straight task in untrained town under untrained weather soft rain sunset as the driving model failed to move forward, we visualized outputs of segmentation and depth maps predicted by perception module. It’s obvious that this failure case is caused by the perception module since the model falsely percepted that there is a car in front of it and in order to avoid collision it did’t start. There is no car actually thus the perception module made false judgement. However, what’s interesting is that sometimes it fools readers to think that there is a car in Fig. 3 because of sun ray reflection on the wet road and the perception module has the similar understanding as these readers. Therefore in some aspects the perception module makes the right judgement instead of wrong’s. For traditional end-to-end learning driving methods(Bojarski et al., 2016b) it’s impossible to reason as they don’t focus on the cause explanation ability which is of great importance for practice use of deep learning driving models.
+
+![](images/2d2cf88b4862b0b42c56af1012bd4a810abf87af683fd3f269ff016d085c468e.jpg)  
+Figure 3: Failed straight task in untrained town under untrained soft rain sunset weather. From predicted segmentation and depth maps, we know that the driving model thinks that there is a car in front of it but actually there isn’t any car in front of it.
+
+# 5.4 FINE-TUNE TEST
+
+Fine-tuneYosinski et al. (2014), which refers to use other well-trained models weights on different target-related dataset as initial weights for training with target dataset instead of using weights initializing methods(Glorot & Bengio, 2010; He et al., 2015; LeCun et al., 2012), is a common trick used in deep learning since empirically it could leads to better generalization on new target dataset. Here in our specific case we refer fine-tune method to be after training perception module we train the weights of the encoder of the perception module as well instead of freezing these weights. In
+
+Table. 3 we compare the performance of fine-tune method and our original proposed method.
+
+Table 3: Quantitive evaluation of original proposal and fine-tune method which doens’t freeze the perception module’s weights during training the driving module. Results shows that the success rate of the fine-tune method drops dramaticaly in the testing town under untained weathers.   
+
+<table><tr><td colspan="2">New town&amp;weather test</td></tr><tr><td>Task</td><td>FINETUNE ORIGINAL</td></tr><tr><td>Straight</td><td>88</td></tr><tr><td>One turn 59</td><td>96 82</td></tr><tr><td>Navigation</td><td>42 78</td></tr><tr><td>Nav. dynamic</td><td>33 62</td></tr></table>
+
+In this comparison we achieved counter-intuition results: after fine-tune the weights of the perception module the driving model achieved worse results than original method which freeze the weights of perception module when training the driving module.
+
+One possible reason is that the generalization ability lies in the perception module instead of the driving module, therefore when we train the perception module again with driving dataset, the ability of generating compressed multi-knowdege information is destoryed. As the fine-tune model couldn’t benefit from the multi-task knowledge anymore, it failed to produce the same generalization ability as the original proposal did.
+
+Furthermore we conduct experiment on visualizing one direction of loss surface by projecting the loss surface to 2 dimension(Goodfellow & Vinyals, 2014) to investigate some qualitative explanation for this comparison result. $x$ axis corresponds to linear interpolation of the weights of original proposed method and weights of compared fine-tuned method after training. Formulation of calculating the weights in this projection direction is Equation. 1.
+
+$$
+\alpha \in [ - 1 , 2 ] , f ( \alpha x _ { f i n e t u n e } + ( 1 - \alpha ) x _ { r g b 0 } )
+$$
+
+$\alpha$ is linear interpolation ratio, $x _ { f i n t u n e }$ and $x _ { r g b 0 }$ are trained weights of fine-tune method and original proposal method. $f ( x )$ is loss function of the whole model while input is considered as different model weights. We draw out the projected loss surface as Fig. 4 by sampling from the interpolation weigthts. From Fig. 4 we can get one possible qualitative reason for worse behavior of fine-tune method from a loss surface perspective: Model weight got by using fine-tune method is stuck in a super flat surface, while model weights of original proposed method successfully finds a local minimum.
+
+# 6 CONCLUSION
+
+In this paper we propose a new driving system for better generalization and accident explanation ability by enabling it to do simpler driving-related perception task before generating commands for diffult driving task. Through multiple experiments we empirically proved the effectiveness of the multi basic perception knowledge for better generalization ability of unobserved town when diversity of training dataset is limited. Besides our proposed model has self-explanation ability by visualizing the predicted segmentation and depth maps from the perception module to determine the cause of driving problems when they happen. One interesting result we acquired by comparing different train strategies is that the generalization ability of driving origins from basic knowledge and lies in weights of the perception module which should not be modified during training with driving dataset. We hope our work could movitivate other researches to use multi-task target related perception knowledge for better performance in robot learning. In future we will investigate more effective network structures.
+
+![](images/70c1612b4c149ecc7c1c3c717db55baf2b1ab70a65b51481f55ba2a3348a9f28.jpg)  
+Figure 4: One perceptive of loss surface by linear interpolation of original proposed method weights and fine-tune method weights. Blue line refers to test loss, red line refers to train loss. From the visualization perspective it’s possibly that finetune method weights are stuck in a flat surface while the original proposed weights sucessfully find a local minimum.
+
+# ACKNOWLEDGMENTS
+
+Thanks to all Prof.Ogata lab members especially Kamuza SASAKI san who teaches me about Deep Learning patiently when I have zero knowledge of what it is. Great thanks to my bros Zehai TU and Pengfei LI who support me no matter how annoying I am in the midnight. Final thanks to my homie Mengcheng SONG for being a Hiphop guide for me and makes me understand about the importance of always ’keep it real’.
+
+# REFERENCES
+
+Mohamed Aly. Real time detection of lane markers in urban streets. In Intelligent Vehicles Symposium, 2008 IEEE, pp. 7–12. IEEE, 2008.
+
+Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoderdecoder architecture for image segmentation. arXiv preprint arXiv:1511.00561, 2015.
+
+Mariusz Bojarski, Anna Choromanska, Krzysztof Choromanski, Bernhard Firner, Larry Jackel, Urs Muller, and Karol Zieba. Visualbackprop: efficient visualization of cnns. arXiv preprint arXiv:1611.05418, 2016a.
+
+Mariusz Bojarski, Davide Del Testa, Daniel Dworakowski, Bernhard Firner, Beat Flepp, Prasoon Goyal, Lawrence D Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, et al. End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316, 2016b.
+
+Chenyi Chen, Ari Seff, Alain Kornhauser, and Jianxiong Xiao. Deepdriving: Learning affordance for direct perception in autonomous driving. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2722–2730, 2015.
+
+Lu Chi and Yadong Mu. Deep steering: Learning end-to-end driving model from spatial and temporal visual cues. arXiv preprint arXiv:1708.03798, 2017.
+
+Felipe Codevilla, Matthias Muller, Alexey Dosovitskiy, Antonio L ¨ opez, and Vladlen Koltun. End-´ to-end driving via conditional imitation learning. arXiv preprint arXiv:1710.02410, 2017.
+
+Alexey Dosovitskiy, German Ros, Felipe Codevilla, Antonio Lopez, and Vladlen Koltun. Carla: An open urban driving simulator. arXiv preprint arXiv:1711.03938, 2017.
+
+Ross Girshick. Fast r-cnn. In Proceedings of the IEEE international conference on computer vision, pp. 1440–1448, 2015.
+
+Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp. 249–256, 2010.
+
+Ian J. Goodfellow and Oriol Vinyals. Qualitatively characterizing neural network optimization problems. CoRR, abs/1412.6544, 2014. URL http://arxiv.org/abs/1412.6544.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pp. 1026–1034, 2015.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012.
+
+Yann A LeCun, Leon Bottou, Genevieve B Orr, and Klaus-Robert M ´ uller. Efficient backprop. In ¨ Neural networks: Tricks of the trade, pp. 9–48. Springer, 2012.
+
+Philip Lenz, Julius Ziegler, Andreas Geiger, and Martin Roser. Sparse scene flow segmentation for moving object detection in urban environments. In Intelligent Vehicles Symposium (IV), 2011 IEEE, pp. 926–932. IEEE, 2011.
+
+Davy Neven, Bert De Brabandere, Stamatios Georgoulis, Marc Proesmans, and Luc Van Gool. Fast scene understanding for autonomous driving. arXiv preprint arXiv:1708.02550, 2017.
+
+Sinno Jialin Pan, Qiang Yang, et al. A survey on transfer learning. IEEE Transactions on knowledge and data engineering, 22(10):1345–1359, 2010.
+
+Eunbyung Park. Groupout: A way to regularize deep convolutional neural network.
+
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014.
+
+Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda Viegas, and Martin Wattenberg. Smoothgrad: ´ removing noise by adding noise. arXiv preprint arXiv:1706.03825, 2017.
+
+Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.
+
+Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. In Computer Vision (ICCV), 2017 IEEE International Conference on, pp. 843–852. IEEE, 2017.
+
+Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks. arXiv preprint arXiv:1703.01365, 2017.
+
+Marvin Teichmann, Michael Weber, Marius Zoellner, Roberto Cipolla, and Raquel Urtasun. Multinet: Real-time joint semantic reasoning for autonomous driving. arXiv preprint arXiv:1612.07695, 2016.
+
+Shimon Ullman. Against direct perception. Behavioral and Brain Sciences, 3(3):373–381, 1980.
+
+Panqu Wang, Pengfei Chen, Ye Yuan, Ding Liu, Zehua Huang, Xiaodi Hou, and Garrison Cottrell. Understanding convolution for semantic segmentation. arXiv preprint arXiv:1702.08502, 2017.
+
+Jason Yosinski, Jeff Clune, Yoshua Bengio, and Hod Lipson. How transferable are features in deep neural networks? In Advances in neural information processing systems, pp. 3320–3328, 2014.

parse/train/B14rPj0qY7/B14rPj0qY7_content_list.json

@@ -0,0 +1,1157 @@
+[
+    {
+        "type": "text",
+        "text": "RETHINKING SELF-DRIVING: MULTI-TASK KNOWLEDGE FOR BETTER GENERALIZATION AND ACCIDENT EXPLANATION ABILITY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            821,
+            171
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            195,
+            398,
+            223
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            261,
+            544,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Current end-to-end deep learning driving models have two problems: (1) Poor generalization ability of unobserved driving environment when diversity of training driving dataset is limited (2) Lack of accident explanation ability when driving models don’t work as expected. To tackle these two problems, rooted on the believe that knowledge of associated easy task is benificial for addressing difficult task, we proposed a new driving model which is composed of perception module for see and think and driving module for behave, and trained it with multi-task perception-related basic knowledge and driving knowledge stepwisely. Specifically segmentation map and depth map (pixel level understanding of images) were considered as what & where and how far knowledge for tackling easier drivingrelated perception problems before generating final control commands for difficult driving task. The results of experiments demonstrated the effectiveness of multitask perception knowledge for better generalization and accident explanation ability. With our method the average sucess rate of finishing most difficult navigation tasks in untrained city of CoRL test surpassed current benchmark method for 15 percent in trained weather and 20 percent in untrained weathers. ",
+        "bbox": [
+            233,
+            292,
+            764,
+            515
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            545,
+            334,
+            559
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Observing progressive improvement in various fields of pattern recognition with end-to-end deep learning based methods(Krizhevsky et al., 2012; Girshick, 2015), self-driving researchers try to revolutionize autonomous car field with the help of end-to-end deep learning techniques(Bojarski et al., 2016b; Chen et al., 2015; Codevilla et al., 2017). Impressive results have been acquired by mapping camera images directly to driving control commands(Bojarski et al., 2016b) with simple structure similar to ones for image classfication task(Simonyan & Zisserman, 2014). Further researches were conducted to improve the performance of deep learning based autonomous driving system, for example, Conditional Imitation Learning(Codevilla et al., 2017) approach has been proposed to solve the ambigious action problem. ",
+        "bbox": [
+            174,
+            575,
+            825,
+            702
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, two crutial problems failed to be spotted: (1) Poor generalization ability of unobserved driving environment given limited diversity of training scenerios. For example, though Dosovitskiy et al. (2017) addressed the driving direction selection problem, it showed poor generalization ability in unseen test town which has different map and building structure than training town’s. This generalization problem is extremely important since collected driving dataset always has limitation of diversity (2) Current end-to-end autonomous approaches lack of accident explanation ability when these models behave unexpectedly. Although saliency map based visualization methods(Smilkov et al., 2017; Sundararajan et al., 2017; Springenberg et al., 2014; Bojarski et al., 2016a) have been proposed to dig into the ’black box’, the only information these methods could bring is the possible attention of the model instead of the perception process of the model. ",
+        "bbox": [
+            174,
+            722,
+            825,
+            861
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We proposed a new driving approach to solve the two aforementioned problems by using multi-task basic perception knowledge. We argue that when end-to-end model is trained to address a specific difficult task, it’s better to train the model with some basic knowledge to solve relevant easier tasks before(Pan et al., 2010). An analogy for this can be observed when human beings learn a difficult knowledge. For example, to solve a complex integration problem, compared with students without basic math knowledge, students who know about basic knowledge of math are able to learn the core of intergration more quickly and solve other similar integration problems instead of memorizing the solution of the specific problem. ",
+        "bbox": [
+            176,
+            882,
+            823,
+            922
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            825,
+            172
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our proposed model consists of two modules: perception module and driving module as in Fig. 1. The perception module is used for learning easier driving-related perception knowledge, which we refer as ability of pixel level understanding of input including what & where and how far knowledge. We trained perception module with segmentation map and depth map first, while the former serves as what & where knowledge and the latter serves as how far knowledge. By visualizing inferenced segmentation and depth results whether perception process works well or not could be inferred. After the perception module was trained to have ability of pixel level understanding of its image input, we freezed the perception module weights and trained driving module with driving dataset. This decomposition of end-to-end driving network strucuture is considered to be mediated perception approach(Ullman, 1980). With our proposed driving structure and stepwise training strategy, the generalization and accident explanation problems were addressed to a certain extent. ",
+        "bbox": [
+            174,
+            194,
+            825,
+            347
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            369,
+            338,
+            385
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Depending on whether mediated perception knowledge are generated, self-driving models are categorized into mediated perception approach(Ullman, 1980) and behavior reflex approach. ",
+        "bbox": [
+            176,
+            401,
+            823,
+            429
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For mediated perception approaches, there are several well-behaved deep learning methods, for example, Deep-Driving method(Chen et al., 2015) fisrtly converts input RGB images to some key perception indicators related to final driving controls. They designed a very simple driving controller based on predicted perception indicators. Problem of this approach is that key perception indicators have limitation of describing unseen scenerios and are difficult to collect in reality. Except for inferencing for final driving controls, there are approaches which focus on inferencing intermediate description of driving situation only. For separate scene understanding task, car detection(Lenz et al., 2011) and lane detection(Aly, 2008) are two main topics in this area. ",
+        "bbox": [
+            174,
+            449,
+            825,
+            560
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Instead of inferencing one perception task at most, multi-task learning method aims at tackling several relevant tasks simultaneously. Teichmann et al. (2016) uses input image to solve both object detection and road segmentation tasks. Branched E-Net(Neven et al., 2017) not only infers for segmentation map, but also depth map of current driving scenarios. These multi-task learning methods shows better result when sharing the encoder of different perception tasks together, but they haven’t really tried to make the car drive either in simulator or reality. ",
+        "bbox": [
+            174,
+            582,
+            825,
+            665
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As for behavior reflex approach which is also called ’end-to-end learning’, NVIDIA firstly proposed a model for mapping input image pixels directly to final driving control output(steer only)(Bojarski et al., 2016b). Some other approaches further atempted to create more robust models, for example, long short-term memory (LSTM) was utilized to make driving models store a memory of past(Chi & Mu, 2017). ",
+        "bbox": [
+            174,
+            686,
+            823,
+            756
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "One problem is that aforementioned methods were tested in dissimlar driving scenerios using different driving dataset, thus it’s hard to determine if model itself is the source of the better driving behavior instead of effectiveness of data(Sun et al., 2017). ",
+        "bbox": [
+            176,
+            777,
+            820,
+            819
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Codevilla et al. (2017) was tested in a public urban driving simulator Dosovitskiy et al. (2017) and sucessed to tackle the ambigous action problem which refers as optimal driving action can’t be inferred from perceptual input alone. Benefit from CoRL test in Dosovitskiy et al. (2017), fair comparision could be conducted using same driving dataset. Codevilla et al. (2017) showed limitation of generalization ability problem in test town different from train town(Dosovitskiy et al., 2017) as in CoRL test training dataset could be only collected from single train town. ",
+        "bbox": [
+            174,
+            827,
+            825,
+            910
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "When the end-to-end driving method behaves badly and causes accidents, accident explanation ability is required. Though saliency-map based visualization methods(Bojarski et al., 2016a; Smilkov et al., 2017) help understand the influence of input on final driving control, it’s extremely hard to derive which module of the model fails when driving problems happen — If the model percepts incorrectly or the driving inference processes wrongly based on good perception information. Driving system was enabled to give quantitative explanation by visualizing inferenced multi-task basic knowledge to solve this problem. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            202
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 FRAMEWORK OF PROPOSED SYSTEM ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            238,
+            508,
+            252
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Basic strucure of the proposed model is shown in Fig. 1. The proposed model has two parts: (1) Multi-task basic knowledge perception module (2) Driving decision branch module. The perception module is used to percept the world by inferencing dpeth map and segmentation map, which is composed of one shared encoder and two decoders for two different basic perception knowledge: (1) Segmentation decoder for generating ’what & where’ information by predicting segmentation maps; (2) Depth decoder for predicting ’how far’ the objects in vision are by inferencing depth maps. The perception module is aimed at extracting encoded feature map containing pixel level understanding information for driving module and qualitative explanation when proposed model doesn’t work as expected by visualizing the predicted segmentation and depth maps to determine if the driving problem is caused by percept process or driving process. ",
+        "bbox": [
+            174,
+            268,
+            825,
+            409
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The driving module enbales the model to generate driving decisions for different direction following guidances. We categorized the real world driving guidance into four types: (1) Following lane (2) Turning left (3) Going straight (4) Turning right as done in Codevilla et al. (2017). For each driving guidance direction, there is a driving branch(which predicts the value of driving controls) corresponding to it, therefore there are four driving guidance branches totally. The output of second last layer in perception module is inputted to the driving module, therefore the training of which could benefit from the multi-knowledge extracted by the perception module. Instead of linear layers, convolution layers are utilized for inferencing final driving controls for each direction, which helps keeping the spatial relation of information and reducing number of parameters as non-negligible quantity of direction branches. ",
+        "bbox": [
+            174,
+            429,
+            825,
+            568
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 MULTI-TASK BASIC KNOWLEDGE PERCEPTION MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            587,
+            609,
+            602
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The perception module is built with residual block proposed in (He et al., 2016) which solves gradient vanishing and ’degradation problem’, and it has a structure similar to Segnet(Badrinarayanan et al., 2015) prosposed for efficient image segmentation task. Huge difference is that in our proposed method there are two different decoders for inferencing both segmentation and depth maps simultaneously instead of segmentation map only. Besides, we constraint the total strides in encoder to 8 for keeping resolution of feature map, as large total stride has negative influence on feature map size reconstuction. Hybrid Dilated Convolution Wang et al. (2017) is adapted as last part of the encoder as it enlarges the receptive field and avoids theoretical issue of gridding problem. Groupout(Park) is also adapted to avoid overfitting problem in the convolution network. ",
+        "bbox": [
+            174,
+            613,
+            825,
+            739
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 DRIVING DECISION BRANCH MODULE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            757,
+            483,
+            772
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The driving module is built with residual block and has a general form as Codevilla et al. (2017) in last output layer for several direction outputs. It is all based on convolutional layers in order to keep the spatial information and reduce parameters motivated by Springenberg et al. (2014). Four different high level driving guidance such as ”turning right” are utilized for selecting which direction branch’s output is supposed to be considered as final driving outputs. Driving outputs contain steering and acceleration/brake, both of them range from -1 to 1. Since there are 4 output branches corresponding to 4 high level driving guidances, 8 feature map size convolution kernels are set in the last layer for output scalar value, in which each two are regarded as driving controls for one driving guidance. To determine the limitation of RGB image, no other information such as current speed or steering angle were used as input. Instead we atempted to predict the current speed based on current RGB image to keep the driving smoothly as done in (Codevilla et al., 2017). The input of the driving module is not from the last layer’s output of the encoder part in the perception module, but the second last layer’s output of the encoder part due to empirically selection for best generalization. ",
+        "bbox": [
+            174,
+            785,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6dc827fdcb69b3a1fa85c7f890f6534bb34f1abd9ff10df5c2beca34f9569196.jpg",
+        "image_caption": [
+            "Figure 1: Basic structure of proposed self-driving system. The components which lie in the red bounding box are refered as parts of perception module. The components which lie in the blue bounding box forms the driving module. In order to see the limiation of RGB image, only current RGB image and driving guidance are used as inputs seperatedly for perception module and driving module. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            251,
+            104,
+            761,
+            367
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            483,
+            825,
+            540
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            561,
+            326,
+            577
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 SYSTEM SETUP ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            593,
+            323,
+            608
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The training dataset is collected in CARLA simulator(Dosovitskiy et al., 2017). CARLA simulator is a self-driving simulator developed by Intel Co. for collecting self-driving related information and evaluating driving model with a standard testing environment named CoRL test. CoRL test is composed of 4 tasks of increasing difficulty: (1) Straight: the goal is straight ahead of the starting position. (2) One turn: getting to the goal takes one turn, left or right. (3) Navigation: navigation with an arbitrary number of turns. (4) Navigation with dynamic obstacles: same as previous task, but with other vehicles and pedestrians(Dosovitskiy et al., 2017). ",
+        "bbox": [
+            174,
+            619,
+            825,
+            718
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The main metric for quantitatively evaluating is the average success rate of finishing seperate tasks in CoRL test. CoRL test contains tests both in trained town and untrained town under both trained and untrained weathers. Test trained town and untrained town are constructed with different maps and different building texture. ",
+        "bbox": [
+            176,
+            739,
+            825,
+            795
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2 DATASET ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            813,
+            279,
+            828
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dataset for training our model could be categorized into 2 items: (1) Perception module training dataset (2) Driving module training dataset. For perception module, we trained it with 35,000 pairs of RGB images, segmentation and depth maps and evaluated with 5,000 pairs. As for driving module, we trained with 455,000 dataset, and evaluated on 62,000 evaluation dataset. Before training our proposed model, two vital data processing methods were used: balancing dataset and data augmentation. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            922
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/89d47467f465d43fe93c6cc1b078937ce494cbc2aa2c5ecf02e082295420d799.jpg",
+        "table_caption": [
+            "Table 1: Quantitive evaluation of methods in the goal-directed navigation tasks in CoRL test. The table reports the percentage of success rate of finishing corresponding task in different condition. Higher means better performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"4\">Training conditions</td><td colspan=\"4\">New town</td><td colspan=\"4\">New weather</td><td colspan=\"4\">New town&amp;weather</td></tr><tr><td>Task</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td><td>MP</td><td>IL</td><td>RL</td><td>OURS</td></tr><tr><td>Straight</td><td>98</td><td>95</td><td>89</td><td>98</td><td>92</td><td>97</td><td>74</td><td>100</td><td>100</td><td>98</td><td>86</td><td>100</td><td>50</td><td>80</td><td>68</td><td>96</td></tr><tr><td>One turn</td><td>82</td><td>89</td><td>34</td><td>87</td><td>61</td><td>59</td><td>12</td><td>81</td><td>95</td><td>90</td><td>16</td><td>88</td><td>50</td><td>48</td><td>20</td><td>82</td></tr><tr><td>Navigation</td><td>80</td><td>86</td><td>14</td><td>81</td><td>24</td><td>40</td><td>3</td><td>72</td><td>94</td><td>84</td><td>2</td><td>88</td><td>47</td><td>44</td><td>6</td><td>78</td></tr><tr><td>Nav. dynamic</td><td>77</td><td>83</td><td>7</td><td>81</td><td>24</td><td>38</td><td>2</td><td>53</td><td>89</td><td>82</td><td>2</td><td>80</td><td>44</td><td>42</td><td>4</td><td>62</td></tr></table>",
+        "bbox": [
+            176,
+            170,
+            823,
+            238
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For fair comparison, we use same driving dataset published by Conditional Imitation Learning(Codevilla et al., 2017) except that we collected extra segmentation and depth maps in train town for training our proposed perception module. ",
+        "bbox": [
+            174,
+            281,
+            825,
+            323
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.1 DATA BALANCING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            339,
+            356,
+            353
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset balancing contributed to better generalization of both perception module and driving module in our experiments as it enables each mini-batch to be a microcosm of the whole dataset. For perception module, dataset were balanced to ensure that each mini-batch contains all different training weathers and an equal amount of going straight and turning situations. For driving module, we balance each training mini-batch to ensure equally distribution of different driving direction guidance, and reorganized large steer(absolute value larger than 0.4) data accounts for 1/3 in each mini-batch, brake situation data acounts for $1 / 3$ , noise steer situation for 1/10. ",
+        "bbox": [
+            174,
+            363,
+            825,
+            460
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.2 DATA AUGMENTATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            477,
+            387,
+            491
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We add guassian noise, coarse dropout, contrast normalization, Guassian blur to both training dataset for perception and driving module for enlarging training dataset distribution. ",
+        "bbox": [
+            174,
+            501,
+            823,
+            530
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3 TRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            546,
+            351,
+            560
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We trained the whole system using a step-wise training method which is firstly we trained the perception module with multi-task basic perception knowledge, then we freezed the weights of perception module and train driving module with driving dataset. For training the perception module, we used mini-batch size 24 and set ratio of segmentation loss and depth loss to be 1.5:1. Softmax categorical crossentropy is used for segmentation loss, binary crossentropy is used for depth loss. Adam of 0.001, which is multiplied by a factor of 0.2 of previous learning rate if validation loss does’t drop for 1 epoch is used as optmizer. L2 weight decay and early stopping are also used for avoid overfitting. As for training the driving module, we consider MSE loss and use Adam with starting learning rate of 0.002 which exponentially decay of 0.9 every epoch. Early stopping and L2 decay are used for regularization. ",
+        "bbox": [
+            174,
+            573,
+            825,
+            712
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS & RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            732,
+            428,
+            748
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1 GENERALIZATION ABILITY TEST ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            765,
+            444,
+            779
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We compare the results of driving performance between our proposal and other methods tested in CoRL test via success rate of finishing each task. The details of results are shown in Table. 1 ",
+        "bbox": [
+            173,
+            791,
+            823,
+            819
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "From Table. 1, though our proposal finished slightly less in training conditions comparing with other methods, our proposal achieved much higher success rate in untrained town environments, which demonstrates our model has much better generalization ability of adapting to untrain town than other methods tested in the CoRL test when trained with limited diversity of training conditions. One important notice is that we use the almost the same driving dataset for training as the method Codevilla et al. (2017) showed in the Table. ??. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            922
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We could also visualize the perception process when the model works. One example of test in untrained town and untrained weather is shown in Fig. 2. ",
+        "bbox": [
+            169,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/38c6d27d6247d2c234bb0cc042e4068451b217e86c064e62c146d63476c9de47.jpg",
+        "image_caption": [
+            "Figure 2: Screenshots of captured single RGB image and our proposal’s inference results which consists of predicted segmentation map and depth map during test in untrained town under untrained weather. Obviously from the inferenced segmentation and depth maps we get information that the driving model knows a car is passing by the left side. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            349,
+            147,
+            647,
+            453
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2 ORIGIN OF BETTER GERNERALIZATION ABILITY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            560,
+            552,
+            575
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Since we observed our training model has better generalization ability in unseen town comparing with other methods when almost the same driving dataset were used to train (except that we collected extra depth maps and segmentation maps in same training environments), we want to investigate the origin of the better generalization ability. There are two possible reasons why our training model has better generalization ability in unseen town: (1) Basic knowledge (segmentation map and depth map) (2) Network structure. Therefore we conduct experiments by comparing performance of two methods: ",
+        "bbox": [
+            174,
+            587,
+            825,
+            684
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Our original proposal: Firstly train perception module with basic knowledge, after training perception module, freeze its weights and train driving module with driving dataset Compared method: Train the encoder of perception module and driving module together with driving dataset. No basic perception knowledge is used for training model. ",
+        "bbox": [
+            212,
+            709,
+            823,
+            771
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Since tests in CoRL cost much time, we limited our evaluation to the most difficult untrained town under untrained weathers test. Results are shown in Table. 2. From the results it’s obvious that multibasic knowledge we use in the training phase is the origin of our proposal’s good generalization ability of untrained town instead of the network structure. Moreover, the network structure could be improved to achieve better performance in the furture. ",
+        "bbox": [
+            174,
+            782,
+            825,
+            853
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3 QUALITATIVE CAUSE EXPLANATION ABILITY OF DRIVING PROBLEMS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            869,
+            700,
+            883
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Besides basic knowledge leads to better generalization ability, it could also be used to give a qualitative explanation of driving problems. Basic knowledge of segmentation map and depth map are output from the perception module during test phase, therefore how the driving module percepts the current scenario could be known by simply visualizing the outputs of segmentation and depth from perception module. Depending on the predicted pixel understanding of the situation, cause of driving problem could be inferred. ",
+        "bbox": [
+            174,
+            895,
+            820,
+            924
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/18d98102513dc8f4e9413cd33b81dfe62af5cdc791fbf4e97145a99c977b2fb7.jpg",
+        "table_caption": [
+            "Table 2: Quantitive evaluation of original proposal which uses segmentataion and depth maps in training phase and compared method which doesn’t use. Results shows that when multi-knowldge is not used for training, the success rate drops hugely in the testing town under untained weathers. It indicates that multi-basic knowledge is the main origin of the good generalization ability in our proposal. ",
+            "New town&weather test "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Task</td><td>COMPARED</td><td>ORIGINAL</td></tr><tr><td>Straight</td><td>91</td><td>96</td></tr><tr><td>One turn</td><td>52</td><td>82</td></tr><tr><td>Navigation</td><td>20</td><td>78</td></tr><tr><td>Nav. dynamic</td><td>16</td><td>62</td></tr></table>",
+        "bbox": [
+            338,
+            202,
+            658,
+            275
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            324,
+            825,
+            380
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "One example is shown in Fig. 3. For a failed straight task in untrained town under untrained weather soft rain sunset as the driving model failed to move forward, we visualized outputs of segmentation and depth maps predicted by perception module. It’s obvious that this failure case is caused by the perception module since the model falsely percepted that there is a car in front of it and in order to avoid collision it did’t start. There is no car actually thus the perception module made false judgement. However, what’s interesting is that sometimes it fools readers to think that there is a car in Fig. 3 because of sun ray reflection on the wet road and the perception module has the similar understanding as these readers. Therefore in some aspects the perception module makes the right judgement instead of wrong’s. For traditional end-to-end learning driving methods(Bojarski et al., 2016b) it’s impossible to reason as they don’t focus on the cause explanation ability which is of great importance for practice use of deep learning driving models. ",
+        "bbox": [
+            173,
+            400,
+            825,
+            554
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d2cf88b4862b0b42c56af1012bd4a810abf87af683fd3f269ff016d085c468e.jpg",
+        "image_caption": [
+            "Figure 3: Failed straight task in untrained town under untrained soft rain sunset weather. From predicted segmentation and depth maps, we know that the driving model thinks that there is a car in front of it but actually there isn’t any car in front of it. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            290,
+            573,
+            707,
+            712
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4 FINE-TUNE TEST ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            811,
+            333,
+            827
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Fine-tuneYosinski et al. (2014), which refers to use other well-trained models weights on different target-related dataset as initial weights for training with target dataset instead of using weights initializing methods(Glorot & Bengio, 2010; He et al., 2015; LeCun et al., 2012), is a common trick used in deep learning since empirically it could leads to better generalization on new target dataset. Here in our specific case we refer fine-tune method to be after training perception module we train the weights of the encoder of the perception module as well instead of freezing these weights. In ",
+        "bbox": [
+            173,
+            839,
+            825,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table. 3 we compare the performance of fine-tune method and our original proposed method. ",
+        "bbox": [
+            169,
+            103,
+            782,
+            118
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e6c1bcb22d3400798d16b5c90c5ee36381d3c9ccc7f6c5c4ae6dc44bd9789e67.jpg",
+        "table_caption": [
+            "Table 3: Quantitive evaluation of original proposal and fine-tune method which doens’t freeze the perception module’s weights during training the driving module. Results shows that the success rate of the fine-tune method drops dramaticaly in the testing town under untained weathers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">New town&amp;weather test</td></tr><tr><td>Task</td><td>FINETUNE ORIGINAL</td></tr><tr><td>Straight</td><td>88</td></tr><tr><td>One turn 59</td><td>96 82</td></tr><tr><td>Navigation</td><td>42 78</td></tr><tr><td>Nav. dynamic</td><td>33 62</td></tr></table>",
+        "bbox": [
+            343,
+            203,
+            653,
+            290
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this comparison we achieved counter-intuition results: after fine-tune the weights of the perception module the driving model achieved worse results than original method which freeze the weights of perception module when training the driving module. ",
+        "bbox": [
+            174,
+            328,
+            825,
+            371
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "One possible reason is that the generalization ability lies in the perception module instead of the driving module, therefore when we train the perception module again with driving dataset, the ability of generating compressed multi-knowdege information is destoryed. As the fine-tune model couldn’t benefit from the multi-task knowledge anymore, it failed to produce the same generalization ability as the original proposal did. ",
+        "bbox": [
+            174,
+            391,
+            825,
+            462
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Furthermore we conduct experiment on visualizing one direction of loss surface by projecting the loss surface to 2 dimension(Goodfellow & Vinyals, 2014) to investigate some qualitative explanation for this comparison result. $x$ axis corresponds to linear interpolation of the weights of original proposed method and weights of compared fine-tuned method after training. Formulation of calculating the weights in this projection direction is Equation. 1. ",
+        "bbox": [
+            174,
+            481,
+            825,
+            553
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/445921737fe1b53c8631e952737c08dc793bb99446cd6bd2b9338054a3825b59.jpg",
+        "text": "$$\n\\alpha \\in [ - 1 , 2 ] , f ( \\alpha x _ { f i n e t u n e } + ( 1 - \\alpha ) x _ { r g b 0 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            574,
+            643,
+            592
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "$\\alpha$ is linear interpolation ratio, $x _ { f i n t u n e }$ and $x _ { r g b 0 }$ are trained weights of fine-tune method and original proposal method. $f ( x )$ is loss function of the whole model while input is considered as different model weights. We draw out the projected loss surface as Fig. 4 by sampling from the interpolation weigthts. From Fig. 4 we can get one possible qualitative reason for worse behavior of fine-tune method from a loss surface perspective: Model weight got by using fine-tune method is stuck in a super flat surface, while model weights of original proposed method successfully finds a local minimum. ",
+        "bbox": [
+            173,
+            604,
+            825,
+            702
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            724,
+            318,
+            739
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper we propose a new driving system for better generalization and accident explanation ability by enabling it to do simpler driving-related perception task before generating commands for diffult driving task. Through multiple experiments we empirically proved the effectiveness of the multi basic perception knowledge for better generalization ability of unobserved town when diversity of training dataset is limited. Besides our proposed model has self-explanation ability by visualizing the predicted segmentation and depth maps from the perception module to determine the cause of driving problems when they happen. One interesting result we acquired by comparing different train strategies is that the generalization ability of driving origins from basic knowledge and lies in weights of the perception module which should not be modified during training with driving dataset. We hope our work could movitivate other researches to use multi-task target related perception knowledge for better performance in robot learning. In future we will investigate more effective network structures. ",
+        "bbox": [
+            174,
+            757,
+            825,
+            922
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/70c1612b4c149ecc7c1c3c717db55baf2b1ab70a65b51481f55ba2a3348a9f28.jpg",
+        "image_caption": [
+            "Figure 4: One perceptive of loss surface by linear interpolation of original proposed method weights and fine-tune method weights. Blue line refers to test loss, red line refers to train loss. From the visualization perspective it’s possibly that finetune method weights are stuck in a flat surface while the original proposed weights sucessfully find a local minimum. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            240,
+            121,
+            761,
+            315
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            433,
+            326,
+            445
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Thanks to all Prof.Ogata lab members especially Kamuza SASAKI san who teaches me about Deep Learning patiently when I have zero knowledge of what it is. Great thanks to my bros Zehai TU and Pengfei LI who support me no matter how annoying I am in the midnight. Final thanks to my homie Mengcheng SONG for being a Hiphop guide for me and makes me understand about the importance of always ’keep it real’. ",
+        "bbox": [
+            174,
+            457,
+            825,
+            526
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            549,
+            285,
+            564
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mohamed Aly. Real time detection of lane markers in urban streets. In Intelligent Vehicles Symposium, 2008 IEEE, pp. 7–12. IEEE, 2008. ",
+        "bbox": [
+            176,
+            573,
+            821,
+            602
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla. Segnet: A deep convolutional encoderdecoder architecture for image segmentation. arXiv preprint arXiv:1511.00561, 2015. ",
+        "bbox": [
+            174,
+            612,
+            823,
+            641
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mariusz Bojarski, Anna Choromanska, Krzysztof Choromanski, Bernhard Firner, Larry Jackel, Urs Muller, and Karol Zieba. Visualbackprop: efficient visualization of cnns. arXiv preprint arXiv:1611.05418, 2016a. ",
+        "bbox": [
+            174,
+            652,
+            823,
+            695
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mariusz Bojarski, Davide Del Testa, Daniel Dworakowski, Bernhard Firner, Beat Flepp, Prasoon Goyal, Lawrence D Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, et al. End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316, 2016b. ",
+        "bbox": [
+            174,
+            707,
+            823,
+            750
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Chenyi Chen, Ari Seff, Alain Kornhauser, and Jianxiong Xiao. Deepdriving: Learning affordance for direct perception in autonomous driving. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2722–2730, 2015. ",
+        "bbox": [
+            173,
+            761,
+            826,
+            804
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Lu Chi and Yadong Mu. Deep steering: Learning end-to-end driving model from spatial and temporal visual cues. arXiv preprint arXiv:1708.03798, 2017. ",
+        "bbox": [
+            168,
+            814,
+            823,
+            843
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Felipe Codevilla, Matthias Muller, Alexey Dosovitskiy, Antonio L ¨ opez, and Vladlen Koltun. End-´ to-end driving via conditional imitation learning. arXiv preprint arXiv:1710.02410, 2017. ",
+        "bbox": [
+            171,
+            854,
+            821,
+            883
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Alexey Dosovitskiy, German Ros, Felipe Codevilla, Antonio Lopez, and Vladlen Koltun. Carla: An open urban driving simulator. arXiv preprint arXiv:1711.03938, 2017. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ross Girshick. Fast r-cnn. In Proceedings of the IEEE international conference on computer vision, pp. 1440–1448, 2015. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp. 249–256, 2010. ",
+        "bbox": [
+            174,
+            140,
+            823,
+            184
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ian J. Goodfellow and Oriol Vinyals. Qualitatively characterizing neural network optimization problems. CoRR, abs/1412.6544, 2014. URL http://arxiv.org/abs/1412.6544. ",
+        "bbox": [
+            169,
+            193,
+            823,
+            222
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pp. 1026–1034, 2015. ",
+        "bbox": [
+            176,
+            231,
+            821,
+            273
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016. ",
+        "bbox": [
+            173,
+            281,
+            826,
+            325
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097–1105, 2012. ",
+        "bbox": [
+            174,
+            333,
+            825,
+            376
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yann A LeCun, Leon Bottou, Genevieve B Orr, and Klaus-Robert M ´ uller. Efficient backprop. In ¨ Neural networks: Tricks of the trade, pp. 9–48. Springer, 2012. ",
+        "bbox": [
+            174,
+            385,
+            823,
+            415
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Philip Lenz, Julius Ziegler, Andreas Geiger, and Martin Roser. Sparse scene flow segmentation for moving object detection in urban environments. In Intelligent Vehicles Symposium (IV), 2011 IEEE, pp. 926–932. IEEE, 2011. ",
+        "bbox": [
+            173,
+            422,
+            825,
+            465
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Davy Neven, Bert De Brabandere, Stamatios Georgoulis, Marc Proesmans, and Luc Van Gool. Fast scene understanding for autonomous driving. arXiv preprint arXiv:1708.02550, 2017. ",
+        "bbox": [
+            173,
+            473,
+            823,
+            503
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sinno Jialin Pan, Qiang Yang, et al. A survey on transfer learning. IEEE Transactions on knowledge and data engineering, 22(10):1345–1359, 2010. ",
+        "bbox": [
+            173,
+            512,
+            823,
+            541
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Eunbyung Park. Groupout: A way to regularize deep convolutional neural network. ",
+        "bbox": [
+            173,
+            549,
+            722,
+            565
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. ",
+        "bbox": [
+            173,
+            574,
+            823,
+            603
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda Viegas, and Martin Wattenberg. Smoothgrad: ´ removing noise by adding noise. arXiv preprint arXiv:1706.03825, 2017. ",
+        "bbox": [
+            173,
+            611,
+            823,
+            641
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jost Tobias Springenberg, Alexey Dosovitskiy, Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014. ",
+        "bbox": [
+            173,
+            648,
+            823,
+            679
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. Revisiting unreasonable effectiveness of data in deep learning era. In Computer Vision (ICCV), 2017 IEEE International Conference on, pp. 843–852. IEEE, 2017. ",
+        "bbox": [
+            173,
+            686,
+            823,
+            729
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks. arXiv preprint arXiv:1703.01365, 2017. ",
+        "bbox": [
+            169,
+            738,
+            825,
+            767
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Marvin Teichmann, Michael Weber, Marius Zoellner, Roberto Cipolla, and Raquel Urtasun. Multinet: Real-time joint semantic reasoning for autonomous driving. arXiv preprint arXiv:1612.07695, 2016. ",
+        "bbox": [
+            173,
+            776,
+            821,
+            819
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Shimon Ullman. Against direct perception. Behavioral and Brain Sciences, 3(3):373–381, 1980. ",
+        "bbox": [
+            169,
+            827,
+            808,
+            844
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Panqu Wang, Pengfei Chen, Ye Yuan, Ding Liu, Zehua Huang, Xiaodi Hou, and Garrison Cottrell. Understanding convolution for semantic segmentation. arXiv preprint arXiv:1702.08502, 2017. ",
+        "bbox": [
+            171,
+            852,
+            820,
+            881
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jason Yosinski, Jeff Clune, Yoshua Bengio, and Hod Lipson. How transferable are features in deep neural networks? In Advances in neural information processing systems, pp. 3320–3328, 2014. ",
+        "bbox": [
+            171,
+            890,
+            823,
+            919
+        ],
+        "page_idx": 9
+    }
+]

parse/train/jLHWRxwc7_f/jLHWRxwc7_f.md

@@ -0,0 +1,289 @@
+# EditGAN: High-Precision Semantic Image Editing
+
+Huan Ling1,2,3,∗ Karsten Kreis1,∗ Daiqing Li 1
+
+Seung Wook Kim1,2,3 Antonio Torralba4 Sanja Fidler1,2,3
+
+1NVIDIA 2University of Toronto 3Vector Institute 4MIT
+
+{huling,kkreis,daiqingl,seungwookk,sfidler}@nvidia.com, torralba@mit.edu
+
+# Abstract
+
+Generative adversarial networks (GANs) have recently found applications in image editing. However, most GAN-based image editing methods often require large-scale datasets with semantic segmentation annotations for training, only provide high level control, or merely interpolate between different images. Here, we propose EditGAN, a novel method for high-quality, high-precision semantic image editing, allowing users to edit images by modifying their highly detailed part segmentation masks, e.g., drawing a new mask for the headlight of a car. EditGAN builds on a GAN framework that jointly models images and their semantic segmentations [1, 2], requiring only a handful of labeled examples – making it a scalable tool for editing. Specifically, we embed an image into the GAN’s latent space and perform conditional latent code optimization according to the segmentation edit, which effectively also modifies the image. To amortize optimization, we find “editing vectors” in latent space that realize the edits. The framework allows us to learn an arbitrary number of editing vectors, which can then be directly applied on other images at interactive rates. We experimentally show that EditGAN can manipulate images with an unprecedented level of detail and freedom, while preserving full image quality.We can also easily combine multiple edits and perform plausible edits beyond EditGAN’s training data. We demonstrate EditGAN on a wide variety of image types and quantitatively outperform several previous editing methods on standard editing benchmark tasks. Project page: https://nv-tlabs.github.io/editGAN.
+
+# 1 Introduction
+
+AI-driven photo and image editing has the potential to streamline the workflow of photographers and content creators and to enable new levels of creativity and digital artistry [3]. AI-based image editing tools have already found their way into consumer software in the form of neural photo editing filters, and the deep learning
+
+![](images/782f0d95cf6c1f39f92812cd3e25c760b0d31805d8af630f0f9c23dfff5334ad.jpg)  
+Figure 1: High-precision semantic image editing with EditGAN.
+
+research community is actively developing further techniques. A particularly promising line of research uses generative adversarial networks (GANs) [4, 5, 6, 7, 8] and either embeds images into the GAN’s latent space or works directly with GAN-generated images. Careful modifications of the latent embeddings then translate to desired changes in generated output, allowing, for example, to coherently change facial expressions in portraits [9, 10, 11, 12, 13, 14, 15, 16], change viewpoint or shapes and textures of cars [17], or to interpolate between different images in a semantically meaningful manner [18, 19, 20, 21].
+
+![](images/c899d3cd93c67236587887acfd6de43587f4198a2a8293fb1b4b06e06d566106.jpg)  
+Figure 2: (1) EditGAN builds on a GAN framework that jointly models images and their semantic segmentations. (2 & 3) Users can modify segmentation masks, based on which we perform optimization in the GAN’s latent space to realize the edit. (4) Users can perform editing simply by applying previously learnt editing vectors and manipulate images at interactive rates.
+
+Most GAN-based image editing methods fall into few categories. Some works rely on GANs conditioning on class labels or pixel-wise semantic segmentation annotations [19, 10, 22, 11], where different conditionings lead to modifications in the output, while others use auxiliary attribute classifiers [23, 15] to guide synthesis and edit images. However, training such conditional GANs or external classifiers requires large labeled datasets. Therefore, these methods are currently limited to image types for which large annotated datasets are available, like portraits [10]. Furthermore, even if annotations are available, most techniques offer only limited editing control, since these annotations usually consist only of high-level global attributes or relatively coarse pixel-wise segmentations. Another line of work focuses on mixing and interpolating features from different images [18, 19, 20, 21], thereby requiring reference images as editing targets and usually also not offering fine control. Other approaches carefully analyze and dissect GANs’ latent spaces, finding disentangled latent variables suitable for editing [24, 25, 12, 13, 14, 26, 27], or control the GANs’ network parameters [25, 28, 16]. Usually, these methods do not enable detailed editing and are often slow.
+
+In this work, we are addressing these limitations and propose EditGAN, a novel GAN-based image editing framework that enables high-precision semantic image editing by allowing users to modify detailed object part segmentations. EditGAN builds on a recently proposed GAN that jointly models both images and their semantic segmentations based on the same underlying latent code [1, 2], and requires as few as 16 labeled examples – allowing it to scale to many object classes and choices of part labels. We achieve editing by modifying the segmentation mask according to a desired edit and optimizing the latent code to be consistent with the new segmentation, thus effectively changing the RGB image. To achieve efficiency, we learn editing vectors in latent space that realize the edits, and that can be directly applied on other images, without any or only few additional optimization steps. We can thus pre-train a library of interesting edits that a user can directly utilize in an interactive tool.
+
+We apply EditGAN on a wide range of images, including images of cars, cats, birds, and human faces, demonstrating unprecedented high-precision editing. We perform quantitative comparisons to multiple baselines and outperform them in metrics such as identity preservation, quality preservation, and target attribute accuracy, while requiring orders of magnitude less annotated training data. EditGAN is the first GAN-driven image editing framework, which simultaneously (i) offers very highprecision editing, (ii) requires only very little annotated training data (and does not rely on external classifiers), (iii) can be run interactively in real time, (iv) allows for straightforward compositionality of multiple edits, (v) and works on real embedded, GAN-generated, and even out-of-domain images.
+
+# 2 Related Work
+
+Image Editing and Manipulation. Image Editing has a long history in computer vision and graphics, as well as machine learning [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 18, 11, 28, 41, 42, 16]. Recently, deep generative models [4, 43, 44], in particular modern GANs [6, 45, 7, 46, 8], received much attention as a promising tool for efficient image editing, as it was found that latent space manipulations often lead to interpretable and predictable changes in output [47, 24, 48, 49, 26, 27, 50].
+
+GAN-based image editing methods can be broadly sorted into a number of categories. (i) One line of work relies on the careful dissection of the GAN’s latent space, aiming to find interpretable and disentangled latent variables, which can be leveraged for image editing, in a fully unsupervised manner [47, 24, 25, 12, 13, 14, 48, 49, 26, 27, 50, 51]. Although powerful, these approaches usually do not result in any high-precision editing capabilities. The editing vectors we are learning in EditGAN would be too hard to find independently without segmentation-based guidance. (ii) Other works utilize GANs that condition on class or pixel-wise semantic segmentation labels to control synthesis and achieve editing [9, 52, 46, 19, 10, 22, 11]. Hence, these works usually rely on large annotated datasets, which are often not available, and even if available, the possible editing operations are tied to whatever labels are available. This stands in stark contrast to EditGAN, which can be trained in a semi-supervised fashion with very little labeled data and where an arbitrary number of high-precision edits can be learnt. (iii) Furthermore, auxiliary attribute classifiers have been used for image manipulation [23, 15], thereby still relying on annotated data and usually only providing high-level control. (iv) Image editing is often explored in the context of “interpolating” between a target and different reference image in sophisticated ways, for example by replacing certain features in a given image with features from a reference images [18, 19, 20, 21]. From the general image editing perspective, the requirement of reference images limits the broad applicability of these techniques and prevents the user from performing specific, detailed edits for which potentially no reference images are available. (v) Recently, different works proposed to directly operate in the parameter space of the GAN instead of the latent space to realize different edits [25, 28, 16]. For example, [25, 28] essentially specialize the generator network for certain images at test time to aid image embedding or “rewrite” the network to achieve desired semantic changes in output. The drawback is that such specializations prevent the model from being used in real-time on different images and with different edits. [16] proposed an approach that more directly analyses the parameter space of a GAN and treats it as a latent space in which to apply edits. However, the method still merely discovers edits in the network’s parameter space, rather than actively defining them like we do. It remains unclear whether their method can combine multiple such edits, as we can, considering that they change the GAN parameters themselves. (vi) Finally, another line of research targets primarily very high-level image and photo stylization and global appearance modifications [37, 53, 54, 55, 52, 56, 46, 57, 41].
+
+Generally, most works only do relatively high-level and not the detailed, high-precision editing, which EditGAN targets. Hence, we consider EditGAN as complementary to this body of work.
+
+GANs and Latent Space Image Embedding. EditGAN builds on top of DatasetGAN [1] and SemanticGAN [2], which proposed to jointly model images and their semantic segmentations using shared latent codes. However, these works leveraged this model design only for semi-supervised learning, not for editing. EditGAN also relies on an encoder, together with optimization, to embed new images to be edited into the GAN’s latent space. This task in itself has been studied extensively in different contexts before, and we are building on these works. Previous papers studied encoder-based methods [58, 59, 60, 61, 62], used primarily optimization-based techniques [63, 64, 65, 66, 67, 68, 69, 26], and developed hybrid approaches [63, 24, 25, 70, 71].
+
+Finally, a concurrent paper [72] shares similarities with DatasetGAN [1], on which our method builds, and explores an editing approach related to our EditGAN as one of its applications. However, our editing approach is methodologically different and leverages editing vectors, and also demonstrates significantly more diverse and stronger experimental results. Furthermore, [73] shares some highlevel ideas with EditGAN; however, it leverages the CLIP [74] model and targets text-driven editing.
+
+# 3 High-Precision Semantic Image Editing with EditGAN
+
+# 3.1 Background
+
+EditGAN’s image generation component is StyleGAN2 [7, 8], currently the state-of-the-art GAN for image synthesis. The StyleGAN2 generator maps latent codes $\mathbf { z } \in { \mathcal { Z } }$ , drawn from a multivariate Normal distribution, into realistic images. A latent code $\mathbf { z }$ is first transformed into an intermediate code $\mathbf { w } \in \mathcal { W }$ by a non-linear mapping function and then further transformed into $K + 1$ vectors, $\mathbf { w } ^ { 0 } , . . . , \mathbf { w } ^ { K }$ , through learned affine transformations. These transformed latent codes are fed into synthesis blocks, whose outputs are deep feature maps.
+
+Deep generative models such as StyleGAN2, which are trained to synthesize highly realistic images, acquire a semantic understanding of the modeled images in their high-dimensional feature space. Recently, DatasetGAN [1] and SemanticGAN [2] built on this insight to learn a joint distribution $p ( \mathbf { x } , \mathbf { y } )$ over images $\mathbf { x }$ and pixel-wise semantic segmentation labels y, while requiring only a handful of labeled examples. EditGAN utilizes this joint distribution $p ( \mathbf { x } , \mathbf { y } )$ to perform high-precision semantic image editing of real and synthesized images.
+
+Both methods [1, 2] model $p ( \mathbf { x } , \mathbf { y } )$ by adding an additional segmentation branch to the image generator, which is a pre-trained StyleGAN [1]. We follow DatasetGAN [1], which applies a simple three-layer multi-layer perceptron classifier on the layer-wise concatenated and appropriately upsampled feature maps. This classifier operates on the concatenated feature maps in a per-pixel fashion and predicts the segmentation label of each pixel.
+
+# 3.2 Segmentation Training and Inference by Embedding Images into GAN’s Latent Space
+
+To both train the segmentation branch and perform segmentation on a new image, we embed an image into the GAN’s latent space using an encoder and optimization. To this end, we build on previous works [66, 62, 2] and train an encoder that embeds images into $\mathcal { W } ^ { + }$ space, which is defined as $\mathcal { W }$ but where the w’s are modeled independently [66, 62]. Our objectives to train this encoder consist of standard pixel-wise L2 and perceptual LPIPS reconstruction losses using both the real training data as well as samples from the GAN itself. For the GAN samples, we also explicitly regularize the encoder with the known underlying latent codes. In practice, we use the encoder to initialize images’ latent space embeddings and then iteratively refine the latent code $\mathbf { w } ^ { + }$ via optimization, again using standard reconstruction objectives.
+
+In that way, we embed the annotated images $\mathbf { x }$ from a dataset labeled with semantic segmentations into latent space, and train the segmentation branch of the generator using standard supervised learning objectives, i.e., the cross entropy loss. We keep the image generator’s weights frozen and only backpropagate the loss to the segmentation branch [1]. After training the segmentation branch, we can formally define a generator $\bar { \tilde { G } } : \mathcal { W } ^ { + }  \mathcal { X } , \mathcal { Y }$ that models the joint distribution $p ( \mathbf { x } , \mathbf { y } )$ of images $\mathbf { x }$ and semantic segmentations y. Details about encoder and segmentation branch training as well as optimization for image embedding can be found in the Appendix.
+
+# 3.3 Finding Semantics in Latent Space via Segmentation Editing
+
+The key idea of EditGAN lies in leveraging the joint distribution $p ( \mathbf { x } , \mathbf { y } )$ of images and semantic segmentations for high-precision image editing. Given a new image $\mathbf { x }$ to be edited, we can embed it into EditGAN’s $\mathcal { W } ^ { + }$ latent space, as described above (alternatively, we can also sample images from the model itself and use those). The segmentation branch will then generate the corresponding segmentation $\mathbf { y }$ , since segmentations and RGB im
+
+![](images/fb823d3601a32de596c1cacd81969ca423dc943ff186a4849f28d8fb75c7fe52.jpg)  
+Figure 3: We modify semantic segmentations and optimize the shared latent code for consistency with the new segmentation within the editing region, and with the RGB appearance outside the editing region. Corresponding gradients are backpropagated through the shared generator. The result is a latent space editing vector $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ .
+
+ages share the same latent codes $\mathbf { w } ^ { + }$ . Using simple interactive digital painting or labeling tools, we can now manually modify the segmentation according to a desired edit. We denote the edited segmentation mask by $\mathbf { y } _ { \mathrm { e d i t e d } }$ . Starting from the embedding $\mathbf { w } ^ { + }$ of the unedited image x and segmentation $\mathbf { y }$ , we can then perform optimization within $\mathcal { W } ^ { + }$ to find a new $\mathbf { w } _ { \mathrm { e d i t e d } } ^ { + } = \mathbf { w } ^ { + } + \delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ consistent with the new segmentation $\mathbf { y } _ { \mathrm { e d i t e d } }$ , while allowing the RGB output $\mathbf { x }$ to change within the editing region.
+
+Formally, we are seeking an editing vector $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + } \in \mathcal { W } ^ { + }$ such that $( \mathbf { x } _ { \mathrm { e d i t e d } } , \mathbf { y } _ { \mathrm { e d i t e d } } ) = \tilde { G } ( \mathbf { w } ^ { + } + \delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + } )$ where $\tilde { G }$ denotes the fixed generator that synthesizes both images and segmentations. Defining $( \mathbf { x } ^ { \prime } , \mathbf { y } ^ { \prime } ) = \tilde { G } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } )$ , we perform optimization to approximate $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ by $\delta \mathbf { w } ^ { + }$ . The region of interest $r$ within which we expect the image to change due to the edit is formally given by
+
+$$
+r = \left\{ p : c _ { p } ^ { \mathbf { y } } \in Q _ { \mathrm { e d i t } } \right\} \cup \left\{ p : c _ { p } ^ { \mathbf { y } _ { \mathrm { e d i t e d } } } \in Q _ { \mathrm { e d i t } } \right\}
+$$
+
+which means that $r$ is defined by all pixels $p$ whose part segmentation labels $c _ { p } ^ { \{ \mathbf { y } , \mathbf { y } _ { \mathrm { e d i t e d } } \} }$ according to either the initial segmentation $\mathbf { y }$ or the edited one $\mathbf { y } _ { \mathrm { e d i t e d } }$ are within an edit-specific pre-specified list
+
+$Q _ { \mathrm { e d i t } }$ of part labels relevant for the edit. For example, when modifying the wheel in a photo of a car $Q _ { \mathrm { e d i t } }$ would contain all part labels related to the wheels, such as tire, spoke, and wheelhub (see Fig. 3). We use a further buffer of 5 pixels to give the GAN freedom in modeling the transition between the edited and non-edited area. In practice, $r$ acts as a binary pixel-wise mask (see Eqs. 2 and 3 below).
+
+Note that $\mathbf { x } _ { \mathrm { e d i t e d } }$ is not available during optimization. After all, $\mathbf { x } _ { \mathrm { e d i t e d } }$ is the edited image we are ultimately intested in. It emerges indirectly when optimizing for the segmentation modification, since images and segmentations are closely tied together in the joint distribution $p ( \mathbf { x } , \mathbf { y } )$ modeled by $\tilde { G }$ We further define $\mathbf { x } ^ { \prime } = \tilde { G } ^ { \mathbf { x } } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } )$ as $\tilde { G }$ ’s image generation and $\mathbf { y } ^ { \prime } = \tilde { G } ^ { \mathbf { y } } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } )$ as $\tilde { G }$ ’s segmentation generation branch.
+
+To find $\delta \mathbf { w } ^ { + }$ , approximating $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ , we use the following losses as minimization targets:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathrm { R G B } } ( \delta \mathbf { w } ^ { + } ) = L _ { \mathrm { L P I P S } } ( \tilde { G } ^ { \mathbf { x } } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } ) \odot ( 1 - r ) , \ \mathbf { x } \odot ( 1 - r ) ) } \\ & { \qquad + L _ { L 2 } ( \tilde { G } ^ { \mathbf { x } } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } ) \odot ( 1 - r ) , \ \mathbf { x } \odot ( 1 - r ) ) } \end{array}
+$$
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { C E } } \big ( \delta \mathbf { w } ^ { + } \big ) = H \big ( \tilde { G } ^ { \mathbf { y } } \big ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } \big ) \odot r , \ \mathbf { y } _ { \mathrm { e d i t e d } } \odot r \big ) } \end{array}
+$$
+
+where $H$ denotes the pixel-wise cross-entropy, $L _ { \mathrm { L P I P S } }$ loss is based on the Learned Perceptual Image Patch Similarity (LPIPS) distance [75], and $L _ { L 2 }$ is a regular pixel-wise L2 loss. $\mathcal { L } _ { \mathrm { R G B } } ( \delta \mathbf { \bar { w } } ^ { + } )$ ensures that the image appearance does not change outside the region of interest, while $\mathcal { L } _ { \mathrm { C E } } ( \delta \mathbf { w } ^ { + } )$ ensures that the target segmentation $\mathbf { y } _ { \mathrm { e d i t e d } }$ is enforced within the editing region (see visualization in Fig. 3). When editing human faces, we also apply the identity loss [62]:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { I D } } ( \delta \mathbf { w } ^ { + } ) = \langle R ( \tilde { G } ^ { \mathbf { x } } ( \mathbf { w } ^ { + } + \delta \mathbf { w } ^ { + } ) ) , R ( \mathbf { x } ) \rangle } \end{array}
+$$
+
+with $R$ denoting the pretrained ArcFace feature extraction network [76] and $\langle \cdot , \cdot \rangle$ cosine-similiarity. The final objective function for optimization then becomes:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { e d i t i n g } } ( \delta \mathbf { w } ^ { + } ) = \lambda _ { 1 } ^ { \mathrm { e d i t i n g } } \mathcal { L } _ { \mathrm { R G B } } ( \delta \mathbf { w } ^ { + } ) + \lambda _ { 2 } ^ { \mathrm { e d t i n g } } \mathcal { L } _ { \mathrm { C E } } ( \delta \mathbf { w } ^ { + } ) + \lambda _ { 3 } ^ { \mathrm { e d t i n g } } \mathcal { L } _ { \mathrm { I D } } ( \delta \mathbf { w } ^ { + } ) } \end{array}
+$$
+
+with hyperparameters $\lambda _ { 1 , \dots , 3 } ^ { \mathrm { e d i t i n g } }$ . The only “learnable” variable is the editing vector $\delta \mathbf { w } ^ { + }$ ; all neural networks are kept fixed. After optimizing $\delta \mathbf { w } ^ { + }$ with the objective function, we can use $\delta \mathbf { w } ^ { + } \approx \delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ Note that there is a certain amount of ambiguity in how the segmentation modification is realized in RGB output. We rely on the GAN generator, trained to synthesize realistic images, to modify the RGB values in the editing region in a plausible way consistent with the segmentation edit.
+
+# 3.4 Different Ways of Editing during Inference
+
+The latent space editing vectors $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ obtained by optimization as described are semantically meaningful and often disentangled with other attributes. Therefore, for new images $\mathbf { x }$ to be edited, we can embed the images into the $\mathcal { W } ^ { + }$ latent space and the same editing operations can be directly performed by applying the previously learnt $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ as $( \mathbf { x } ^ { \prime } , \mathbf { y } ^ { \prime } ) = G ( \mathbf { w } ^ { + } + s _ { \mathrm { e d i t } } \delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + } )$ without doing any optimization from scratch again. In other words, the learnt editing vectors $\bar { \delta } \bar { \mathbf { w } } ^ { + }$ amortize the iterative optimization that was necessary to achieve the edit initially. For well-disentangled editing operations, $\mathbf { x } ^ { \prime }$ can be used directly as the edited image $\mathbf { x } _ { \mathrm { e d i t e d } }$ . Note that we introduced $s _ { \mathrm { e d i t } }$ , a scalar editing coefficient, which effectively scales and controls the editing magnitude during inference. For $s _ { \mathrm { e d i t } } = 0$ , we do not do any editing at all, while for $s _ { \mathrm { e d i t } } > 1$ we manipulate the images with an effectively larger editing operation in latent space, leading to exaggerated effects.
+
+Unfortunately, disentanglement is not always perfect and the editing vectors $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ do not always translate perfectly to other images. We can remove editing artifacts in other regions of the image by a few additional optimization steps at test time. Specifically, we can use the exact same minimization obas s as above, using the initial prediction . This assumes that the editing vector $\mathbf { y } ^ { \prime }$ , obtained after applying the editing vector ll induces a plausible segmentation chang $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ $\mathbf { y } _ { \mathrm { e d i t e d } }$   
+applied on other images and that artifacts only arise in RGB output. The RGB objective $\mathcal { L } _ { \mathrm { { R G B } } }$ then removes these editing artifacts outside the editing region, while $\mathcal { L } _ { \mathrm { C E } }$ ensures that the modified segmentation stays as predicted by the editing vector.
+
+Summarizing, we can perform image editing with EditGAN in three different modes:
+
+• Real-time Editing with Editing Vectors. For localized, well-disentangled edits we perform editing purely by applying previously learnt editing vectors with varying scales $s _ { \mathrm { e d i t } }$ and manipulate images at interactive rates.
+
+![](images/742a614d56b78b2c1585a7e070b2c2ba2262df73e8b0ab63e51925ccf624d04e.jpg)  
+Figure 4: Examples of segmentation-driven edits with EditGAN. Results are based on editing with editing vectors and 30 steps self-supervised refinement. Blue boxes: Original images. Orange boxes: Zoom-in views.
+
+• Vector-based Editing with Self-Supervised Refinement. For localized edits that are not perfectly disentangled with other parts of the image, we can remove editing artifacts by additional optimization at test time, while initializing the edit using the learnt editing vectors. • Optimization-based Editing. Image-specific and very large edits do not transfer to other images via editing vectors. For such operations, we perform optimization from scratch.
+
+# 4 Experiments
+
+We extensively evaluate EditGAN on images across four different categories: Cars ( $3 8 4 \times 5 1 2$ spatial resolution), Birds $( 5 1 2 \times 5 1 2 )$ , Cats $( 2 5 6 \times 2 5 6 )$ , and Faces $( 1 0 2 4 \times 1 0 2 4 )$ .
+
+Implementation We train our segmentation branch as described in Sec. 3.2 using 16, 16, 30, and 30 image-mask pairs as labeled training data for Faces, Cars, Birds, and Cats, respectively. We utilize very highly-detailed part segmentations from [1]. The annotation scheme for faces is shown in Fig. 7, all others are presented in the Appendix. When editing is done purely optimization-based or when learning the editing vectors, we always perform 100 steps of optimization using Adam [77]. For Car, Cat, and Faces, we use real images from DatasetGAN’s test set that were not part of GAN training to demonstrate editing functionality. These images are first embedded into EditGAN’s latent space via an encoder and optimization as described in Sec. 3.2. For Birds, we show editing on GAN-generated images. Model details and hyperparameters are provided in the Appendix.
+
+# 4.1 Qualitative Results
+
+In-Domain Results In Fig. 4, we demonstrate our EditGAN framework when applying previously learnt editing vectors $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ on novel images and refining with 30 steps of optimization. Our editing operations preserve high image quality and are well disentangled for all classes. We also show the ability to combine multiple different edits in Fig. 5. To the best of our knowledge, no previous methods can perform as complex and high-precision edits as we do, while preserving image quality and subject identity. In Fig. 8, we demonstrate that we can even perform extremely high-precision edits, such as rotating a car’s wheel spoke or dilating pupils. EditGAN can edit semantic parts of objects that consist of only few pixels. At the same time, we can use EditGAN to perform large-scale modifications, too: In Fig. 9, we present how we can remove the entire roof of a car or convert it to a station wagon-like vehicle, simply by modifying the segmentation mask accordingly and optimizing. It is worth noting that several of our editing operations generate plausible manipulated images unlike those appearing in the GAN training data. For example, the training data does not include cats with overly large eyes or ears. Nevertheless, we achieve such edits in a high-quality manner.
+
+![](images/af4bf814241ab3da1430ddc5310405757b5f5cc1f2f6882f1581f9a97675afad.jpg)  
+Figure 5: We combine multiple edits. Results are based on editing with editing vectors and 30 steps selfsupervised refinement. Blue boxes: Original images. Edits in detail: Second row, first person: open eyes, add hair, add mustache. Second person: smile, look left. Third row, first car: remove mirror, remove door handle, shrink wheels. Second car: remove license plate, enlarge wheels. Third row, bird: longer beak, bigger belly, head up. Third row, cat: open mouth, bigger ear, bigger eyes.
+
+The edits in Figs. 4, 5 and 8 are based on learnt editing vectors with self-supervised refinement. However, without such refinement usually only very minor artifacts occur, as shown in Fig. 10, hence allowing for real-time high-precision semantic image editing (discussed in detail below).
+
+Out-of-Domain Results We demonstrate the generalization capability of EditGAN to out-ofdomain data on the MetFaces [8] data set. We use our EditGAN model trained on FFHQ [8], and create editing vectors $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ using in-domain real faces. We then embed out-of-domain MetFaces partraits (with 100 steps optimization) and apply the editing vectors with 30 steps self-supervised refinement. The results are shown in Fig. 6. We find that our editing operations seamlessly translate even to such far out-of-domain examples.
+
+# 4.2 Quantitative Results
+
+To quantitatively measure EditGAN’s image editing capabilities, we use the smile edit benchmark introduced by MaskGAN [10]. Faces with neutral expressions are converted into smiling faces and performance is measured by three metrics: a. Semantic Correctness: Using a pre-trained smile attribute classifier, we measure whether the faces show smiling expressions after editing. b. Distribution-level Image Quality: Frechet Inception Distance (FID) [78, 79] and Kernel Inception Distance (KID) [80] are calculated between 400 edited test images and the CelebA-HD test dataset. c.
+
+![](images/a61605ec5f7b2608b329439b051ff89b4dd3b4fd77ff0d41e5416083b44f10ec.jpg)  
+Figure 6: We combine multiple edits on out-of-domain images. Results are based on editing with editing vectors and 30 steps self-supervised refinement. Edits in detail: First row, first example: look left, frown. Second example: smile, look right. Second row, first example: open eyes, lift eyebrow. Second example: open eyes.
+
+Identity Preservation: Using the pretrained ArcFace feature extraction network [76], we measure whether the subjects’ identity is maintained when applying the edit. Specifically, we report cosinesimiliarity between original and edited images. Further details can be found in the Appendix.
+
+For our EditGAN, we simply learn a smiling editing vector $\delta \mathbf { w } _ { \mathrm { e d i t } } ^ { + }$ using a hold-out neutral expression face image. We embed it into EditGAN, infer its pixel-wise segmentation labels, and manually modify the segmentation towards a smile. Then we perform optimization in latent space, as described above, to learn the editing vector. For the results in Tab. 1, it is applied with unit scale $s _ { \mathrm { e d i t } } { = } 1$ on new images. We do
+
+<table><tr><td>Metric</td><td>Annot.</td><td>#Mask #Attribute Annot.</td><td>Attribute Acc.(%)↑</td><td>FID↓</td><td>KID↓</td><td>ID Score ↑</td></tr><tr><td>MaskGAN [10]</td><td>30.000</td><td></td><td>77.3</td><td></td><td>46.84 0.020</td><td>0.4611</td></tr><tr><td>LocalEditing [18]</td><td>-</td><td></td><td>26.0</td><td>41.26</td><td>0.012</td><td>0.5823</td></tr><tr><td>LocalEditing - Encoding4Editing [81]</td><td>-</td><td>-</td><td>41.75</td><td>48.28</td><td>0.016</td><td>0.6603</td></tr><tr><td>InterFaceGAN [13]</td><td>-</td><td>30.000</td><td>83.5</td><td>39.42</td><td>0.010</td><td>0.7295</td></tr><tr><td>EditGAN (ours)</td><td>16</td><td>-</td><td>91.5</td><td>41.74</td><td>0.013</td><td>0.7047</td></tr><tr><td>EditGAN+30 (ours)</td><td>16</td><td>-</td><td>85.8</td><td>40.83</td><td>0.012</td><td>0.7452</td></tr><tr><td>StyleGAN2 Distillation [82]</td><td>-</td><td>30.000</td><td>98.3</td><td>45.09 0.013</td><td></td><td>0.7823</td></tr></table>
+
+Table 1: Quantitative comparisons to multiple baselines on the smile edit benchmark.
+
+not use the identity loss (Eq. 4) in this experiment, since identity preservation is already a target metric itself. We compare our method with three strong baselines: (i) $M a s k G A N ^ { 2 }$ [10]: It takes non-smiling images, their segmentation masks, and a target smiling segmentation mask as inputs. Note that training MaskGAN requires large annotated datasets, in contrast to us. We also compare to (ii) LocalEditing3 [18]: It clusters GAN features to achieve local editing and relies on reference images, in this case images of faces with smiling expressions. Another baseline we use is (iii) InterFace $G A N ^ { 4 }$ [13]: Similar to EditGAN, InterFaceGAN aims at finding editing vectors in latent space. However, it uses auxiliary attribute classifiers, relies on large annotated datasets, and can generally not achieve the fine editing control of our EditGAN. Finally, we compare to (iv) StyleGAN2 Distillation5 [82], which creates an alternative approach that does not require real image embeddings and also relies on an editing-vector model to create a training dataset.
+
+Results are reported in Tab. 1. Using 1, $8 7 5 \times$ less training labels, we outperform MaskGAN on all three metrics. We similarly obtain significantly stronger results than LocalEditing. In our observation, LocalEditing does not work well on real image embeddings. We further exploit a better encoder [81] for the LocalEditing baseline, which leads to a significant improvement in attribute accuracy and ID score, but slightly worse FID & KID scores. We find that EditGAN outperforms InterFaceGAN on identity preservation and attribute classification accuracy, while InterFaceGAN reaches slightly better FID & KID scores (for the results in Tab. 1, the latent space edits learnt by InterfaceGAN are also applied with unit scale, like for EditGAN). In Fig. 11, we report a more detailed comparison to InterFaceGAN, where we apply the smile editing vectors with different scale coefficients from zero to two. As shown, when the editing vector scale is small, the identity score is high while the smiling attribute score is low, since the modification of the original images is minimal. We find that our realtime editing with editing vectors is on-par with InterFaceGAN. When we perform self-supervised refinement at test time, EditGAN outperforms InterFaceGAN. In Tab. 1, we also compare with StyleGAN2 Distillation [82], which achieves strong performance. However, StyleGAN2 Distillation relies on pre-trained classifiers, like InterfaceGAN, and only enables relatively high-level editing of image attributes for which large-scale annotations exit. Moreover, it distills edits into separate Pixel2PixelHD networks, such that a new network needs to be trained for each edit, limiting broad, user-interactive applicability. Hence, we consider StyleGAN2 Distillation orthogonal to our EditGAN.
+
+![](images/82aed2cce7459a336ae87233a9042f1ee642601d6b485bb205aecab5ad27d17e.jpg)  
+Figure 7: Face part labeling schema [1].
+
+![](images/ec5e57176ee9dd96a0c35e7e44b1e68c3c05f10a2598c6a27b653ace1bbfbc45.jpg)  
+Figure 8: High-precision editing with EditGAN for extreme details. Left: We rotate Rotate Wheel Spoke Change pupil Sizethe spoke. Right: We modify pupil size. Results are based on editing with editing vectors and 30 steps self-supervised refinement.
+
+![](images/40b140c5ee1e246522137b6ac9a2945eff98f726b22711f6d4416174a8e77e7b.jpg)  
+Figure 9: Pure optimization-based editing. We demonstrate large-scale semantic edits that do not transfer seamlessly to other images via editing vectors. Hence, we perform optimization from scratch.
+
+![](images/a1abbd5adb6d1505d2819a994d24a10e48d6a51e57149c772524e86d426ec6f8.jpg)  
+Figure 10: Left: We apply learnt editing vectors with varying scales (see 5 markers in FID plots) both without (top row for each class) and with (bottom row for each class) additional 30-step self-supervised refinement to correct artifacts. Red boxes denote original images. For each class, the leftmost image is the one used to learn the editing vector, with the editing result next to it and orginal and modified segmentations below. Right: Visual quality after editing with different scales as measured by FID with and without refinement.
+
+Running Time We carefully measure the run time of our editing on an NVIDIA Tesla V100 GPU. Conditional optimization, given an edited segmentation mask, with 30 (60) optimization steps takes 11.4 (18.9) seconds. This operation provides us the editing vector. Application of editing vectors is almost instantaneous, taking only 0.4 seconds, therefore allowing for complex real-time interactive editing. A 10 (30) step self-supervised refinement would add an additional 4.2 (9.5) seconds.
+
+# 4.3 Ablation Studies: Self-Supervised Refinement and Editing Vector Scale
+
+Fig. 11 also contains a quantitative ablation study on the number of additional optimization steps done when initializing an edit with a learnt editing vector and refining with additional optimization. Generally, the more refinement steps we perform, the better the performance our model can achieve. As shown in Fig. 11, we find that further optimization can indeed slightly improve performance. Specifically, here we improve the trade-off between maintaining identity and achieving the desired semantic operation when performing editing with different scalings $s _ { \mathrm { e d i t } }$ of the editing vector. However, performing many steps of optimization leads to a run-time vs. performance trade-off, and our results suggest that the improvement beyond 30 additional optimization steps becomes marginal.
+
+In Fig. 10, we analyze the editing vector scale and self-supervised refinement visually and with respect to perceptual metrics. As highlighted in the zoom-in areas, small artifacts can appear due to imperfect disentanglement in latent space when applying editing operations with large scales. Self-supervised refinement successfully cleans these editing errors up. We also apply the same edit with different scales on 400 test images and measure FID with respect to 10,000 data from GAN training, inspired by the analyses in [16]. We can clearly see that image quality degrades as measured by FID, the stronger the edit is applied. We also observe small improvements with the iterative refinement on this metric, although the difference is small. Further details are in the Appendix. We conclude that for most editing operations, real-time editing without iterative refinement already performs very well. However, to clean up artifacts and maintain highest image quality possible, self-supervised refinement with a couple of additional optimization steps is always available.
+
+Additional experiments are presented in the Appendix.
+
+# 5 Conclusions
+
+Limitations Like all GAN-based image editing methods, EditGAN is limited to images that can be modeled by the GAN. This makes EditGAN’s application on, for instance, photos of vivid city scenes challenging. Although most of our high-precision edits readily transfer to other images via learnt editing vectors, we also encountered challenging edits that required iterative optimization on each example. Future research therefore includes speeding up the optimization for such edits as well as building better generative models with more disentangled latent spaces.
+
+![](images/690211948c1cfdaeb4947e26111732183937f423e3528f4344ff12d15a1cbf6a.jpg)  
+Figure 11: InterFaceGAN’s and EditGAN’s performance on the smile edit benchmark for different editing vector scalings (scale increases from top-left points towards bottomright points; see main text and Appendix for details). For EditGAN, we optionally add 10, 30 or 60 additional optimization steps.
+
+Summary We propose EditGAN, a novel method for high-precision, high-quality semantic image editing. It relies on a GAN that jointly models RGB images and their pixel-wise semantic segmentations and that requires only very few annotated data for training. Editing is achieved by performing optimization in latent space while conditioning on edited segmentation masks. This optimization can be amortized into editing vectors in latent space, which can be applied on other images directly, allowing for real-time interactive editing without any or only little further optimization. We demonstrate a broad variety of editing operations on different kinds of images, achieving an unprecedented level of flexibility and freedom in terms of editing, while preserving high image quality.
+
+# 6 Broader Impact
+
+Where previous generative modeling-based image editing methods offer only limited high-level editing capabilities, our method provides users unprecedented high-precision semantic editing possibilities. Our proposed techniques can be used for artistic purposes and creative expression and benefit designers, photographers, and content creators [3]. AI-driven image editing tools like ours promise to democratize high-quality image editing. Related methods have already found their way into everyday applications in the form of neural photo editing filters. On a larger scale, the ability to synthesize data with specific attributes can be leveraged in training and finetuning machine learning models.
+
+At the same time, more precise photo editing also offers opportunities for advanced photo manipulation for nefarious purposes. The recent progress of generative models and AI-driven photo editing has profound implications on image authenticity and beyond, which is an area of active debate [83]. As one potential way to tackle these challenges, methods for automatically validating real images and detecting manipulated or fake images are being developed by the research community [84, 85]. Furthermore, generative models like ours are usually only as good as the data they were trained on. Therefore, biases in the underlying datasets are still present in the synthesized images and preserved even when applying our proposed editing methods. It is therefore important to be aware of such biases in the underlying data and counteract them, for example by actively collecting more representative data or by using bias correction methods, an area of active research [86, 87, 88, 89].
+
+# Funding Statement
+
+This work was funded by NVIDIA. Huan Ling and Seung Wook Kim acknowledge additional revenue in the form of student scholarships from University of Toronto and the Vector Institute, which are not in direct support of this work.
+
+# References
+
+[1] Yuxuan Zhang, Huan Ling, Jun Gao, Kangxue Yin, Jean-Francois Lafleche, Adela Barriuso, Antonio Torralba, and Sanja Fidler. Datasetgan: Efficient labeled data factory with minimal human effort. arXiv preprint arXiv:2104.06490, 2021.   
+[2] Daiqing Li, Junlin Yang, Karsten Kreis, Antonio Torralba, and Sanja Fidler. Semantic segmentation with generative models: Semi-supervised learning and strong out-of-domain generalization. arXiv preprint arXiv:2104.05833, 2021.   
+[3] J. Bailey. The tools of generative art, from flash to neural networks. Art in America, 2020.   
+[4] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pages 2672–2680, 2014.   
+[5] Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015.   
+[6] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196, 2017.   
+[7] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4401–4410, 2019.   
+[8] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8110–8119, 2020.   
+[9] Yunjey Choi, Minje Choi, Munyoung Kim, Jung-Woo Ha, Sunghun Kim, and Jaegul Choo. Stargan: Unified generative adversarial networks for multi-domain image-to-image translation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018.   
+[10] Cheng-Han Lee, Ziwei Liu, Lingyun Wu, and Ping Luo. Maskgan: Towards diverse and interactive facial image manipulation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   
+[11] Rongliang Wu, Gongjie Zhang, Shijian Lu, and Tao Chen. Cascade ef-gan: Progressive facial expression editing with local focuses. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   
+[12] Yujun Shen, Jinjin Gu, Xiaoou Tang, and Bolei Zhou. Interpreting the latent space of gans for semantic face editing. In CVPR, 2020.   
+[13] Yujun Shen, Ceyuan Yang, Xiaoou Tang, and Bolei Zhou. Interfacegan: Interpreting the disentangled face representation learned by gans. TPAMI, 2020.   
+[14] Yazeed Alharbi and Peter Wonka. Disentangled image generation through structured noise injection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   
+[15] Xianxu Hou, Xiaokang Zhang, Linlin Shen, Zhihui Lai, and Jun Wan. Guidedstyle: Attribute knowledge guided style manipulation for semantic face editing. arXiv preprint arXiv:2012.11856, 2020.   
+[16] Anton Cherepkov, Andrey Voynov, and Artem Babenko. Navigating the gan parameter space for semantic image editing. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021.   
+[17] Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yinan Zhang, Antonio Torralba, and Sanja Fidler. Image gans meet differentiable rendering for inverse graphics and interpretable 3d neural rendering. arXiv preprint arXiv:2010.09125, 2020.   
+[18] Edo Collins, Raja Bala, Bob Price, and Sabine Süsstrunk. Editing in style: Uncovering the local semantics of GANs. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   
+[19] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. Sean: Image synthesis with semantic regionadaptive normalization. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   
+[20] Kathleen M Lewis, Srivatsan Varadharajan, and Ira Kemelmacher-Shlizerman. Vogue: Try-on by stylegan interpolation optimization. arXiv preprint arXiv:2101.02285, 2021.   
+[21] Hyunsu Kim, Yunjey Choi, Junho Kim, Sungjoo Yoo, and Youngjung Uh. Exploiting spatial dimensions of latent in gan for real-time image editing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   
+[22] Shu-Yu Chen, Wanchao Su, Lin Gao, Shihong Xia, and Hongbo Fu. Deepfacedrawing: Deep generation of face images from sketches. ACM Trans. Graph., 39(4), 2020.   
+[23] Z. He, W. Zuo, M. Kan, S. Shan, and X. Chen. Attgan: Facial attribute editing by only changing what you want. IEEE Transactions on Image Processing, 28(11):5464–5478, Nov 2019.   
+[24] David Bau, Jun-Yan Zhu, Hendrik Strobelt, Bolei Zhou, Joshua B. Tenenbaum, William T. Freeman, and Antonio Torralba. Gan dissection: Visualizing and understanding generative adversarial networks. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   
+[25] David Bau, Hendrik Strobelt, William Peebles, Jonas Wulff, Bolei Zhou, Jun-Yan Zhu, and Antonio Torralba. Semantic photo manipulation with a generative image prior. ACM Trans. Graph., 38(4), 2019.   
+[26] Antoine Plumerault, Hervé Le Borgne, and Céline Hudelot. Controlling generative models with continuous factors of variations. In International Conference on Learning Representations, 2020.   
+[27] Erik Härkönen, Aaron Hertzmann, Jaakko Lehtinen, and Sylvain Paris. Ganspace: Discovering interpretable gan controls. In Proc. NeurIPS, 2020.   
+[28] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. Rewriting a deep generative model. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   
+[29] George Wolberg. Digital Image Warping. IEEE Computer Society Press, Washington, DC, USA, 1st edition, 1994.   
+[30] Alexei A. Efros and William T. Freeman. Image quilting for texture synthesis and transfer. SIGGRAPH ’01, page 341–346, New York, NY, USA, 2001. Association for Computing Machinery.   
+[31] Aaron Hertzmann, Charles E. Jacobs, Nuria Oliver, Brian Curless, and David H. Salesin. Image analogies. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’01, page 327–340, New York, NY, USA, 2001. Association for Computing Machinery.   
+[32] E. Reinhard, M. Adhikhmin, B. Gooch, and P. Shirley. Color transfer between images. IEEE Computer Graphics and Applications, 21(5):34–41, 2001.   
+[33] Patrick Pérez, Michel Gangnet, and Andrew Blake. Poisson image editing. SIGGRAPH ’03, page 313–318, New York, NY, USA, 2003. Association for Computing Machinery.   
+[34] Scott Schaefer, Travis McPhail, and Joe Warren. Image deformation using moving least squares. ACM Trans. Graph., 25(3):533–540, 2006.   
+[35] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. Graph., 28(3), 2009.   
+[36] Michael W. Tao, Micah K. Johnson, and Sylvain Paris. Error-tolerant image compositing. In ECCV, 2010.   
+[37] Leon A. Gatys, Alexander S. Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.   
+[38] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223–2232, 2017.   
+[39] Tiziano Portenier, Qiyang Hu, Attila Szabó, Siavash Arjomand Bigdeli, Paolo Favaro, and Matthias Zwicker. Faceshop: Deep sketch-based face image editing. ACM Trans. Graph., 37(4), 2018.   
+[40] Huan Ling, David Acuna, Karsten Kreis, Seung Wook Kim, and Sanja Fidler. Variational amodal object completion. Advances in Neural Information Processing Systems, 2020.   
+[41] Taesung Park, Jun-Yan Zhu, Oliver Wang, Jingwan Lu, Eli Shechtman, Alexei A. Efros, and Richard Zhang. Swapping autoencoder for deep image manipulation. In Advances in Neural Information Processing Systems, 2020.   
+[42] Seung Wook Kim, Jonah Philion, Antonio Torralba, and Sanja Fidler. DriveGAN: Towards a Controllable High-Quality Neural Simulation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021.   
+[43] Diederik P Kingma and Max Welling. Auto-encoding variational bayes. In The International Conference on Learning Representations (ICLR), 2014.   
+[44] Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic backpropagation and approximate inference in deep generative models. In International Conference on Machine Learning, pages 1278–1286, 2014.   
+[45] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2019.   
+[46] Taesung Park, Ming-Yu Liu, Ting-Chun Wang, and Jun-Yan Zhu. Semantic image synthesis with spatiallyadaptive normalization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2337–2346, 2019.   
+[47] Lore Goetschalckx, Alex Andonian, Aude Oliva, and Phillip Isola. Ganalyze: Toward visual definitions of cognitive image properties. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), October 2019.   
+[48] Ali Jahanian\*, Lucy Chai\*, and Phillip Isola. On the "steerability" of generative adversarial networks. In International Conference on Learning Representations, 2020.   
+[49] Andrey Voynov and Artem Babenko. Unsupervised discovery of interpretable directions in the gan latent space. In International Conference on Machine Learning, pages 9786–9796. PMLR, 2020.   
+[50] Binxu Wang and Carlos R Ponce. A geometric analysis of deep generative image models and its applications. In International Conference on Learning Representations, 2021.   
+[51] Yujun Shen and Bolei Zhou. Closed-form factorization of latent semantics in gans. In CVPR, 2021.   
+[52] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8798–8807, 2018.   
+[53] Fujun Luan, Sylvain Paris, Eli Shechtman, and Kavita Bala. Deep photo style transfer. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.   
+[54] Ming-Yu Liu, Thomas Breuel, and Jan Kautz. Unsupervised image-to-image translation networks. In Advances in neural information processing systems, pages 700–708, 2017.   
+[55] Yijun Li, Ming-Yu Liu, Xueting Li, Ming-Hsuan Yang, and Jan Kautz. A closed-form solution to photorealistic image stylization. In Proceedings of the European Conference on Computer Vision (ECCV), 2018.   
+[56] H. Kazemi, S. Iranmanesh, and N. Nasrabadi. Style and content disentanglement in generative adversarial networks. In 2019 IEEE Winter Conference on Applications of Computer Vision (WACV), pages 848–856, Los Alamitos, CA, USA, jan 2019. IEEE Computer Society.   
+[57] Jaejun Yoo, Youngjung Uh, Sanghyuk Chun, Byeongkyu Kang, and Jung-Woo Ha. Photorealistic style transfer via wavelet transforms. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), 2019.   
+[58] Guim Perarnau, Joost van de Weijer, Bogdan Raducanu, and Jose M. Álvarez. Invertible conditional gans for image editing. arXiv preprint arXiv:1611.06355, 2016.   
+[59] Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell. Adversarial feature learning. arXiv preprint arXiv:1605.09782, 2016.   
+[60] Andrew Brock, Theodore Lim, James M. Ritchie, and Nick Weston. Neural photo editing with introspective adversarial networks. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.   
+[61] Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Alex Lamb, Martín Arjovsky, Olivier Mastropietro, and Aaron C. Courville. Adversarially learned inference. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.   
+[62] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel CohenOr. Encoding in style: a stylegan encoder for image-to-image translation. arXiv preprint arXiv:2008.00951, 2020.   
+[63] Jun-Yan Zhu, Philipp Krähenbühl, Eli Shechtman, and Alexei A Efros. Generative visual manipulation on the natural image manifold. In European conference on computer vision, pages 597–613. Springer, 2016.   
+[64] R. A. Yeh, C. Chen, T. Y. Lim, A. G. Schwing, M. Hasegawa-Johnson, and M. N. Do. Semantic image inpainting with deep generative models. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 6882–6890, 2017.   
+[65] Zachary C. Lipton and Subarna Tripathi. Precise recovery of latent vectors from generative adversarial networks. arXiv preprint arXiv:1702.04782, 2017.   
+[66] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE International Conference on Computer Vision, pages 4432–4441, 2019.   
+[67] Minyoung Huh, Richard Zhang, Jun-Yan Zhu, Sylvain Paris, and Aaron Hertzmann. Transforming and projecting images into class-conditional generative networks. arXiv preprint arXiv:2005.01703, 2020.   
+[68] A. Creswell and A. A. Bharath. Inverting the generator of a generative adversarial network. IEEE Transactions on Neural Networks and Learning Systems, 30(7):1967–1974, 2019.   
+[69] A. Raj, Y. Li, and Y. Bresler. Gan-based projector for faster recovery with convergence guarantees in linear inverse problems. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 5601–5610, 2019.   
+[70] D. Bau, J. Zhu, J. Wulff, W. Peebles, B. Zhou, H. Strobelt, and A. Torralba. Seeing what a gan cannot generate. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 4501–4510, 2019.   
+[71] Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. In-domain gan inversion for real image editing. arXiv preprint arXiv:2004.00049, 2020.   
+[72] Jianjin Xu and Changxi Zheng. Linear semantics in generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9351–9360, 2021.   
+[73] David Bau, Alex Andonian, Audrey Cui, YeonHwan Park, Ali Jahanian, Aude Oliva, and Antonio Torralba. Paint by word. arXiv preprint arXiv:2103.10951, 2021.   
+[74] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. arXiv preprint arXiv:2103.00020, 2021.   
+[75] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586–595, 2018.   
+[76] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4690–4699, 2019.   
+[77] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.   
+[78] Maximilian Seitzer. pytorch-fid: FID Score for PyTorch. https://github.com/mseitzer/ pytorch-fid, August 2020. Version 0.1.1.   
+[79] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems 30, pages 6626–6637. Curran Associates, Inc., 2017.   
+[80] Mikołaj Binkowski, Danica J. Sutherland, Michael Arbel, and Arthur Gretton. Demystifying MMD GANs.´ In International Conference on Learning Representations, 2018.   
+[81] Omer Tov, Yuval Alaluf, Yotam Nitzan, Or Patashnik, and Daniel Cohen-Or. Designing an encoder for stylegan image manipulation. ACM Transactions on Graphics (TOG), 40(4):1–14, 2021.   
+[82] Yuri Viazovetskyi, Vladimir Ivashkin, and Evgeny Kashin. Stylegan2 distillation for feed-forward image manipulation. In European Conference on Computer Vision, pages 170–186. Springer, 2020.   
+[83] Cristian Vaccari and Andrew Chadwick. Deepfakes and disinformation: Exploring the impact of synthetic political video on deception, uncertainty, and trust in news. Social Media $^ +$ Society, 6(1):2056305120903408, 2020.   
+[84] Thanh Thi Nguyen, Quoc Viet Hung Nguyen, Cuong M. Nguyen, Dung Nguyen, Duc Thanh Nguyen, and Saeid Nahavandi. Deep learning for deepfakes creation and detection: A survey. arXiv preprint arXiv:1909.11573, 2021.   
+[85] Yisroel Mirsky and Wenke Lee. The creation and detection of deepfakes: A survey. ACM Comput. Surv., 54(1), 2021.   
+[86] Aditya Grover, Jiaming Song, Ashish Kapoor, Kenneth Tran, Alekh Agarwal, Eric J Horvitz, and Stefano Ermon. Bias correction of learned generative models using likelihood-free importance weighting. In Advances in Neural Information Processing Systems, 2019.   
+[87] Kristy Choi, Aditya Grover, Trisha Singh, Rui Shu, and Stefano Ermon. Fair generative modeling via weak supervision. In Proceedings of the 37th International Conference on Machine Learning, 2020.   
+[88] Ning Yu, Ke Li, Peng Zhou, Jitendra Malik, Larry Davis, and Mario Fritz. Inclusive GAN: improving data and minority coverage in generative models. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXII, 2020.   
+[89] Jinhee Lee, Haeri Kim, Youngkyu Hong, and Hye Won Chung. Self-diagnosing gan: Diagnosing underrepresented samples in generative adversarial networks. arXiv preprint arXiv:2102.12033, 2021.

parse/train/jLHWRxwc7_f/jLHWRxwc7_f_content_list.json

@@ -0,0 +1,1165 @@
+[
+    {
+        "type": "text",
+        "text": "EditGAN: High-Precision Semantic Image Editing ",
+        "text_level": 1,
+        "bbox": [
+            192,
+            122,
+            807,
+            148
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Huan Ling1,2,3,∗ Karsten Kreis1,∗ Daiqing Li 1 ",
+        "bbox": [
+            295,
+            199,
+            714,
+            215
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Seung Wook Kim1,2,3 Antonio Torralba4 Sanja Fidler1,2,3 ",
+        "bbox": [
+            276,
+            234,
+            779,
+            252
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1NVIDIA 2University of Toronto 3Vector Institute 4MIT ",
+        "bbox": [
+            312,
+            263,
+            691,
+            279
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{huling,kkreis,daiqingl,seungwookk,sfidler}@nvidia.com, torralba@mit.edu ",
+        "bbox": [
+            266,
+            285,
+            756,
+            296
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            332,
+            535,
+            348
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generative adversarial networks (GANs) have recently found applications in image editing. However, most GAN-based image editing methods often require large-scale datasets with semantic segmentation annotations for training, only provide high level control, or merely interpolate between different images. Here, we propose EditGAN, a novel method for high-quality, high-precision semantic image editing, allowing users to edit images by modifying their highly detailed part segmentation masks, e.g., drawing a new mask for the headlight of a car. EditGAN builds on a GAN framework that jointly models images and their semantic segmentations [1, 2], requiring only a handful of labeled examples – making it a scalable tool for editing. Specifically, we embed an image into the GAN’s latent space and perform conditional latent code optimization according to the segmentation edit, which effectively also modifies the image. To amortize optimization, we find “editing vectors” in latent space that realize the edits. The framework allows us to learn an arbitrary number of editing vectors, which can then be directly applied on other images at interactive rates. We experimentally show that EditGAN can manipulate images with an unprecedented level of detail and freedom, while preserving full image quality.We can also easily combine multiple edits and perform plausible edits beyond EditGAN’s training data. We demonstrate EditGAN on a wide variety of image types and quantitatively outperform several previous editing methods on standard editing benchmark tasks. Project page: https://nv-tlabs.github.io/editGAN. ",
+        "bbox": [
+            233,
+            364,
+            766,
+            654
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            680,
+            310,
+            696
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "AI-driven photo and image editing has the potential to streamline the workflow of photographers and content creators and to enable new levels of creativity and digital artistry [3]. AI-based image editing tools have already found their way into consumer software in the form of neural photo editing filters, and the deep learning ",
+        "bbox": [
+            174,
+            709,
+            393,
+            845
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/782f0d95cf6c1f39f92812cd3e25c760b0d31805d8af630f0f9c23dfff5334ad.jpg",
+        "image_caption": [
+            "Figure 1: High-precision semantic image editing with EditGAN. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            411,
+            681,
+            816,
+            830
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "research community is actively developing further techniques. A particularly promising line of research uses generative adversarial networks (GANs) [4, 5, 6, 7, 8] and either embeds images into the GAN’s latent space or works directly with GAN-generated images. Careful modifications of the latent embeddings then translate to desired changes in generated output, allowing, for example, to coherently change facial expressions in portraits [9, 10, 11, 12, 13, 14, 15, 16], change viewpoint or shapes and textures of cars [17], or to interpolate between different images in a semantically meaningful manner [18, 19, 20, 21]. ",
+        "bbox": [
+            176,
+            847,
+            823,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/c899d3cd93c67236587887acfd6de43587f4198a2a8293fb1b4b06e06d566106.jpg",
+        "image_caption": [
+            "Figure 2: (1) EditGAN builds on a GAN framework that jointly models images and their semantic segmentations. (2 & 3) Users can modify segmentation masks, based on which we perform optimization in the GAN’s latent space to realize the edit. (4) Users can perform editing simply by applying previously learnt editing vectors and manipulate images at interactive rates. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            64,
+            820,
+            242
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            313,
+            825,
+            383
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Most GAN-based image editing methods fall into few categories. Some works rely on GANs conditioning on class labels or pixel-wise semantic segmentation annotations [19, 10, 22, 11], where different conditionings lead to modifications in the output, while others use auxiliary attribute classifiers [23, 15] to guide synthesis and edit images. However, training such conditional GANs or external classifiers requires large labeled datasets. Therefore, these methods are currently limited to image types for which large annotated datasets are available, like portraits [10]. Furthermore, even if annotations are available, most techniques offer only limited editing control, since these annotations usually consist only of high-level global attributes or relatively coarse pixel-wise segmentations. Another line of work focuses on mixing and interpolating features from different images [18, 19, 20, 21], thereby requiring reference images as editing targets and usually also not offering fine control. Other approaches carefully analyze and dissect GANs’ latent spaces, finding disentangled latent variables suitable for editing [24, 25, 12, 13, 14, 26, 27], or control the GANs’ network parameters [25, 28, 16]. Usually, these methods do not enable detailed editing and are often slow. ",
+        "bbox": [
+            173,
+            390,
+            825,
+            569
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we are addressing these limitations and propose EditGAN, a novel GAN-based image editing framework that enables high-precision semantic image editing by allowing users to modify detailed object part segmentations. EditGAN builds on a recently proposed GAN that jointly models both images and their semantic segmentations based on the same underlying latent code [1, 2], and requires as few as 16 labeled examples – allowing it to scale to many object classes and choices of part labels. We achieve editing by modifying the segmentation mask according to a desired edit and optimizing the latent code to be consistent with the new segmentation, thus effectively changing the RGB image. To achieve efficiency, we learn editing vectors in latent space that realize the edits, and that can be directly applied on other images, without any or only few additional optimization steps. We can thus pre-train a library of interesting edits that a user can directly utilize in an interactive tool. ",
+        "bbox": [
+            174,
+            575,
+            825,
+            714
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We apply EditGAN on a wide range of images, including images of cars, cats, birds, and human faces, demonstrating unprecedented high-precision editing. We perform quantitative comparisons to multiple baselines and outperform them in metrics such as identity preservation, quality preservation, and target attribute accuracy, while requiring orders of magnitude less annotated training data. EditGAN is the first GAN-driven image editing framework, which simultaneously (i) offers very highprecision editing, (ii) requires only very little annotated training data (and does not rely on external classifiers), (iii) can be run interactively in real time, (iv) allows for straightforward compositionality of multiple edits, (v) and works on real embedded, GAN-generated, and even out-of-domain images. ",
+        "bbox": [
+            174,
+            719,
+            825,
+            832
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            843,
+            321,
+            859
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image Editing and Manipulation. Image Editing has a long history in computer vision and graphics, as well as machine learning [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 18, 11, 28, 41, 42, 16]. Recently, deep generative models [4, 43, 44], in particular modern GANs [6, 45, 7, 46, 8], received much attention as a promising tool for efficient image editing, as it was found that latent space manipulations often lead to interpretable and predictable changes in output [47, 24, 48, 49, 26, 27, 50]. ",
+        "bbox": [
+            176,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            92,
+            823,
+            119
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "GAN-based image editing methods can be broadly sorted into a number of categories. (i) One line of work relies on the careful dissection of the GAN’s latent space, aiming to find interpretable and disentangled latent variables, which can be leveraged for image editing, in a fully unsupervised manner [47, 24, 25, 12, 13, 14, 48, 49, 26, 27, 50, 51]. Although powerful, these approaches usually do not result in any high-precision editing capabilities. The editing vectors we are learning in EditGAN would be too hard to find independently without segmentation-based guidance. (ii) Other works utilize GANs that condition on class or pixel-wise semantic segmentation labels to control synthesis and achieve editing [9, 52, 46, 19, 10, 22, 11]. Hence, these works usually rely on large annotated datasets, which are often not available, and even if available, the possible editing operations are tied to whatever labels are available. This stands in stark contrast to EditGAN, which can be trained in a semi-supervised fashion with very little labeled data and where an arbitrary number of high-precision edits can be learnt. (iii) Furthermore, auxiliary attribute classifiers have been used for image manipulation [23, 15], thereby still relying on annotated data and usually only providing high-level control. (iv) Image editing is often explored in the context of “interpolating” between a target and different reference image in sophisticated ways, for example by replacing certain features in a given image with features from a reference images [18, 19, 20, 21]. From the general image editing perspective, the requirement of reference images limits the broad applicability of these techniques and prevents the user from performing specific, detailed edits for which potentially no reference images are available. (v) Recently, different works proposed to directly operate in the parameter space of the GAN instead of the latent space to realize different edits [25, 28, 16]. For example, [25, 28] essentially specialize the generator network for certain images at test time to aid image embedding or “rewrite” the network to achieve desired semantic changes in output. The drawback is that such specializations prevent the model from being used in real-time on different images and with different edits. [16] proposed an approach that more directly analyses the parameter space of a GAN and treats it as a latent space in which to apply edits. However, the method still merely discovers edits in the network’s parameter space, rather than actively defining them like we do. It remains unclear whether their method can combine multiple such edits, as we can, considering that they change the GAN parameters themselves. (vi) Finally, another line of research targets primarily very high-level image and photo stylization and global appearance modifications [37, 53, 54, 55, 52, 56, 46, 57, 41]. ",
+        "bbox": [
+            174,
+            126,
+            825,
+            526
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Generally, most works only do relatively high-level and not the detailed, high-precision editing, which EditGAN targets. Hence, we consider EditGAN as complementary to this body of work. ",
+        "bbox": [
+            176,
+            532,
+            820,
+            560
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "GANs and Latent Space Image Embedding. EditGAN builds on top of DatasetGAN [1] and SemanticGAN [2], which proposed to jointly model images and their semantic segmentations using shared latent codes. However, these works leveraged this model design only for semi-supervised learning, not for editing. EditGAN also relies on an encoder, together with optimization, to embed new images to be edited into the GAN’s latent space. This task in itself has been studied extensively in different contexts before, and we are building on these works. Previous papers studied encoder-based methods [58, 59, 60, 61, 62], used primarily optimization-based techniques [63, 64, 65, 66, 67, 68, 69, 26], and developed hybrid approaches [63, 24, 25, 70, 71]. ",
+        "bbox": [
+            174,
+            566,
+            825,
+            678
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Finally, a concurrent paper [72] shares similarities with DatasetGAN [1], on which our method builds, and explores an editing approach related to our EditGAN as one of its applications. However, our editing approach is methodologically different and leverages editing vectors, and also demonstrates significantly more diverse and stronger experimental results. Furthermore, [73] shares some highlevel ideas with EditGAN; however, it leverages the CLIP [74] model and targets text-driven editing. ",
+        "bbox": [
+            174,
+            684,
+            825,
+            753
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 High-Precision Semantic Image Editing with EditGAN ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            776,
+            661,
+            795
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Background ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            804,
+            299,
+            819
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "EditGAN’s image generation component is StyleGAN2 [7, 8], currently the state-of-the-art GAN for image synthesis. The StyleGAN2 generator maps latent codes $\\mathbf { z } \\in { \\mathcal { Z } }$ , drawn from a multivariate Normal distribution, into realistic images. A latent code $\\mathbf { z }$ is first transformed into an intermediate code $\\mathbf { w } \\in \\mathcal { W }$ by a non-linear mapping function and then further transformed into $K + 1$ vectors, $\\mathbf { w } ^ { 0 } , . . . , \\mathbf { w } ^ { K }$ , through learned affine transformations. These transformed latent codes are fed into synthesis blocks, whose outputs are deep feature maps. ",
+        "bbox": [
+            174,
+            827,
+            825,
+            911
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Deep generative models such as StyleGAN2, which are trained to synthesize highly realistic images, acquire a semantic understanding of the modeled images in their high-dimensional feature space. Recently, DatasetGAN [1] and SemanticGAN [2] built on this insight to learn a joint distribution $p ( \\mathbf { x } , \\mathbf { y } )$ over images $\\mathbf { x }$ and pixel-wise semantic segmentation labels y, while requiring only a handful of labeled examples. EditGAN utilizes this joint distribution $p ( \\mathbf { x } , \\mathbf { y } )$ to perform high-precision semantic image editing of real and synthesized images. ",
+        "bbox": [
+            173,
+            90,
+            825,
+            175
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Both methods [1, 2] model $p ( \\mathbf { x } , \\mathbf { y } )$ by adding an additional segmentation branch to the image generator, which is a pre-trained StyleGAN [1]. We follow DatasetGAN [1], which applies a simple three-layer multi-layer perceptron classifier on the layer-wise concatenated and appropriately upsampled feature maps. This classifier operates on the concatenated feature maps in a per-pixel fashion and predicts the segmentation label of each pixel. ",
+        "bbox": [
+            174,
+            180,
+            825,
+            251
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Segmentation Training and Inference by Embedding Images into GAN’s Latent Space ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            255,
+            810,
+            270
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To both train the segmentation branch and perform segmentation on a new image, we embed an image into the GAN’s latent space using an encoder and optimization. To this end, we build on previous works [66, 62, 2] and train an encoder that embeds images into $\\mathcal { W } ^ { + }$ space, which is defined as $\\mathcal { W }$ but where the w’s are modeled independently [66, 62]. Our objectives to train this encoder consist of standard pixel-wise L2 and perceptual LPIPS reconstruction losses using both the real training data as well as samples from the GAN itself. For the GAN samples, we also explicitly regularize the encoder with the known underlying latent codes. In practice, we use the encoder to initialize images’ latent space embeddings and then iteratively refine the latent code $\\mathbf { w } ^ { + }$ via optimization, again using standard reconstruction objectives. ",
+        "bbox": [
+            173,
+            273,
+            825,
+            398
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In that way, we embed the annotated images $\\mathbf { x }$ from a dataset labeled with semantic segmentations into latent space, and train the segmentation branch of the generator using standard supervised learning objectives, i.e., the cross entropy loss. We keep the image generator’s weights frozen and only backpropagate the loss to the segmentation branch [1]. After training the segmentation branch, we can formally define a generator $\\bar { \\tilde { G } } : \\mathcal { W } ^ { + }  \\mathcal { X } , \\mathcal { Y }$ that models the joint distribution $p ( \\mathbf { x } , \\mathbf { y } )$ of images $\\mathbf { x }$ and semantic segmentations y. Details about encoder and segmentation branch training as well as optimization for image embedding can be found in the Appendix. ",
+        "bbox": [
+            173,
+            404,
+            826,
+            503
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 Finding Semantics in Latent Space via Segmentation Editing ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            512,
+            635,
+            526
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The key idea of EditGAN lies in leveraging the joint distribution $p ( \\mathbf { x } , \\mathbf { y } )$ of images and semantic segmentations for high-precision image editing. Given a new image $\\mathbf { x }$ to be edited, we can embed it into EditGAN’s $\\mathcal { W } ^ { + }$ latent space, as described above (alternatively, we can also sample images from the model itself and use those). The segmentation branch will then generate the corresponding segmentation $\\mathbf { y }$ , since segmentations and RGB im",
+        "bbox": [
+            173,
+            537,
+            408,
+            715
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/fb823d3601a32de596c1cacd81969ca423dc943ff186a4849f28d8fb75c7fe52.jpg",
+        "image_caption": [
+            "Figure 3: We modify semantic segmentations and optimize the shared latent code for consistency with the new segmentation within the editing region, and with the RGB appearance outside the editing region. Corresponding gradients are backpropagated through the shared generator. The result is a latent space editing vector $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            423,
+            534,
+            823,
+            637
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ages share the same latent codes $\\mathbf { w } ^ { + }$ . Using simple interactive digital painting or labeling tools, we can now manually modify the segmentation according to a desired edit. We denote the edited segmentation mask by $\\mathbf { y } _ { \\mathrm { e d i t e d } }$ . Starting from the embedding $\\mathbf { w } ^ { + }$ of the unedited image x and segmentation $\\mathbf { y }$ , we can then perform optimization within $\\mathcal { W } ^ { + }$ to find a new $\\mathbf { w } _ { \\mathrm { e d i t e d } } ^ { + } = \\mathbf { w } ^ { + } + \\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ consistent with the new segmentation $\\mathbf { y } _ { \\mathrm { e d i t e d } }$ , while allowing the RGB output $\\mathbf { x }$ to change within the editing region. ",
+        "bbox": [
+            173,
+            717,
+            826,
+            786
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Formally, we are seeking an editing vector $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + } \\in \\mathcal { W } ^ { + }$ such that $( \\mathbf { x } _ { \\mathrm { e d i t e d } } , \\mathbf { y } _ { \\mathrm { e d i t e d } } ) = \\tilde { G } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + } )$ where $\\tilde { G }$ denotes the fixed generator that synthesizes both images and segmentations. Defining $( \\mathbf { x } ^ { \\prime } , \\mathbf { y } ^ { \\prime } ) = \\tilde { G } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } )$ , we perform optimization to approximate $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ by $\\delta \\mathbf { w } ^ { + }$ . The region of interest $r$ within which we expect the image to change due to the edit is formally given by ",
+        "bbox": [
+            173,
+            792,
+            825,
+            854
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/98fe13a07967cfe2137e2e43e22097f5a9fd8aa0b6ce75299f95b38cddcf6d96.jpg",
+        "text": "$$\nr = \\left\\{ p : c _ { p } ^ { \\mathbf { y } } \\in Q _ { \\mathrm { e d i t } } \\right\\} \\cup \\left\\{ p : c _ { p } ^ { \\mathbf { y } _ { \\mathrm { e d i t e d } } } \\in Q _ { \\mathrm { e d i t } } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            856,
+            642,
+            876
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which means that $r$ is defined by all pixels $p$ whose part segmentation labels $c _ { p } ^ { \\{ \\mathbf { y } , \\mathbf { y } _ { \\mathrm { e d i t e d } } \\} }$ according to either the initial segmentation $\\mathbf { y }$ or the edited one $\\mathbf { y } _ { \\mathrm { e d i t e d } }$ are within an edit-specific pre-specified list ",
+        "bbox": [
+            173,
+            882,
+            828,
+            912
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$Q _ { \\mathrm { e d i t } }$ of part labels relevant for the edit. For example, when modifying the wheel in a photo of a car $Q _ { \\mathrm { e d i t } }$ would contain all part labels related to the wheels, such as tire, spoke, and wheelhub (see Fig. 3). We use a further buffer of 5 pixels to give the GAN freedom in modeling the transition between the edited and non-edited area. In practice, $r$ acts as a binary pixel-wise mask (see Eqs. 2 and 3 below). ",
+        "bbox": [
+            174,
+            90,
+            826,
+            147
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note that $\\mathbf { x } _ { \\mathrm { e d i t e d } }$ is not available during optimization. After all, $\\mathbf { x } _ { \\mathrm { e d i t e d } }$ is the edited image we are ultimately intested in. It emerges indirectly when optimizing for the segmentation modification, since images and segmentations are closely tied together in the joint distribution $p ( \\mathbf { x } , \\mathbf { y } )$ modeled by $\\tilde { G }$ We further define $\\mathbf { x } ^ { \\prime } = \\tilde { G } ^ { \\mathbf { x } } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } )$ as $\\tilde { G }$ ’s image generation and $\\mathbf { y } ^ { \\prime } = \\tilde { G } ^ { \\mathbf { y } } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } )$ as $\\tilde { G }$ ’s segmentation generation branch. ",
+        "bbox": [
+            174,
+            152,
+            825,
+            227
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To find $\\delta \\mathbf { w } ^ { + }$ , approximating $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ , we use the following losses as minimization targets: ",
+        "bbox": [
+            169,
+            232,
+            753,
+            248
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5d61e5a8c48279e5f5820d2d42faac559d3c5a64f2640bb466442b42effa5401.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { \\mathrm { R G B } } ( \\delta \\mathbf { w } ^ { + } ) = L _ { \\mathrm { L P I P S } } ( \\tilde { G } ^ { \\mathbf { x } } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } ) \\odot ( 1 - r ) , \\ \\mathbf { x } \\odot ( 1 - r ) ) } \\\\ & { \\qquad + L _ { L 2 } ( \\tilde { G } ^ { \\mathbf { x } } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } ) \\odot ( 1 - r ) , \\ \\mathbf { x } \\odot ( 1 - r ) ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            282,
+            251,
+            715,
+            292
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e36b47bffd390476c6000b5ff9551822e952968dc0237018bda1dcacad7edf74.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { C E } } \\big ( \\delta \\mathbf { w } ^ { + } \\big ) = H \\big ( \\tilde { G } ^ { \\mathbf { y } } \\big ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } \\big ) \\odot r , \\ \\mathbf { y } _ { \\mathrm { e d i t e d } } \\odot r \\big ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            328,
+            297,
+            669,
+            316
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $H$ denotes the pixel-wise cross-entropy, $L _ { \\mathrm { L P I P S } }$ loss is based on the Learned Perceptual Image Patch Similarity (LPIPS) distance [75], and $L _ { L 2 }$ is a regular pixel-wise L2 loss. $\\mathcal { L } _ { \\mathrm { R G B } } ( \\delta \\mathbf { \\bar { w } } ^ { + } )$ ensures that the image appearance does not change outside the region of interest, while $\\mathcal { L } _ { \\mathrm { C E } } ( \\delta \\mathbf { w } ^ { + } )$ ensures that the target segmentation $\\mathbf { y } _ { \\mathrm { e d i t e d } }$ is enforced within the editing region (see visualization in Fig. 3). When editing human faces, we also apply the identity loss [62]: ",
+        "bbox": [
+            173,
+            319,
+            826,
+            388
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ef4b99d1b708797e0ea8d558b7a7b49dfde1afde3527d68c7835fd9d6737e886.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { I D } } ( \\delta \\mathbf { w } ^ { + } ) = \\langle R ( \\tilde { G } ^ { \\mathbf { x } } ( \\mathbf { w } ^ { + } + \\delta \\mathbf { w } ^ { + } ) ) , R ( \\mathbf { x } ) \\rangle } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            391,
+            642,
+            410
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "with $R$ denoting the pretrained ArcFace feature extraction network [76] and $\\langle \\cdot , \\cdot \\rangle$ cosine-similiarity. The final objective function for optimization then becomes: ",
+        "bbox": [
+            171,
+            412,
+            825,
+            448
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3b5df6fc9922305b7fbdbddc8e4bc41629d9f62c276c26c8c8539b8f15ed4291.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { e d i t i n g } } ( \\delta \\mathbf { w } ^ { + } ) = \\lambda _ { 1 } ^ { \\mathrm { e d i t i n g } } \\mathcal { L } _ { \\mathrm { R G B } } ( \\delta \\mathbf { w } ^ { + } ) + \\lambda _ { 2 } ^ { \\mathrm { e d t i n g } } \\mathcal { L } _ { \\mathrm { C E } } ( \\delta \\mathbf { w } ^ { + } ) + \\lambda _ { 3 } ^ { \\mathrm { e d t i n g } } \\mathcal { L } _ { \\mathrm { I D } } ( \\delta \\mathbf { w } ^ { + } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            248,
+            450,
+            750,
+            470
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "with hyperparameters $\\lambda _ { 1 , \\dots , 3 } ^ { \\mathrm { e d i t i n g } }$ . The only “learnable” variable is the editing vector $\\delta \\mathbf { w } ^ { + }$ ; all neural networks are kept fixed. After optimizing $\\delta \\mathbf { w } ^ { + }$ with the objective function, we can use $\\delta \\mathbf { w } ^ { + } \\approx \\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ Note that there is a certain amount of ambiguity in how the segmentation modification is realized in RGB output. We rely on the GAN generator, trained to synthesize realistic images, to modify the RGB values in the editing region in a plausible way consistent with the segmentation edit. ",
+        "bbox": [
+            173,
+            474,
+            826,
+            550
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 Different Ways of Editing during Inference ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            558,
+            513,
+            573
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The latent space editing vectors $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ obtained by optimization as described are semantically meaningful and often disentangled with other attributes. Therefore, for new images $\\mathbf { x }$ to be edited, we can embed the images into the $\\mathcal { W } ^ { + }$ latent space and the same editing operations can be directly performed by applying the previously learnt $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ as $( \\mathbf { x } ^ { \\prime } , \\mathbf { y } ^ { \\prime } ) = G ( \\mathbf { w } ^ { + } + s _ { \\mathrm { e d i t } } \\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + } )$ without doing any optimization from scratch again. In other words, the learnt editing vectors $\\bar { \\delta } \\bar { \\mathbf { w } } ^ { + }$ amortize the iterative optimization that was necessary to achieve the edit initially. For well-disentangled editing operations, $\\mathbf { x } ^ { \\prime }$ can be used directly as the edited image $\\mathbf { x } _ { \\mathrm { e d i t e d } }$ . Note that we introduced $s _ { \\mathrm { e d i t } }$ , a scalar editing coefficient, which effectively scales and controls the editing magnitude during inference. For $s _ { \\mathrm { e d i t } } = 0$ , we do not do any editing at all, while for $s _ { \\mathrm { e d i t } } > 1$ we manipulate the images with an effectively larger editing operation in latent space, leading to exaggerated effects. ",
+        "bbox": [
+            173,
+            583,
+            825,
+            722
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Unfortunately, disentanglement is not always perfect and the editing vectors $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ do not always translate perfectly to other images. We can remove editing artifacts in other regions of the image by a few additional optimization steps at test time. Specifically, we can use the exact same minimization obas s as above, using the initial prediction . This assumes that the editing vector $\\mathbf { y } ^ { \\prime }$ , obtained after applying the editing vector ll induces a plausible segmentation chang $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ $\\mathbf { y } _ { \\mathrm { e d i t e d } }$   \napplied on other images and that artifacts only arise in RGB output. The RGB objective $\\mathcal { L } _ { \\mathrm { { R G B } } }$ then removes these editing artifacts outside the editing region, while $\\mathcal { L } _ { \\mathrm { C E } }$ ensures that the modified segmentation stays as predicted by the editing vector. ",
+        "bbox": [
+            174,
+            728,
+            825,
+            839
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Summarizing, we can perform image editing with EditGAN in three different modes: ",
+        "bbox": [
+            174,
+            844,
+            730,
+            861
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "• Real-time Editing with Editing Vectors. For localized, well-disentangled edits we perform editing purely by applying previously learnt editing vectors with varying scales $s _ { \\mathrm { e d i t } }$ and manipulate images at interactive rates. ",
+        "bbox": [
+            217,
+            869,
+            823,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/742a614d56b78b2c1585a7e070b2c2ba2262df73e8b0ab63e51925ccf624d04e.jpg",
+        "image_caption": [
+            "Figure 4: Examples of segmentation-driven edits with EditGAN. Results are based on editing with editing vectors and 30 steps self-supervised refinement. Blue boxes: Original images. Orange boxes: Zoom-in views. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            94,
+            823,
+            483
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Vector-based Editing with Self-Supervised Refinement. For localized edits that are not perfectly disentangled with other parts of the image, we can remove editing artifacts by additional optimization at test time, while initializing the edit using the learnt editing vectors. • Optimization-based Editing. Image-specific and very large edits do not transfer to other images via editing vectors. For such operations, we perform optimization from scratch. ",
+        "bbox": [
+            218,
+            526,
+            826,
+            602
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            613,
+            312,
+            631
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We extensively evaluate EditGAN on images across four different categories: Cars ( $3 8 4 \\times 5 1 2$ spatial resolution), Birds $( 5 1 2 \\times 5 1 2 )$ , Cats $( 2 5 6 \\times 2 5 6 )$ , and Faces $( 1 0 2 4 \\times 1 0 2 4 )$ . ",
+        "bbox": [
+            176,
+            637,
+            823,
+            666
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation We train our segmentation branch as described in Sec. 3.2 using 16, 16, 30, and 30 image-mask pairs as labeled training data for Faces, Cars, Birds, and Cats, respectively. We utilize very highly-detailed part segmentations from [1]. The annotation scheme for faces is shown in Fig. 7, all others are presented in the Appendix. When editing is done purely optimization-based or when learning the editing vectors, we always perform 100 steps of optimization using Adam [77]. For Car, Cat, and Faces, we use real images from DatasetGAN’s test set that were not part of GAN training to demonstrate editing functionality. These images are first embedded into EditGAN’s latent space via an encoder and optimization as described in Sec. 3.2. For Birds, we show editing on GAN-generated images. Model details and hyperparameters are provided in the Appendix. ",
+        "bbox": [
+            173,
+            672,
+            825,
+            797
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 Qualitative Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            808,
+            346,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In-Domain Results In Fig. 4, we demonstrate our EditGAN framework when applying previously learnt editing vectors $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ on novel images and refining with 30 steps of optimization. Our editing operations preserve high image quality and are well disentangled for all classes. We also show the ability to combine multiple different edits in Fig. 5. To the best of our knowledge, no previous methods can perform as complex and high-precision edits as we do, while preserving image quality and subject identity. In Fig. 8, we demonstrate that we can even perform extremely high-precision edits, such as rotating a car’s wheel spoke or dilating pupils. EditGAN can edit semantic parts of objects that consist of only few pixels. At the same time, we can use EditGAN to perform large-scale modifications, too: In Fig. 9, we present how we can remove the entire roof of a car or convert it to a station wagon-like vehicle, simply by modifying the segmentation mask accordingly and optimizing. It is worth noting that several of our editing operations generate plausible manipulated images unlike those appearing in the GAN training data. For example, the training data does not include cats with overly large eyes or ears. Nevertheless, we achieve such edits in a high-quality manner. ",
+        "bbox": [
+            174,
+            828,
+            823,
+            911
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/af4bf814241ab3da1430ddc5310405757b5f5cc1f2f6882f1581f9a97675afad.jpg",
+        "image_caption": [
+            "Figure 5: We combine multiple edits. Results are based on editing with editing vectors and 30 steps selfsupervised refinement. Blue boxes: Original images. Edits in detail: Second row, first person: open eyes, add hair, add mustache. Second person: smile, look left. Third row, first car: remove mirror, remove door handle, shrink wheels. Second car: remove license plate, enlarge wheels. Third row, bird: longer beak, bigger belly, head up. Third row, cat: open mouth, bigger ear, bigger eyes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            225,
+            50,
+            772,
+            465
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            542,
+            825,
+            641
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The edits in Figs. 4, 5 and 8 are based on learnt editing vectors with self-supervised refinement. However, without such refinement usually only very minor artifacts occur, as shown in Fig. 10, hence allowing for real-time high-precision semantic image editing (discussed in detail below). ",
+        "bbox": [
+            174,
+            646,
+            825,
+            689
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Out-of-Domain Results We demonstrate the generalization capability of EditGAN to out-ofdomain data on the MetFaces [8] data set. We use our EditGAN model trained on FFHQ [8], and create editing vectors $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ using in-domain real faces. We then embed out-of-domain MetFaces partraits (with 100 steps optimization) and apply the editing vectors with 30 steps self-supervised refinement. The results are shown in Fig. 6. We find that our editing operations seamlessly translate even to such far out-of-domain examples. ",
+        "bbox": [
+            174,
+            705,
+            825,
+            790
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 Quantitative Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            801,
+            354,
+            815
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To quantitatively measure EditGAN’s image editing capabilities, we use the smile edit benchmark introduced by MaskGAN [10]. Faces with neutral expressions are converted into smiling faces and performance is measured by three metrics: a. Semantic Correctness: Using a pre-trained smile attribute classifier, we measure whether the faces show smiling expressions after editing. b. Distribution-level Image Quality: Frechet Inception Distance (FID) [78, 79] and Kernel Inception Distance (KID) [80] are calculated between 400 edited test images and the CelebA-HD test dataset. c. ",
+        "bbox": [
+            174,
+            827,
+            826,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a61605ec5f7b2608b329439b051ff89b4dd3b4fd77ff0d41e5416083b44f10ec.jpg",
+        "image_caption": [
+            "Figure 6: We combine multiple edits on out-of-domain images. Results are based on editing with editing vectors and 30 steps self-supervised refinement. Edits in detail: First row, first example: look left, frown. Second example: smile, look right. Second row, first example: open eyes, lift eyebrow. Second example: open eyes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            243,
+            89,
+            756,
+            284
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Identity Preservation: Using the pretrained ArcFace feature extraction network [76], we measure whether the subjects’ identity is maintained when applying the edit. Specifically, we report cosinesimiliarity between original and edited images. Further details can be found in the Appendix. ",
+        "bbox": [
+            174,
+            334,
+            826,
+            376
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For our EditGAN, we simply learn a smiling editing vector $\\delta \\mathbf { w } _ { \\mathrm { e d i t } } ^ { + }$ using a hold-out neutral expression face image. We embed it into EditGAN, infer its pixel-wise segmentation labels, and manually modify the segmentation towards a smile. Then we perform optimization in latent space, as described above, to learn the editing vector. For the results in Tab. 1, it is applied with unit scale $s _ { \\mathrm { e d i t } } { = } 1$ on new images. We do ",
+        "bbox": [
+            174,
+            382,
+            452,
+            520
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/8b942210047dc63610e55e8490b2b13d8ffe356c22805fd5ed9a16d4f01ac883.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>Annot.</td><td>#Mask #Attribute Annot.</td><td>Attribute Acc.(%)↑</td><td>FID↓</td><td>KID↓</td><td>ID Score ↑</td></tr><tr><td>MaskGAN [10]</td><td>30.000</td><td></td><td>77.3</td><td></td><td>46.84 0.020</td><td>0.4611</td></tr><tr><td>LocalEditing [18]</td><td>-</td><td></td><td>26.0</td><td>41.26</td><td>0.012</td><td>0.5823</td></tr><tr><td>LocalEditing - Encoding4Editing [81]</td><td>-</td><td>-</td><td>41.75</td><td>48.28</td><td>0.016</td><td>0.6603</td></tr><tr><td>InterFaceGAN [13]</td><td>-</td><td>30.000</td><td>83.5</td><td>39.42</td><td>0.010</td><td>0.7295</td></tr><tr><td>EditGAN (ours)</td><td>16</td><td>-</td><td>91.5</td><td>41.74</td><td>0.013</td><td>0.7047</td></tr><tr><td>EditGAN+30 (ours)</td><td>16</td><td>-</td><td>85.8</td><td>40.83</td><td>0.012</td><td>0.7452</td></tr><tr><td>StyleGAN2 Distillation [82]</td><td>-</td><td>30.000</td><td>98.3</td><td>45.09 0.013</td><td></td><td>0.7823</td></tr></table>",
+        "bbox": [
+            467,
+            385,
+            821,
+            489
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Quantitative comparisons to multiple baselines on the smile edit benchmark. ",
+        "bbox": [
+            465,
+            492,
+            823,
+            517
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "not use the identity loss (Eq. 4) in this experiment, since identity preservation is already a target metric itself. We compare our method with three strong baselines: (i) $M a s k G A N ^ { 2 }$ [10]: It takes non-smiling images, their segmentation masks, and a target smiling segmentation mask as inputs. Note that training MaskGAN requires large annotated datasets, in contrast to us. We also compare to (ii) LocalEditing3 [18]: It clusters GAN features to achieve local editing and relies on reference images, in this case images of faces with smiling expressions. Another baseline we use is (iii) InterFace $G A N ^ { 4 }$ [13]: Similar to EditGAN, InterFaceGAN aims at finding editing vectors in latent space. However, it uses auxiliary attribute classifiers, relies on large annotated datasets, and can generally not achieve the fine editing control of our EditGAN. Finally, we compare to (iv) StyleGAN2 Distillation5 [82], which creates an alternative approach that does not require real image embeddings and also relies on an editing-vector model to create a training dataset. ",
+        "bbox": [
+            173,
+            520,
+            825,
+            672
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results are reported in Tab. 1. Using 1, $8 7 5 \\times$ less training labels, we outperform MaskGAN on all three metrics. We similarly obtain significantly stronger results than LocalEditing. In our observation, LocalEditing does not work well on real image embeddings. We further exploit a better encoder [81] for the LocalEditing baseline, which leads to a significant improvement in attribute accuracy and ID score, but slightly worse FID & KID scores. We find that EditGAN outperforms InterFaceGAN on identity preservation and attribute classification accuracy, while InterFaceGAN reaches slightly better FID & KID scores (for the results in Tab. 1, the latent space edits learnt by InterfaceGAN are also applied with unit scale, like for EditGAN). In Fig. 11, we report a more detailed comparison to InterFaceGAN, where we apply the smile editing vectors with different scale coefficients from zero to two. As shown, when the editing vector scale is small, the identity score is high while the smiling attribute score is low, since the modification of the original images is minimal. We find that our realtime editing with editing vectors is on-par with InterFaceGAN. When we perform self-supervised refinement at test time, EditGAN outperforms InterFaceGAN. In Tab. 1, we also compare with StyleGAN2 Distillation [82], which achieves strong performance. However, StyleGAN2 Distillation relies on pre-trained classifiers, like InterfaceGAN, and only enables relatively high-level editing of image attributes for which large-scale annotations exit. Moreover, it distills edits into separate Pixel2PixelHD networks, such that a new network needs to be trained for each edit, limiting broad, user-interactive applicability. Hence, we consider StyleGAN2 Distillation orthogonal to our EditGAN. ",
+        "bbox": [
+            173,
+            679,
+            825,
+            844
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/82aed2cce7459a336ae87233a9042f1ee642601d6b485bb205aecab5ad27d17e.jpg",
+        "image_caption": [
+            "Figure 7: Face part labeling schema [1]. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            89,
+            318,
+            176
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/ec5e57176ee9dd96a0c35e7e44b1e68c3c05f10a2598c6a27b653ace1bbfbc45.jpg",
+        "image_caption": [
+            "Figure 8: High-precision editing with EditGAN for extreme details. Left: We rotate Rotate Wheel Spoke Change pupil Sizethe spoke. Right: We modify pupil size. Results are based on editing with editing vectors and 30 steps self-supervised refinement. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            333,
+            90,
+            818,
+            171
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/40b140c5ee1e246522137b6ac9a2945eff98f726b22711f6d4416174a8e77e7b.jpg",
+        "image_caption": [
+            "Figure 9: Pure optimization-based editing. We demonstrate large-scale semantic edits that do not transfer seamlessly to other images via editing vectors. Hence, we perform optimization from scratch. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            217,
+            821,
+            279
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/a1abbd5adb6d1505d2819a994d24a10e48d6a51e57149c772524e86d426ec6f8.jpg",
+        "image_caption": [
+            "Figure 10: Left: We apply learnt editing vectors with varying scales (see 5 markers in FID plots) both without (top row for each class) and with (bottom row for each class) additional 30-step self-supervised refinement to correct artifacts. Red boxes denote original images. For each class, the leftmost image is the one used to learn the editing vector, with the editing result next to it and orginal and modified segmentations below. Right: Visual quality after editing with different scales as measured by FID with and without refinement. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            313,
+            800,
+            491
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            568,
+            825,
+            651
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Running Time We carefully measure the run time of our editing on an NVIDIA Tesla V100 GPU. Conditional optimization, given an edited segmentation mask, with 30 (60) optimization steps takes 11.4 (18.9) seconds. This operation provides us the editing vector. Application of editing vectors is almost instantaneous, taking only 0.4 seconds, therefore allowing for complex real-time interactive editing. A 10 (30) step self-supervised refinement would add an additional 4.2 (9.5) seconds. ",
+        "bbox": [
+            174,
+            665,
+            825,
+            736
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3 Ablation Studies: Self-Supervised Refinement and Editing Vector Scale ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            743,
+            707,
+            758
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Fig. 11 also contains a quantitative ablation study on the number of additional optimization steps done when initializing an edit with a learnt editing vector and refining with additional optimization. Generally, the more refinement steps we perform, the better the performance our model can achieve. As shown in Fig. 11, we find that further optimization can indeed slightly improve performance. Specifically, here we improve the trade-off between maintaining identity and achieving the desired semantic operation when performing editing with different scalings $s _ { \\mathrm { e d i t } }$ of the editing vector. However, performing many steps of optimization leads to a run-time vs. performance trade-off, and our results suggest that the improvement beyond 30 additional optimization steps becomes marginal. ",
+        "bbox": [
+            173,
+            766,
+            826,
+            877
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 10, we analyze the editing vector scale and self-supervised refinement visually and with respect to perceptual metrics. As highlighted in the zoom-in areas, small artifacts can appear due to imperfect disentanglement in latent space when applying editing operations with large scales. Self-supervised refinement successfully cleans these editing errors up. We also apply the same edit with different scales on 400 test images and measure FID with respect to 10,000 data from GAN training, inspired by the analyses in [16]. We can clearly see that image quality degrades as measured by FID, the stronger the edit is applied. We also observe small improvements with the iterative refinement on this metric, although the difference is small. Further details are in the Appendix. We conclude that for most editing operations, real-time editing without iterative refinement already performs very well. However, to clean up artifacts and maintain highest image quality possible, self-supervised refinement with a couple of additional optimization steps is always available. ",
+        "bbox": [
+            173,
+            883,
+            821,
+            911
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            90,
+            826,
+            215
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Additional experiments are presented in the Appendix. ",
+        "bbox": [
+            176,
+            222,
+            532,
+            237
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusions ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            250,
+            307,
+            267
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Limitations Like all GAN-based image editing methods, EditGAN is limited to images that can be modeled by the GAN. This makes EditGAN’s application on, for instance, photos of vivid city scenes challenging. Although most of our high-precision edits readily transfer to other images via learnt editing vectors, we also encountered challenging edits that required iterative optimization on each example. Future research therefore includes speeding up the optimization for such edits as well as building better generative models with more disentangled latent spaces. ",
+        "bbox": [
+            174,
+            277,
+            549,
+            416
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/690211948c1cfdaeb4947e26111732183937f423e3528f4344ff12d15a1cbf6a.jpg",
+        "image_caption": [
+            "Figure 11: InterFaceGAN’s and EditGAN’s performance on the smile edit benchmark for different editing vector scalings (scale increases from top-left points towards bottomright points; see main text and Appendix for details). For EditGAN, we optionally add 10, 30 or 60 additional optimization steps. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            562,
+            220,
+            802,
+            337
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Summary We propose EditGAN, a novel method for high-precision, high-quality semantic image editing. It relies on a GAN that jointly models RGB images and their pixel-wise semantic segmentations and that requires only very few annotated data for training. Editing is achieved by performing optimization in latent space while conditioning on edited segmentation masks. This optimization can be amortized into editing vectors in latent space, which can be applied on other images directly, allowing for real-time interactive editing without any or only little further optimization. We demonstrate a broad variety of editing operations on different kinds of images, achieving an unprecedented level of flexibility and freedom in terms of editing, while preserving high image quality. ",
+        "bbox": [
+            173,
+            428,
+            826,
+            540
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 Broader Impact ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            553,
+            339,
+            569
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Where previous generative modeling-based image editing methods offer only limited high-level editing capabilities, our method provides users unprecedented high-precision semantic editing possibilities. Our proposed techniques can be used for artistic purposes and creative expression and benefit designers, photographers, and content creators [3]. AI-driven image editing tools like ours promise to democratize high-quality image editing. Related methods have already found their way into everyday applications in the form of neural photo editing filters. On a larger scale, the ability to synthesize data with specific attributes can be leveraged in training and finetuning machine learning models. ",
+        "bbox": [
+            174,
+            579,
+            825,
+            676
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "At the same time, more precise photo editing also offers opportunities for advanced photo manipulation for nefarious purposes. The recent progress of generative models and AI-driven photo editing has profound implications on image authenticity and beyond, which is an area of active debate [83]. As one potential way to tackle these challenges, methods for automatically validating real images and detecting manipulated or fake images are being developed by the research community [84, 85]. Furthermore, generative models like ours are usually only as good as the data they were trained on. Therefore, biases in the underlying datasets are still present in the synthesized images and preserved even when applying our proposed editing methods. It is therefore important to be aware of such biases in the underlying data and counteract them, for example by actively collecting more representative data or by using bias correction methods, an area of active research [86, 87, 88, 89]. ",
+        "bbox": [
+            174,
+            683,
+            825,
+            821
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Funding Statement ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            838,
+            336,
+            856
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This work was funded by NVIDIA. Huan Ling and Seung Wook Kim acknowledge additional revenue in the form of student scholarships from University of Toronto and the Vector Institute, which are not in direct support of this work. ",
+        "bbox": [
+            176,
+            869,
+            823,
+            911
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            90,
+            266,
+            106
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[1] Yuxuan Zhang, Huan Ling, Jun Gao, Kangxue Yin, Jean-Francois Lafleche, Adela Barriuso, Antonio Torralba, and Sanja Fidler. Datasetgan: Efficient labeled data factory with minimal human effort. arXiv preprint arXiv:2104.06490, 2021.   \n[2] Daiqing Li, Junlin Yang, Karsten Kreis, Antonio Torralba, and Sanja Fidler. Semantic segmentation with generative models: Semi-supervised learning and strong out-of-domain generalization. arXiv preprint arXiv:2104.05833, 2021.   \n[3] J. Bailey. The tools of generative art, from flash to neural networks. Art in America, 2020.   \n[4] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pages 2672–2680, 2014.   \n[5] Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015.   \n[6] Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. arXiv preprint arXiv:1710.10196, 2017.   \n[7] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4401–4410, 2019.   \n[8] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8110–8119, 2020.   \n[9] Yunjey Choi, Minje Choi, Munyoung Kim, Jung-Woo Ha, Sunghun Kim, and Jaegul Choo. Stargan: Unified generative adversarial networks for multi-domain image-to-image translation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018.   \n[10] Cheng-Han Lee, Ziwei Liu, Lingyun Wu, and Ping Luo. Maskgan: Towards diverse and interactive facial image manipulation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   \n[11] Rongliang Wu, Gongjie Zhang, Shijian Lu, and Tao Chen. Cascade ef-gan: Progressive facial expression editing with local focuses. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   \n[12] Yujun Shen, Jinjin Gu, Xiaoou Tang, and Bolei Zhou. Interpreting the latent space of gans for semantic face editing. In CVPR, 2020.   \n[13] Yujun Shen, Ceyuan Yang, Xiaoou Tang, and Bolei Zhou. Interfacegan: Interpreting the disentangled face representation learned by gans. TPAMI, 2020.   \n[14] Yazeed Alharbi and Peter Wonka. Disentangled image generation through structured noise injection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   \n[15] Xianxu Hou, Xiaokang Zhang, Linlin Shen, Zhihui Lai, and Jun Wan. Guidedstyle: Attribute knowledge guided style manipulation for semantic face editing. arXiv preprint arXiv:2012.11856, 2020.   \n[16] Anton Cherepkov, Andrey Voynov, and Artem Babenko. Navigating the gan parameter space for semantic image editing. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021.   \n[17] Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yinan Zhang, Antonio Torralba, and Sanja Fidler. Image gans meet differentiable rendering for inverse graphics and interpretable 3d neural rendering. arXiv preprint arXiv:2010.09125, 2020.   \n[18] Edo Collins, Raja Bala, Bob Price, and Sabine Süsstrunk. Editing in style: Uncovering the local semantics of GANs. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   \n[19] Peihao Zhu, Rameen Abdal, Yipeng Qin, and Peter Wonka. Sean: Image synthesis with semantic regionadaptive normalization. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2020.   \n[20] Kathleen M Lewis, Srivatsan Varadharajan, and Ira Kemelmacher-Shlizerman. Vogue: Try-on by stylegan interpolation optimization. arXiv preprint arXiv:2101.02285, 2021.   \n[21] Hyunsu Kim, Yunjey Choi, Junho Kim, Sungjoo Yoo, and Youngjung Uh. Exploiting spatial dimensions of latent in gan for real-time image editing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021.   \n[22] Shu-Yu Chen, Wanchao Su, Lin Gao, Shihong Xia, and Hongbo Fu. Deepfacedrawing: Deep generation of face images from sketches. ACM Trans. Graph., 39(4), 2020.   \n[23] Z. He, W. Zuo, M. Kan, S. Shan, and X. Chen. Attgan: Facial attribute editing by only changing what you want. IEEE Transactions on Image Processing, 28(11):5464–5478, Nov 2019.   \n[24] David Bau, Jun-Yan Zhu, Hendrik Strobelt, Bolei Zhou, Joshua B. Tenenbaum, William T. Freeman, and Antonio Torralba. Gan dissection: Visualizing and understanding generative adversarial networks. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   \n[25] David Bau, Hendrik Strobelt, William Peebles, Jonas Wulff, Bolei Zhou, Jun-Yan Zhu, and Antonio Torralba. Semantic photo manipulation with a generative image prior. ACM Trans. Graph., 38(4), 2019.   \n[26] Antoine Plumerault, Hervé Le Borgne, and Céline Hudelot. Controlling generative models with continuous factors of variations. In International Conference on Learning Representations, 2020.   \n[27] Erik Härkönen, Aaron Hertzmann, Jaakko Lehtinen, and Sylvain Paris. Ganspace: Discovering interpretable gan controls. In Proc. NeurIPS, 2020.   \n[28] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. Rewriting a deep generative model. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   \n[29] George Wolberg. Digital Image Warping. IEEE Computer Society Press, Washington, DC, USA, 1st edition, 1994.   \n[30] Alexei A. Efros and William T. Freeman. Image quilting for texture synthesis and transfer. SIGGRAPH ’01, page 341–346, New York, NY, USA, 2001. Association for Computing Machinery.   \n[31] Aaron Hertzmann, Charles E. Jacobs, Nuria Oliver, Brian Curless, and David H. Salesin. Image analogies. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’01, page 327–340, New York, NY, USA, 2001. Association for Computing Machinery.   \n[32] E. Reinhard, M. Adhikhmin, B. Gooch, and P. Shirley. Color transfer between images. IEEE Computer Graphics and Applications, 21(5):34–41, 2001.   \n[33] Patrick Pérez, Michel Gangnet, and Andrew Blake. Poisson image editing. SIGGRAPH ’03, page 313–318, New York, NY, USA, 2003. Association for Computing Machinery.   \n[34] Scott Schaefer, Travis McPhail, and Joe Warren. Image deformation using moving least squares. ACM Trans. Graph., 25(3):533–540, 2006.   \n[35] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. Graph., 28(3), 2009.   \n[36] Michael W. Tao, Micah K. Johnson, and Sylvain Paris. Error-tolerant image compositing. In ECCV, 2010.   \n[37] Leon A. Gatys, Alexander S. Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.   \n[38] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223–2232, 2017.   \n[39] Tiziano Portenier, Qiyang Hu, Attila Szabó, Siavash Arjomand Bigdeli, Paolo Favaro, and Matthias Zwicker. Faceshop: Deep sketch-based face image editing. ACM Trans. Graph., 37(4), 2018.   \n[40] Huan Ling, David Acuna, Karsten Kreis, Seung Wook Kim, and Sanja Fidler. Variational amodal object completion. Advances in Neural Information Processing Systems, 2020.   \n[41] Taesung Park, Jun-Yan Zhu, Oliver Wang, Jingwan Lu, Eli Shechtman, Alexei A. Efros, and Richard Zhang. Swapping autoencoder for deep image manipulation. In Advances in Neural Information Processing Systems, 2020.   \n[42] Seung Wook Kim, Jonah Philion, Antonio Torralba, and Sanja Fidler. DriveGAN: Towards a Controllable High-Quality Neural Simulation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021.   \n[43] Diederik P Kingma and Max Welling. Auto-encoding variational bayes. In The International Conference on Learning Representations (ICLR), 2014.   \n[44] Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic backpropagation and approximate inference in deep generative models. In International Conference on Machine Learning, pages 1278–1286, 2014.   \n[45] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2019.   \n[46] Taesung Park, Ming-Yu Liu, Ting-Chun Wang, and Jun-Yan Zhu. Semantic image synthesis with spatiallyadaptive normalization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2337–2346, 2019.   \n[47] Lore Goetschalckx, Alex Andonian, Aude Oliva, and Phillip Isola. Ganalyze: Toward visual definitions of cognitive image properties. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), October 2019.   \n[48] Ali Jahanian\\*, Lucy Chai\\*, and Phillip Isola. On the \"steerability\" of generative adversarial networks. In International Conference on Learning Representations, 2020.   \n[49] Andrey Voynov and Artem Babenko. Unsupervised discovery of interpretable directions in the gan latent space. In International Conference on Machine Learning, pages 9786–9796. PMLR, 2020.   \n[50] Binxu Wang and Carlos R Ponce. A geometric analysis of deep generative image models and its applications. In International Conference on Learning Representations, 2021.   \n[51] Yujun Shen and Bolei Zhou. Closed-form factorization of latent semantics in gans. In CVPR, 2021.   \n[52] Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8798–8807, 2018.   \n[53] Fujun Luan, Sylvain Paris, Eli Shechtman, and Kavita Bala. Deep photo style transfer. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.   \n[54] Ming-Yu Liu, Thomas Breuel, and Jan Kautz. Unsupervised image-to-image translation networks. In Advances in neural information processing systems, pages 700–708, 2017.   \n[55] Yijun Li, Ming-Yu Liu, Xueting Li, Ming-Hsuan Yang, and Jan Kautz. A closed-form solution to photorealistic image stylization. In Proceedings of the European Conference on Computer Vision (ECCV), 2018.   \n[56] H. Kazemi, S. Iranmanesh, and N. Nasrabadi. Style and content disentanglement in generative adversarial networks. In 2019 IEEE Winter Conference on Applications of Computer Vision (WACV), pages 848–856, Los Alamitos, CA, USA, jan 2019. IEEE Computer Society.   \n[57] Jaejun Yoo, Youngjung Uh, Sanghyuk Chun, Byeongkyu Kang, and Jung-Woo Ha. Photorealistic style transfer via wavelet transforms. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), 2019.   \n[58] Guim Perarnau, Joost van de Weijer, Bogdan Raducanu, and Jose M. Álvarez. Invertible conditional gans for image editing. arXiv preprint arXiv:1611.06355, 2016.   \n[59] Jeff Donahue, Philipp Krähenbühl, and Trevor Darrell. Adversarial feature learning. arXiv preprint arXiv:1605.09782, 2016.   \n[60] Andrew Brock, Theodore Lim, James M. Ritchie, and Nick Weston. Neural photo editing with introspective adversarial networks. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.   \n[61] Vincent Dumoulin, Ishmael Belghazi, Ben Poole, Alex Lamb, Martín Arjovsky, Olivier Mastropietro, and Aaron C. Courville. Adversarially learned inference. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.   \n[62] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel CohenOr. Encoding in style: a stylegan encoder for image-to-image translation. arXiv preprint arXiv:2008.00951, 2020.   \n[63] Jun-Yan Zhu, Philipp Krähenbühl, Eli Shechtman, and Alexei A Efros. Generative visual manipulation on the natural image manifold. In European conference on computer vision, pages 597–613. Springer, 2016.   \n[64] R. A. Yeh, C. Chen, T. Y. Lim, A. G. Schwing, M. Hasegawa-Johnson, and M. N. Do. Semantic image inpainting with deep generative models. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 6882–6890, 2017.   \n[65] Zachary C. Lipton and Subarna Tripathi. Precise recovery of latent vectors from generative adversarial networks. arXiv preprint arXiv:1702.04782, 2017.   \n[66] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE International Conference on Computer Vision, pages 4432–4441, 2019.   \n[67] Minyoung Huh, Richard Zhang, Jun-Yan Zhu, Sylvain Paris, and Aaron Hertzmann. Transforming and projecting images into class-conditional generative networks. arXiv preprint arXiv:2005.01703, 2020.   \n[68] A. Creswell and A. A. Bharath. Inverting the generator of a generative adversarial network. IEEE Transactions on Neural Networks and Learning Systems, 30(7):1967–1974, 2019.   \n[69] A. Raj, Y. Li, and Y. Bresler. Gan-based projector for faster recovery with convergence guarantees in linear inverse problems. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 5601–5610, 2019.   \n[70] D. Bau, J. Zhu, J. Wulff, W. Peebles, B. Zhou, H. Strobelt, and A. Torralba. Seeing what a gan cannot generate. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 4501–4510, 2019.   \n[71] Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. In-domain gan inversion for real image editing. arXiv preprint arXiv:2004.00049, 2020.   \n[72] Jianjin Xu and Changxi Zheng. Linear semantics in generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9351–9360, 2021.   \n[73] David Bau, Alex Andonian, Audrey Cui, YeonHwan Park, Ali Jahanian, Aude Oliva, and Antonio Torralba. Paint by word. arXiv preprint arXiv:2103.10951, 2021.   \n[74] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. arXiv preprint arXiv:2103.00020, 2021.   \n[75] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586–595, 2018.   \n[76] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4690–4699, 2019.   \n[77] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.   \n[78] Maximilian Seitzer. pytorch-fid: FID Score for PyTorch. https://github.com/mseitzer/ pytorch-fid, August 2020. Version 0.1.1.   \n[79] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems 30, pages 6626–6637. Curran Associates, Inc., 2017.   \n[80] Mikołaj Binkowski, Danica J. Sutherland, Michael Arbel, and Arthur Gretton. Demystifying MMD GANs.´ In International Conference on Learning Representations, 2018.   \n[81] Omer Tov, Yuval Alaluf, Yotam Nitzan, Or Patashnik, and Daniel Cohen-Or. Designing an encoder for stylegan image manipulation. ACM Transactions on Graphics (TOG), 40(4):1–14, 2021.   \n[82] Yuri Viazovetskyi, Vladimir Ivashkin, and Evgeny Kashin. Stylegan2 distillation for feed-forward image manipulation. In European Conference on Computer Vision, pages 170–186. Springer, 2020.   \n[83] Cristian Vaccari and Andrew Chadwick. Deepfakes and disinformation: Exploring the impact of synthetic political video on deception, uncertainty, and trust in news. Social Media $^ +$ Society, 6(1):2056305120903408, 2020.   \n[84] Thanh Thi Nguyen, Quoc Viet Hung Nguyen, Cuong M. Nguyen, Dung Nguyen, Duc Thanh Nguyen, and Saeid Nahavandi. Deep learning for deepfakes creation and detection: A survey. arXiv preprint arXiv:1909.11573, 2021.   \n[85] Yisroel Mirsky and Wenke Lee. The creation and detection of deepfakes: A survey. ACM Comput. Surv., 54(1), 2021.   \n[86] Aditya Grover, Jiaming Song, Ashish Kapoor, Kenneth Tran, Alekh Agarwal, Eric J Horvitz, and Stefano Ermon. Bias correction of learned generative models using likelihood-free importance weighting. In Advances in Neural Information Processing Systems, 2019.   \n[87] Kristy Choi, Aditya Grover, Trisha Singh, Rui Shu, and Stefano Ermon. Fair generative modeling via weak supervision. In Proceedings of the 37th International Conference on Machine Learning, 2020.   \n[88] Ning Yu, Ke Li, Peng Zhou, Jitendra Malik, Larry Davis, and Mario Fritz. Inclusive GAN: improving data and minority coverage in generative models. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXII, 2020.   \n[89] Jinhee Lee, Haeri Kim, Youngkyu Hong, and Hye Won Chung. Self-diagnosing gan: Diagnosing underrepresented samples in generative adversarial networks. arXiv preprint arXiv:2102.12033, 2021. ",
+        "bbox": [
+            171,
+            98,
+            828,
+            920
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            77,
+            828,
+            920
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            42,
+            828,
+            916
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            70,
+            828,
+            919
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            92,
+            828,
+            382
+        ],
+        "page_idx": 14
+    }
+]

parse/train/jQSBcVURlpW/jQSBcVURlpW.md

@@ -0,0 +1,511 @@
+# LEARNING ALGEBRAIC REPRESENTATION FOR ABSTRACT SPATIAL-TEMPORAL REASONING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic generalization. This observation lies in the central debate (Fodor et al., 1988; Fodor & McLaughlin, 1990) between connectionist and classicist, wherein the latter continually advocates an algebraic treatment in cognitive architectures. In this work, we follow the classicist’s call and propose a hybrid approach to improve systematic generalization in reasoning. Specifically, we showcase a prototype with algebraic representations for the abstract spatial-temporal reasoning task of Raven’s Progressive Matrices (RPM) and present the ALgebra-Aware Neuro-Semi-Symbolic $\mathbf { \bar { \Gamma } } ( \mathbf { A L A N S ^ { 2 } } ,$ ) learner. The ALANS2 learner is motivated by abstract algebra and the representation theory. It consists of a neural visual perception frontend and an algebraic abstract reasoning backend: the frontend summarizes the visual information from object-based representations, while the backend transforms it into an algebraic structure and induces the hidden operator on-the-fly. The induced operator is later executed to predict the answer’s representation, and the choice most similar to the prediction is selected as the solution. Extensive experiments show that by incorporating an algebraic treatment, the ALANS2 learner outperforms various pure connectionist models in domains requiring systematic generalization. We further show that the algebraic representation learned can be decoded by isomorphism and used to generate an answer.
+
+# 1 INTRODUCTION
+
+“Thought is in fact a kind of Algebra.”
+
+—William James (James, 1891)
+
+Imagine you are given two alphabetical sequences of $\ " { c } , b , a \ "$ and $\cdot d , c , b ^ { \nu }$ , and asked to fill in the missing element in $" e , d , ? "$ . In nearly no time will one realize the answer to be $c$ . However, more surprising for human learning is that, effortlessly and instantaneously, we can “freely generalize” (Marcus, 2001) the solution to any partial consecutive ordered sequences. While believed to be innate in early development for human infants (Marcus et al., 1999), such systematic generalizability has constantly been missing and proven to be particularly challenging in existing connectionist models (Lake & Baroni, 2018; Bahdanau et al., 2019). In fact, such an ability to entertain a given thought and semantically related contents strongly implies an abstract algebra-like treatment (Fodor et al., 1988); in literature, it is referred to as the “language of thought” (Fodor, 1975), “physical symbol system” (Newell, 1980), and “algebraic mind” (Marcus, 2001). However, in stark contrast, existing connectionist models tend only to capture statistical correlation (Lake & Baroni, 2018; Kansky et al., 2017; Chollet, 2019), rather than providing any account for a structural inductive bias where systematic algebra can be carried out to facilitate generalization.
+
+This contrast instinctively raises a question—what constitutes such an algebraic inductive bias? We argue that the foundation of the modeling counterpart to the algebraic treatment in early human development (Marcus, 2001; Marcus et al., 1999) lies in algebraic computations set up on mathematical axioms, a form of formalized human intuition and the starting point of modern mathematical reasoning (Heath et al., 1956; Maddy, 1988). Of particular importance to the basic building blocks of algebra is the Peano Axiom (Peano, 1889). In the Peano Axiom, the essential components of algebra, the algebraic set and corresponding operators over it, are governed by three statements: (1) the existence of at least one element in the field to study (“zero” element), (2) a successor function that is recursively applied to all elements and can, therefore, span the entire field, and (3) the principle of mathematical induction. Building on such a fundamental axiom, we begin to form the notion of an algebraic set and induce the operator along with it to construct an algebraic structure. We hypothesize that such a treatment of algebraic computations set up on fundamental axioms is essential for a model’s systematic generalizability, the lack of which will only make it sub-optimal.
+
+To demonstrate the benefits of such an algebraic treatment in systematic generalization, we showcase a prototype for Raven’s Progressive Matrices (RPM) (Raven, 1936; Raven & Court, 1998), an exemplar task for abstract spatial-temporal reasoning (Santoro et al., 2018; Zhang et al., 2019a). In this task, an agent is given an incomplete $3 \times 3$ matrix consisting of eight context panels with the last one missing, and asked to pick one answer from a set of eight choices that best completes the matrix. Human’s reasoning capability of solving this abstract reasoning task has been commonly regarded as an indicator of “general intelligence” (Carpenter et al., 1990) and “fluid intelligence” (Spearman, 1923; 1927; Hofstadter, 1995; Jaeggi et al., 2008). In spite of the task being one that ideally requires abstraction, algebraization, induction, and generalization (Raven, 1936; Raven & Court, 1998; Carpenter et al., 1990), recent endeavors unanimously propose pure connectionist models that attempt to circumvent such intrinsic cognitive requirements (Santoro et al., 2018; Zhang et al., 2019a;b; Wang et al., 2020; Zheng et al., 2019; Hu et al., 2020; Wu et al., 2020). However, these methods’ inefficiency is also evident in systematic generalization; they struggle to extrapolate to domains beyond training, as pointed out in (Santoro et al., 2018; Zhang et al., 2019b) and shown later in this paper.
+
+To address the issue, we introduce the ALgebra-Aware Neuro-Semi-Symbolic (ALANS2) learner. At a high-level, the ALANS2 learner is embedded in a general neuro-symbolic architecture (Yi et al., 2018; Mao et al., 2019; Han et al., 2019; Yi et al., 2020) but has on-the-fly operator learnability and hence semi-symbolic. Specifically, it consists of a neural visual perception frontend and an algebraic abstract reasoning backend. For each RPM instance, the neural visual perception frontend first slides a window over each panel to obtain the object-based representations (Kansky et al., 2017; Wu et al., 2017) for every object. A belief inference engine latter aggregates all object-based representations in each panel to produce the probabilistic belief state. The algebraic abstract reasoning backend then takes the belief states of the eight context panels, treats them as snapshots on an algebraic structure, lifts them into a matrix-based algebraic representation built on the Peano Axiom and the representation theory (Humphreys, 2012), and induces the hidden operator in the algebraic structure by solving an inner optimization (Colson et al., 2007; Bard, 2013). The algebraic representation for the answer is predicted by executing the induced operator: its corresponding set element is decoded by isomorphism established in the representation theory, and the final answer is selected as the one most similar to the prediction.
+
+The ALANS2 learner enjoys several benefits in abstract reasoning with an algebraic treatment:
+
+1. Unlike previous monolithic models, the ALANS2 learner offers a more interpretable account of the entire abstract reasoning process: the neural visual perception frontend extracts object-based representations and produces belief states of panels by explicit probability inference, whereas the algebraic abstract reasoning backend induces the hidden operator in the algebraic structure. The corresponding representation for the final answer is obtained by executing the induced operator, and the choice panel with minimum distance is selected. This process much resembles the topdown bottom-up strategy in human reasoning: humans reason by inducing the hidden relation, executing it to generate a feasible solution in mind, and choosing the most similar answer available (Carpenter et al., 1990). Such a strategy is missing in recent literature (Santoro et al., 2018; Zhang et al., 2019a;b; Wang et al., 2020; Zheng et al., 2019; Hu et al., 2020; Wu et al., 2020).   
+2. While keeping the semantic interpretability and end-to-end trainability in existing neurosymbolic frameworks (Yi et al., 2018; Mao et al., 2019; Han et al., 2019; Yi et al., 2020), ALANS2 is what we call semi-symbolic in the sense that the symbolic operator can be learned and concluded on-the-fly without manual definition for every one of them. Such an inductive ability also enables a greater extent of the desired generalizability.   
+3. By decoding the predicted representation in the algebraic structure, we can also generate an answer that satisfies the hidden relation in the context.
+
+This work makes three major contributions: (1) We propose the ALANS2 learner. Compared to existing monolithic models, the ALANS2 learner adopts a neuro-semi-symbolic design, where the problem-solving process is decomposed into neural visual perception and algebraic abstract reasoning. (2) To demonstrate the efficacy of incorporating an algebraic treatment in abstract spatialtemporal reasoning, we show the superior systematic generalization ability of the proposed ALANS2 learner in various extrapolatory RPM domains. (3) We present analyses into both neural visual perception and algebraic abstract reasoning. We also show the generative potential of ALANS2.
+
+# 2 RELATED WORK
+
+Quest for Symbolized Manipulation The idea to treat thinking as a mental language can be dated back to Augustine (Augustine, 1876; Wittgenstein, 1953). Since the 1970s, this school of thought has undergone a dramatic revival as the quest for a symbolized manipulation in cognitive modeling, such as “language of thought” (Fodor, 1975), “physical symbol system” (Newell, 1980), and “algebraic mind” (Marcus, 2001). In their study, connectionist’s task-specific superiority and inability to generalize beyond training (Kansky et al., 2017; Chollet, 2019; Santoro et al., 2018; Zhang et al., 2019a) have been hypothetically linked to a lack of such symbolized algebraic manipulation (Lake & Baroni, 2018; Chollet, 2019; Marcus, 2020). With evidence that an algebraic treatment adopted in early human development (Marcus et al., 1999) can potentially address the issue (Bahdanau et al., 2019; Mao et al., 2019; Marcus, 2020), classicist (Fodor et al., 1988) approaches for generalizable reasoning used in programs (McCarthy, 1960) and blocks world (Winograd, 1971) have resurrected. As a hybrid approach to bridge connectionist and classicist, recent developments lead to neuro-symbolic architectures. In particular, Yi et al. (2018) demonstrate a neuro-symbolic prototype for visual question answering, where a perception module and a language parsing module are separately trained, and the predefined logic operators associated with language tokens are chained to process the visual information. Mao et al. (2019) soften the predefined operators to afford end-to-end training with only question answers. Han et al. (2019) and Yi et al. (2020) use the hybrid architecture for metaconcept learning and temporal causal learning, respectively. ALANS2 follows the classicist’s call but adopts a neuro-semi-symbolic architecture: it is end-to-end trainable as opposed to Yi et al. (2018; 2020) and the operator can be learned and concluded on-the-fly without manual specification (Yi et al., 2018; Mao et al., 2019; Han et al., 2019; Yi et al., 2020).
+
+Abstract Visual Reasoning Recent works by Santoro et al. (2018) and Zhang et al. (2019a) arouse the community’s interest in abstract visual reasoning, where the task of Raven’s Progressive Matrices (RPM) is introduced as such a measure for intelligent agents. Initially proposed as an intelligence quotient test for humans (Raven, 1936; Raven & Court, 1998), RPM is believed to be strongly correlated with human’s general intelligence (Carpenter et al., 1990) and fluid intelligence (Spearman, 1923; 1927; Hofstadter, 1995; Jaeggi et al., 2008). Early RPM-solving systems employ symbolic representations based on hand-designed features and assume access to the underlying logics (Carpenter et al., 1990; Lovett et al., 2009; 2010; Lovett & Forbus, 2017). Another stream of research on RPM recruits similarity-based metrics to select the most similar answer from the choices (Little et al., 2012; McGreggor & Goel, 2014; McGreggor et al., 2014; Mekik et al., 2018; Shegheva & Goel, 2018). However, their hand-defined visual features are unable to handle uncertainty from imperfect perception, and directly assuming access to the logic operations simplifies the problem. Recently proposed data-driven approaches arise from the availability of large datasets: Santoro et al. (2018) extend a pedagogical RPM generation method (Wang & Su, 2015), whereas Zhang et al. (2019a) use a stochastic image grammar (Zhu et al., 2007) and introduce structural annotations in it, which Hu et al. (2020) further refine to avoid shortcut solutions by statistics in candidate panels. Despite the fact that RPM intrinsically requires one to perform abstraction, algebraization, induction, and generalization, existing methods bypass such cognitive requirements using a single feedforward pass in connectionist models: Santoro et al. (2018) use a relational module (Santoro et al., 2017), Steenbrugge et al. (2018) augment it with a VAE (Kingma & Welling, 2013), Zhang et al. (2019a) assemble a dynamic tree, Hill et al. (2019) arrange the data in a contrasting manner, Zhang et al. (2019b) propose a contrast module, Zheng et al. (2019) formulate it in a student-teacher setting, Wang et al. (2020) build a multiplex graph network, Hu et al. (2020) aggregate features from a hierarchical decomposition, and Wu et al. (2020) apply a scattering transformation to learn objects, attributes, and relations. In contrast, ALANS2 attempts to fulfill the cognitive requirements in a neuro-semi-symbolic framework: the perception frontend abstracts out visual information, and the reasoning backend induces the hidden operator in an algebraic structure.
+
+# 3 THE ALANS2 LEARNER
+
+In this section, we introduce the ALANS2 learner for the RPM problem. In each RPM instance, an agent is given an incomplete $3 \times 3$ panel matrix with the last entry missing and asked to induce the operator hidden in the matrix and choose from eight choice panels one that follows it. Formally, let the answer variable be denoted as $y$ , the context panels as $\{ \bar { I _ { o , i } } \} _ { i = 1 } ^ { 8 }$ , and choice panels as $\{ I _ { c , i } \} _ { i = 1 } ^ { 8 }$ Then the problem can be formulated as estimating $P ( y \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } )$ . According to the common design (Santoro et al., 2018; Zhang et al., 2019a; Carpenter et al., 1990), there is one operator that governs each panel attribute. Hence, by assuming independence among attributes, we
+
+![](images/c4183cca09d7b0e7909b164df057bfdf3e4ac55d600a3ed8f39831b9519bb7f1.jpg)  
+Figure 1: An overview of the ALANS2 learner. For an RPM instance, the neural visual perception module produces the belief states for all panels: an object CNN extracts object attribute distributions for each image region, and a belief inference engine marginalizes them out to obtain panel attribute distributions. For each panel attribute, the algebraic abstract reasoning module transforms the belief states into matrix-based algebraic representations and induces hidden operators by solving inner optimizations. The answer representations are obtained by executing the induced operators, and the choice most similar to the prediction is selected as the solution. An example of the underlying discrete algebra and its correspondence is also shown on the right.
+
+propose to factorize the probability asź
+
+$$
+P ( y = n \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } ) \alpha \prod _ { a } \sum _ { T ^ { a } } P ( y ^ { a } = n \mid T ^ { a } , \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } ) P ( \mathcal { T } ^ { a } \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) ,
+$$
+
+where $y ^ { a }$ denotes the answer selection based only on attribute $a$ and ${ \mathcal { T } } ^ { a }$ the operator on $a$
+
+Overview As shown in Fig. 1, the ALANS2 learner decomposes the process into perception and reasoning: the neural visual perception frontend extracts the belief states from each of the sixteen panels, whereas the algebraic abstract reasoning backend views an instance as an example in an abstract algebra structure, transforms belief states into algebraic representations by representation theory, induces the hidden operators, and executes the operators to predict the representation of the answer. Therefore, in Eq. (1), the operator distribution is modeled by the fitness of an operator and the answer distribution by the distance between the predicted representation and that of a candidate.
+
+# 3.1 NEURAL VISUAL PERCEPTION
+
+The neural visual perception frontend consists of an object CNN and a belief inference engine. It is responsible for extracting the belief states for each of the sixteen (context and choice) panels.
+
+Object CNN For each panel, we use a sliding window to traverse the spatial domain of the image and feed each image region into an object CNN. The CNN has four branches, producing for each region its object attribute distributions, including objectiveness (if the region contains an object), type, size, and color. Distributions of type, size, and color are conditioned on an object’s existence.
+
+Belief Inference Engine The belief inference engine summarizes the panel attribute distributions (over position, number, type, size, and color) by marginalizing out all object attribute distributions (over objectiveness, type, size, and color). As an example, the distribution of the panel attribute of Number can be computed as such: for $N$ image regions and their predicted objectiveness
+
+$$
+P ( { \mathrm { N u m b e r } } = k ) = \sum _ { R ^ { o } } \prod _ { j = 1 } ^ { N } P ( r _ { j } ^ { o } = R _ { j } ^ { o } ) ,
+$$
+
+where $P ( r _ { j } ^ { o } )$ denotes the $j$ th region’s estimated objectiveness distribution, and $R ^ { o }$ is a binary sequence of length $N$ that sums to $k$ . All panel attribute distributions compose the belief state of a panel. In the following, we denote the belief state as $b$ and the distribution of an attribute $a$ as $P ( b ^ { a } )$ .
+
+# 3.2 ALGEBRAIC ABSTRACT REASONING
+
+Given the belief states of both context and choice panels, the algebraic abstract reasoning backend concerns the induction of hidden operators and the prediction of answer representations for each attribute. The fitness of induced operators is used for estimating the operator distribution and the difference between the prediction and the choice panel for estimating the answer distribution.
+
+Algebraic Underpinning Without loss of generality, here we assume row-wise operators. For each attribute, under perfect perception, the first two rows in an RPM instance provide snapshots into an example of magma (Hausmann & Ore, 1937) constrained to an integer-indexed set, the simplest group-like algebra structure that is closed under a binary operator. To see this, note that an accurate perception module would see each panel attribute as a deterministic set element. Therefore, RPM instances with unary operators, such as progression, are magma examples with special binary operators where one operand is constant. Instances with binary operators, such as arithmetics, directly follow the magma properties. Those with ternary operators are ones with unary operators on a three-tuple set defined on rows.
+
+Algebraic Representation A systematic algebraic view allows us to felicitously recruit ideas in representation theory (Humphreys, 2012) to glean the hidden properties in the abstract structures: it makes abstract algebra amenable by reducing it onto linear algebra. Following the same spirit, we propose to lift both the set elements and the hidden operators to a learnable matrix space. To encode the set element, we employ the Peano Axiom (Peano, 1889). According to the Peano Axiom, an integer-indexed set can be constructed by (1) a zero element (0), (2) a successor function $( S ( \cdot ) )$ , and (3) the principle of mathematical induction, such that the $k$ th element is encoded as $S ^ { k } ( \mathbf { 0 } )$ . Specifically, we instantiate the zero element as a learnable matrix $M _ { 0 }$ and the successor function as the matrix-matrix product parameterized by $M$ . In an attribute-specific manner, the representation of an attribute taking the $k$ th value is $( M ^ { a } ) ^ { k } M _ { 0 } ^ { a }$ . For operators, we consider them to live in a learnable matrix group of a corresponding dimension, such that the action of an operator on a set can be represented as matrix multiplication. Such algebraic representations establish an isomorphism between the matrix space and the abstract algebraic structure: abstract elements on the algebraic structure have a bijective mapping to/from the matrix space, and inducing the abstract relation can be reduced to solving for a matrix operator. See Fig. 2 for a graphical illustration of the isomorphism.
+
+![](images/bda9a228593fa82a5da228ce2de1601fb10827e29755aa2f4fa07f2d41d50455.jpg)  
+Figure 2: Isomorphism between the abstract algebra and the matrix-based representation. Operator induction reduced to matrices.
+
+Operator Induction Operator induction concerns about finding a concrete operator in the abstract algebraic structure. By the property of closure, we formulate it as an inner-level regularized linear regression problem: a binary operator ÿ $\mathcal { T } _ { b } ^ { a }$ in a magma example for attribute $a$ minimizes
+
+$$
+\underset { T } { \arg \operatorname* { m i n } } \ell _ { b } ^ { a } ( T ) = \sum _ { i } \mathbb { E } \left[ \| M ( b _ { o , i } ^ { a } ) T M ( b _ { o , i + 1 } ^ { a } ) - M ( b _ { o , i + 2 } ^ { a } ) \| _ { F } ^ { 2 } \right] + \lambda _ { b } ^ { a } \| T \| _ { F } ^ { 2 } ,
+$$
+
+where under visual uncertainty, we take the expectation with respect to the distributions in the belief states of context panels $P ( b _ { o , i } ^ { \bar { a } } )$ in the first two rows, and denote its algebraic representation as ${ \cal M } ( b _ { o , i } ^ { a } )$ . For unary operators, one operand can be treated as constant and absorbed into $\tau$ . Note that Eq. (3) admits a closed-form solution (see Appendix for details). Therefore, the operator can be learned and adapted for different instances of binary relations and concluded on-the-fly. Such a design also simplifies the recent neuro-symbolic approaches, where every single symbol operator needs to be hand-defined (Yi et al., 2018; Mao et al., 2019; Han et al., 2019; Yi et al., 2020). Instead, we only specify an inner-level optimization framework and allow symbolic operators to be quickly induced based on the neural observations, while keeping the semantic interpretability in the neurosymbolic methods. Therefore, we term such a design semi-symbolic.
+
+The operator probability in Eq. (1) is then modeled by each operator type’s fitness, e.g., for binary,
+
+$$
+P ( \mathcal T ^ { a } = \mathcal T _ { b } ^ { a } \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) \propto \exp ( - \ell _ { b } ^ { a } ( \mathcal T _ { b } ^ { a } ) ) .
+$$
+
+Operator Execution To predict the algebraic representation of the answer, we solve another innerlevel optimization similar to Eq. (3), but now treating the representation of the answer as a variable:
+
+$$
+\widehat { M _ { b } ^ { a } } = \underset { M } { \arg \operatorname* { m i n } } \ell _ { b } ^ { a } ( M ) = { \mathbb E } [ \| M ( b _ { o , 7 } ^ { a } ) \mathcal { T } _ { b } ^ { a } M ( b _ { o , 8 } ^ { a } ) - M \| _ { F } ^ { 2 } ] ,
+$$
+
+where the expectation is taken with respect to context panels in the last row. The optimization also admits a closed-form solution (see Appendix for details), which corresponds to the execution of the induced operator in Eq. (3).
+
+The predicted representation is decoded probabilistically as the predicted belief state of the solution,
+
+$$
+P ( \widehat { b ^ { a } } = k \mid \overline { { { \mathcal T } } } ^ { a } ) \propto \exp ( - \Vert \widehat { M ^ { a } } - ( M ^ { \bar { a } } ) ^ { k } M _ { 0 } ^ { a } \Vert _ { F } ^ { 2 } ) .
+$$
+
+Answer Selection Based on Eqs. (1) and (4), estimating the answer distribution is now boiled down to estimating the conditional answer distributions for each attribute. Here, we propose to model it based on the Jensen–Shannon Divergence (JSD) of the predicted belief state and that of a choice,
+
+$$
+P ( y ^ { a } = n \mid \mathcal { T } ^ { a } , \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } ) \propto \exp ( - \mathbb { D } _ { \mathrm { J S D } } ( P ( \widehat { b ^ { a } } \mid \mathcal { T } ^ { a } ) \| P ( b _ { c , n } ^ { a } ) ) ) .
+$$
+
+Discussion The algebraic abstract reasoning module offers a computational and interpretable counterpart to human-like reasoning in RPM (Carpenter et al., 1990). Specifically, the induction component resembles the fluid intelligence, where one quickly induces the hidden operator by observing the context panels. The execution component synthesizes an image by executing the induced operator, and the choice most similar to the image is selected as the answer. We also note that by decoding the predicted representation in Eq. (6), a solution can be generated: by sequentially selecting the most probable operator and the most probable attribute value, a rendering engine can directly render the solution. The reasoning backend also enables end-to-end training: by integrating the belief states from neural perception, the module conducts both induction and execution in a soft manner, such that the gradients can be back-propagated and the learner jointly trained.
+
+# 3.3 LEARNING OBJECTIVE
+
+We train the entire $\mathrm { \ A L A N S ^ { 2 } }$ learner by minimizing the cross-entropy loss between the estimated answer distribution and the ground-truth selection, i.e.,
+
+$$
+\operatorname * { m i n } _ { \theta , \{ M _ { 0 } ^ { a } \} , \{ M ^ { a } \} } \ell ( P ( y \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } ) , y _ { \star } ) ,
+$$
+
+where $\ell ( \cdot )$ denotes the cross-entropy loss, $y _ { \star }$ the ground-truth selection, $\theta$ the parameters in the object CNN, and $\{ M _ { 0 } ^ { a } \}$ and $\{ M ^ { a } \}$ the zero elements and the successor functions for element encodings, respectively. Note notations are simplified by making the dependency on parameters implicit.
+
+However, we notice in practice that with only the cross-entropy loss on the ground-truth selection, the ALANS2 learner experiences difficulty in convergence. Without a proper guidance, the object CNN does not produce meaningful object-based representations. Therefore, following the discussion in (Santoro et al., 2018; Zhang et al., 2019a; Wang et al., 2020), we augment training with an auxiliary loss on the distribution of the operator, i.e.,
+
+$$
+\operatorname* { m i n } _ { \theta , \{ M _ { 0 } ^ { a } \} , \{ M ^ { a } \} } \ell ( P ( \boldsymbol { y } | \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } , \{ I _ { c , i } \} _ { i = 1 } ^ { 8 } ) , \boldsymbol { y } _ { \star } ) + \sum _ { a } \lambda ^ { a } \ell ( P ( \mathcal { T } ^ { a } | \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) , \boldsymbol { y } _ { \star } ^ { a } ) ,
+$$
+
+where $y _ { \star } ^ { a }$ denotes the ground-truth operator selection for attribute $a$ , and $\lambda ^ { a }$ balances the trade-off.
+
+# 4 EXPERIMENTS
+
+A cognitive architecture with systematic generalization is believed to demonstrate the following three principles (Fodor et al., 1988; Marcus, 2001; 2020): (1) systematicity, (2) productivity, and (3) localism. Systematicity requires an architecture to be able to entertain “semantically related” contents after understanding a given thought. Productivity states that the awareness of a constituent implies that of a recursive application of the constituent, and vice versa for localism.
+
+To verify the effectiveness of an algebraic treatment in systematic generalization, we showcase the superiority of the proposed ALANS2 learner on the three principles in the abstract spatial-temporal reasoning task of RPM. Specifically, we use the generation methods proposed in Zhang et al. (2019a) and Hu et al. (2020) to generate RPM problems and carefully split training and testing to construct the three regimes. The former generates candidates by perturbing only one attribute of the correct answer while the later modifies attribute values in a hierarchical manner to avoid shortcut solutions by pure statistics. Both methods categorize relations in RPM into three types, according to Carpenter et al. (1990): unary (Constant and Progression), binary (Arithmetic), and ternary (Distribution of Three), each of which comes with several instances. Grounding the principles into learning abstract relations in RPM, we fix the configuration to be $3 \times 3$ Grid and generate the following data splits for evaluation (see Appendix for details):
+
+• Systematicity: the training set contains only a subset of instances for each type of relation, while the test set all other relation instances.
+
+• Productivity: as the binary relation results from a recursive application of the unary relation, the training set contains only unary relations, whereas the test set only binary relations. • Localism: the training and testing sets in the productivity split are swapped to study localism.
+
+We follow Zhang et al. (2019a) to generate 10, 000 instances for each split and assign 6 folds for training, 2 folds for validation, and 2 folds for testing.
+
+Experimental Setup We evaluate the systematic generalizability of the proposed ALANS2 learner on the above three splits, and compare the ALANS2 learner with other baselines, including ResNet, ResNet+DRT (Zhang et al., 2019a), WReN (Santoro et al., 2018), CoPINet (Zhang et al., 2019b), MXGNet (Wang et al., 2020), LEN (Zheng et al., 2019), HriNet (Hu et al., 2020), and SCL (Wu et al., 2020). We use either official or public implementations that reproduce the original results.
+
+Table 1: Model performance on different aspects of systematic generalization. The performance is measured by accuracy and reported on the test sets. Upper: results on datasets generated by Zhang et al. (2019a). Lower: results on datasets generated by Hu et al. (2020).   
+
+<table><tr><td>Method</td><td>MXGNet</td><td>ResNet+DRT</td><td>ResNet</td><td>HriNet</td><td>LEN</td><td>WReN</td><td>SCL</td><td>CoPINet</td><td>ALANS2</td><td>ALANS²-Ind</td></tr><tr><td>Systematicity</td><td>20.95%</td><td>33.00%</td><td>27.35%</td><td>28.05%</td><td>40.15%</td><td>35.20%</td><td>37.35%</td><td>59.30%</td><td>78.45%</td><td>52.70%</td></tr><tr><td>Productivity</td><td>30.40%</td><td>27.95%</td><td>27.05%</td><td>31.45%</td><td>42.30%</td><td>56.95%</td><td>51.10%</td><td>60.00%</td><td>79.95%</td><td>36.45%</td></tr><tr><td>Localism</td><td>28.80%</td><td>24.90%</td><td>23.05%</td><td>29.70%</td><td>39.65%</td><td>38.70%</td><td>47.75%</td><td>60.10%</td><td>80.50%</td><td>59.80%</td></tr><tr><td>Average</td><td>26.72%</td><td>28.62%</td><td>25.82%</td><td>29.73%</td><td>40.70%</td><td>43.62%</td><td>45.40%</td><td>59.80%</td><td>79.63%</td><td>48.65%</td></tr><tr><td>Systematicity</td><td>13.35%</td><td>13.50%</td><td>14.20%</td><td>21.00%</td><td>17.40%</td><td>15.00%</td><td>24.90%</td><td>18.35%</td><td>64.80%</td><td>52.80%</td></tr><tr><td>Productivity</td><td>14.10%</td><td>16.10%</td><td>20.70%</td><td>20.35%</td><td>19.70%</td><td>17.95%</td><td>22.20%</td><td>29.10%</td><td>65.55%</td><td>32.10%</td></tr><tr><td>Localism</td><td>15.80%</td><td>13.85%</td><td>17.45%</td><td>24.60%</td><td>20.15%</td><td>19.70%</td><td>29.95%</td><td>31.85%</td><td>65.90%</td><td>50.70%</td></tr><tr><td>Average</td><td>14.42%</td><td>14.48%</td><td>17.45%</td><td>21.98%</td><td>19.08%</td><td>17.55%</td><td>25.68%</td><td>26.43%</td><td>65.42%</td><td>45.20%</td></tr></table>
+
+Systematic Generalization Table 1 shows the performance of various models on systematic generalization, i.e., systematicity, productivity, and localism. Compared to results reported in Santoro et al. (2018); Zhang et al. (2019a;b); Wang et al. (2020); Zheng et al. (2019); Hu et al. (2020); Wu et al. (2020), all pure connectionist models experience a devastating performance drop when it comes to the critical cognitive requirements on systematic generalization, indicating that pure connectionist models fail to perform abstraction, algebraization, induction, or generalization needed in solving the abstract reasoning task; instead, they seem to only take a shortcut to bypass them. In particular, MXGNet (Wang et al., 2020)’s superiority is diminishing in systematic generalization. Despite of learning with structural annotations, ResNet+DRT (Zhang et al., 2019a) does not fare better than its base model. The recently proposed HriNet (Hu et al., 2020) slightly improves on ResNet in this aspect, with LEN (Zheng et al., 2019) being only marginally better. WReN (Santoro et al., 2018), on the other hand, shows oscillating performance across the three regimes. Evaluated under systematic generation, SCL (Wu et al., 2020) and CoPINet (Zhang et al., 2019b) also far deviate from their “superior performance”. These observations suggest that pure connectionist models highly likely learn from variation in visual appearance rather than the algebra underlying the problem.
+
+Embedded in a neural-semi-symbolic framework, the proposed ALANS2 learner improves on systematic generalization by a large margin. With an algebra-aware design, the model is considerably stable across different principles of systematic generalization. The algebraic representations learned in relations of either a constituent or a recursive composition naturally support productivity and localism, while semi-symbolic inner optimization further allows various instances of an operator type to be induced from the algebraic representations and boosts systematicity. The importance of the algebraic representations is made more significant in the ablation study: ALANS2-Ind, with algebraic representation replaced by independent encodings and the algebraic isomorphism broken, shows inferior performance. The ALANS2 learner also enables diagnostic tests into its jointly learned perception module and reasoning module, in contrast to the black-box-like connectionist counterparts.
+
+Analysis into Perception and Reasoning The neural-semi-symbolic design allows analyses into both perception and reasoning. To evaluate the neural perception module and the algebraic reasoning module, we extract region-based object attribute annotations from the dataset generation methods (Zhang et al., 2019a; Hu et al., 2020) and categorize all relations into three types, i.e., unary, binary, and ternary, respectively.
+
+Table 2 shows the perception module’s performance on the test sets in the three regimes of systematic generalization. We note that in order for the ALANS2 learner to achieve the desired results shown in Table 1, ALANS2 learns to construct the concept of objectiveness perfectly. The model also shows a fairly accurate prediction accuracy on the attributes of type and size. However, on the texture-related concept of color, ALANS2 fails to develop a reliable notion on it. Despite that, the general prediction accuracy of the perception module is still surprising, considering that the perception module is only jointly learned with ground-truth annotations on answer selections. The relatively lower accuracy on color could be attributed to its larger space compared to other attributes.
+
+Table 2: Perception accuracy of the proposed ALANS2 learner, measured by whether the module can correctly predict an attribute’s value. Left: results on datasets genereted by Zhang et al. (2019a). Right: results on datasets genereted by Hu et al. (2020).   
+
+<table><tr><td>Object Attribute</td><td>Objectiveness</td><td>Type</td><td>Size</td><td>Color</td></tr><tr><td>Systematicity</td><td>100.00%</td><td>99.95%</td><td>94.65%</td><td>71.35%</td></tr><tr><td>Productivity</td><td>100.00%</td><td>99.97%</td><td>98.04%</td><td>77.61%</td></tr><tr><td>Localism</td><td>100.00%</td><td>95.65%</td><td>98.56%</td><td>80.05%</td></tr><tr><td>Average</td><td>100.00%</td><td>98.52%</td><td>97.08%</td><td>76.34%</td></tr></table>
+
+<table><tr><td>Object Attribute</td><td>Objectiveness</td><td>Type</td><td>Size</td><td>Color</td></tr><tr><td>Systematicity</td><td>100.00%</td><td>96.34%</td><td>92.36%</td><td>63.98%</td></tr><tr><td>Productivity</td><td>100.00%</td><td>94.28%</td><td>97.00%</td><td>69.89%</td></tr><tr><td>Localism</td><td>100.00%</td><td>95.80%</td><td>98.36%</td><td>60.35%</td></tr><tr><td>Average</td><td>100.00%</td><td>95.47%</td><td>95.91%</td><td>64.74%</td></tr></table>
+
+Table 3: Reasoning accuracy of the proposed ALANS2 learner, measured by whether the module can correctly predict the type of a relation on an attribute. Left: results on datasets genereted by Zhang et al. (2019a). Right: results on datasets generated by Hu et al. (2020).   
+
+<table><tr><td>Relation on</td><td>Position</td><td>Number</td><td>Type</td><td>Size</td><td>Color</td></tr><tr><td>Systematicity</td><td>69.96%</td><td>80.34%</td><td>83.50%</td><td>80.85%</td><td>28.85%</td></tr><tr><td>Productivity</td><td>-</td><td>99.10%</td><td>87.95%</td><td>68.50%</td><td>23.10%</td></tr><tr><td>Localism</td><td>-</td><td>70.55%</td><td>36.65%</td><td>42.30%</td><td>33.20%</td></tr><tr><td>Average</td><td>69.96%</td><td>83.33%</td><td>69.37%</td><td>63.88%</td><td>28.38%</td></tr></table>
+
+<table><tr><td>Relation on</td><td>Position</td><td>Number</td><td>Type</td><td>Size</td><td>Color</td></tr><tr><td>Systematicity</td><td>72.04%</td><td>82.14%</td><td>81.50%</td><td>80.80%</td><td>40.40%</td></tr><tr><td>Productivity</td><td>-</td><td>98.75%</td><td>89.50%</td><td>72.10%</td><td>33.95%</td></tr><tr><td>Localism</td><td>-</td><td>74.70%</td><td>44.25%</td><td>56.40%</td><td>54.20%</td></tr><tr><td>Average</td><td>72.04%</td><td>85.20%</td><td>71.75%</td><td>69.77%</td><td>42.85%</td></tr></table>
+
+Table 3 lists the reasoning module’s performance during testing for the three aspects. Note that on position, the unary operator (shifting) and binary operator (set arithemtics) do not systematically imply each other. Hence, we do not count them as probes into productivity and localism. In general, we notice that the better the perception accuracy on one attribute, the better the performance on reasoning. However, we also note that despite the relatively accurate perception of objectiveness, type, and size, near perfect reasoning is never guaranteed. This deficiency is due to the perception uncertainty handled by expectation in Eq. (3): in spite of correctness when we take arg max, marginalizing by expectation will unavoidably introduce noise into the reasoning process. Therefore, an ideal reasoning module requires the perception frontend to be not only correct but also certain. Computationally, one can sample from the perception module and optimize Eq. (9) using REINFORCE (Williams, 1992). However, the credit assignment problem and variance in gradient estimation will further complicate training.
+
+Generative Potential Compared to existing discriminative-only RPM-solving methods, the proposed ALANS2 learner is unique in its generative potential. As mentioned above, the final panel attribute can be decoded by sequentially selecting the most probable hidden operator and the attribute value. When equipped with a rendering engine, a solution can be generated. Here, we use the rendering program released by Zhang et al. (2019a) to demonstrate such a generative potential in the proposed ALANS2 learner. Fig. 3 shows examples where the solutions are generated by ALANS2. Such a generative ability is a computational counterpart to human reasoning: ALANS2 selects the one most similar to a synthesized image from the pool of candidates, which resembles human’s top-down bottom-up reasoning.
+
+![](images/167d7ff1e6c918f88ecea5e319ce78c422fc28f09d1aa035a57ff6e0723f7821.jpg)  
+Figure 3: Examples of RPM instances with the missing entries filled by solutions generated by the ALANS2 learner. Ground-truth relations are also listed. Note the generated results do not look exactly like the correct choices due to random rotations during rendering, but they are semantically correct.
+
+# 5 CONCLUSION
+
+In this work, we propose the ALgebra-Aware Neuro-Semi-Symbolic $( { \mathrm { A L A N S } } ^ { 2 }$ ) learner, echoing a normative theory in the connectionist-classicist debate that an algebraic treatment in a cognitive architecture should improve a model’s systematic generalization ability. In experiments, we show that with such an algebraic treatment, the neuro-semi-symbolic learner achieves superior performance in three RPM domains reflective of systematic generalization.
+
+# REFERENCES
+
+Saint Augustine. The confessions. Clark, 1876.
+
+Dzmitry Bahdanau, Shikhar Murty, Michael Noukhovitch, Thien Huu Nguyen, Harm de Vries, and Aaron Courville. Systematic generalization: What is required and can it be learned? In International Conference on Learning Representations (ICLR), 2019.
+
+Jonathan F Bard. Practical bilevel optimization: algorithms and applications, volume 30. Springer Science & Business Media, 2013.
+
+Patricia A Carpenter, Marcel A Just, and Peter Shell. What one intelligence test measures: a theoretical account of the processing in the raven progressive matrices test. Psychological Review, 97 (3):404, 1990.
+
+Franc¸ois Chollet. The measure of intelligence. arXiv preprint arXiv:1911.01547, 2019.
+
+William W Cohen. Tensorlog: A differentiable deductive database. arXiv preprint arXiv:1605.06523, 2016.
+
+Benoˆıt Colson, Patrice Marcotte, and Gilles Savard. An overview of bilevel optimization. Annals of operations research, 153(1):235–256, 2007.
+
+Liya Ding. Neural prolog-the concepts, construction and mechanism. In 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, volume 4, pp. 3603–3608. IEEE, 1995.
+
+Richard Evans and Edward Grefenstette. Learning explanatory rules from noisy data. Journal of Artificial Intelligence Research, 61:1–64, 2018.
+
+Jerry Fodor and Brian P McLaughlin. Connectionism and the problem of systematicity: Why smolensky’s solution doesn’t work. Cognition, 35(2):183–204, 1990.
+
+Jerry A Fodor. The language of thought, volume 5. Harvard university press, 1975.
+
+Jerry A Fodor, Zenon W Pylyshyn, et al. Connectionism and cognitive architecture: A critical analysis. Cognition, 28(1-2):3–71, 1988.
+
+Manoel VM Franc¸a, Gerson Zaverucha, and Artur S d’Avila Garcez. Fast relational learning using bottom clause propositionalization with artificial neural networks. Machine learning, 94(1):81– 104, 2014.
+
+Artur S Avila Garcez and Gerson Zaverucha. The connectionist inductive learning and logic programming system. Applied Intelligence, 11(1):59–77, 1999.
+
+Artur S d’Avila Garcez, Krysia B Broda, and Dov M Gabbay. Neural-symbolic learning systems: foundations and applications. Springer Science & Business Media, 2012.
+
+Chi Han, Jiayuan Mao, Chuang Gan, Josh Tenenbaum, and Jiajun Wu. Visual concept-metaconcept learning. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019.
+
+Bernard A Hausmann and Oystein Ore. Theory of quasi-groups. American Journal of Mathematics, 59(4):983–1004, 1937.
+
+Thomas Little Heath et al. The thirteen books of Euclid’s Elements. Courier Corporation, 1956.
+
+Felix Hill, Adam Santoro, David GT Barrett, Ari S Morcos, and Timothy Lillicrap. Learning to make analogies by contrasting abstract relational structure. In International Conference on Learning Representations (ICLR), 2019.
+
+S Hiolldobler. A structured connectionist unification algorithm. In Proceedings of the National Conference of the American Association on Artificial Intelligence, volume 90, pp. 587–593, 1990.
+
+Douglas R Hofstadter. Fluid concepts and creative analogies: Computer models of the fundamental mechanisms of thought. Basic books, 1995.
+
+Sheng Hu, Yuqing Ma, Xianglong Liu, Yanlu Wei, and Shihao Bai. Hierarchical rule induction network for abstract visual reasoning. arXiv preprint arXiv:2002.06838, 2020.
+
+James E Humphreys. Introduction to Lie algebras and representation theory, volume 9. Springer Science & Business Media, 2012.
+
+Susanne M Jaeggi, Martin Buschkuehl, John Jonides, and Walter J Perrig. Improving fluid intelligence with training on working memory. Proceedings of the National Academy of Sciences, 105 (19):6829–6833, 2008.
+
+William James. The Principles of Psychology. Henry Holt and Company, 1891.
+
+Ken Kansky, Tom Silver, David A Mely, Mohamed Eldawy, Miguel L ´ azaro-Gredilla, Xinghua Lou, ´ Nimrod Dorfman, Szymon Sidor, Scott Phoenix, and Dileep George. Schema networks: Zeroshot transfer with a generative causal model of intuitive physics. In Proceedings of International Conference on Machine Learning (ICML), 2017.
+
+Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), 2014.
+
+Diederik $\mathrm { \bf P }$ Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
+
+Ekaterina Komendantskaya. Unification neural networks: unification by error-correction learning. Logic Journal of the IGPL, 19(6):821–847, 2011.
+
+Brenden Lake and Marco Baroni. Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks. In Proceedings of International Conference on Machine Learning (ICML), 2018.
+
+Peter Lancaster. Explicit solutions of linear matrix equations. SIAM review, 12(4):544–566, 1970.
+
+Yann LeCun, Leon Bottou, Yoshua Bengio, Patrick Haffner, et al. Gradient-based learning applied ´ to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998.
+
+Daniel R Little, Stephan Lewandowsky, and Thomas L Griffiths. A bayesian model of rule induction in raven’s progressive matrices. In Proceedings of the Annual Meeting of the Cognitive Science Society (CogSci), 2012.
+
+Andrew Lovett and Kenneth Forbus. Modeling visual problem solving as analogical reasoning. Psychological Review, 124(1):60, 2017.
+
+Andrew Lovett, Emmett Tomai, Kenneth Forbus, and Jeffrey Usher. Solving geometric analogy problems through two-stage analogical mapping. Cognitive Science, 33(7):1192–1231, 2009.
+
+Andrew Lovett, Kenneth Forbus, and Jeffrey Usher. A structure-mapping model of raven’s progressive matrices. In Proceedings of the Annual Meeting of the Cognitive Science Society (CogSci), 2010.
+
+Penelope Maddy. Believing the axioms. i. The Journal of Symbolic Logic, 53(2):481–511, 1988.
+
+Robin Manhaeve, Sebastijan Dumancic, Angelika Kimmig, Thomas Demeester, and Luc De Raedt. Deepproblog: Neural probabilistic logic programming. In Advances in Neural Information Processing Systems, pp. 3749–3759, 2018.
+
+Jiayuan Mao, Chuang Gan, Pushmeet Kohli, Joshua B Tenenbaum, and Jiajun Wu. The neurosymbolic concept learner: Interpreting scenes, words, and sentences from natural supervision. In International Conference on Learning Representations (ICLR), 2019.
+
+Gary Marcus. The algebraic mind. Cambridge, MA: MIT Press, 2001.
+
+Gary Marcus. The next decade in ai: four steps towards robust artificial intelligence. arXiv preprint arXiv:2002.06177, 2020.
+
+Gary F Marcus, Sugumaran Vijayan, S Bandi Rao, and Peter M Vishton. Rule learning by sevenmonth-old infants. Science, 283(5398):77–80, 1999.
+
+John McCarthy. Programs with common sense. RLE and MIT computation center, 1960.
+
+Keith McGreggor and Ashok Goel. Confident reasoning on raven’s progressive matrices tests. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2014.
+
+Keith McGreggor, Maithilee Kunda, and Ashok Goel. Fractals and ravens. Artificial Intelligence, 215:1–23, 2014.
+
+Can Serif Mekik, Ron Sun, and David Yun Dai. Similarity-based reasoning, raven’s matrices, and general intelligence. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), 2018.
+
+Allen Newell. Physical symbol systems. Cognitive science, 4(2):135–183, 1980.
+
+Giuseppe Peano. Arithmetices principia: Nova methodo exposita. Fratres Bocca, 1889.
+
+James C Raven. Mental tests used in genetic studies: The performance of related individuals on tests mainly educative and mainly reproductive. Master’s thesis, University of London, 1936.
+
+John C Raven and John Hugh Court. Raven’s progressive matrices and vocabulary scales. Oxford pyschologists Press, 1998.
+
+Tim Rocktaschel and Sebastian Riedel. End-to-end differentiable proving. In ¨ Advances in Neural Information Processing Systems, pp. 3788–3800, 2017.
+
+Adam Santoro, David Raposo, David G Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap. A simple neural network module for relational reasoning. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2017.
+
+Adam Santoro, Felix Hill, David Barrett, Ari Morcos, and Timothy Lillicrap. Measuring abstract reasoning in neural networks. In Proceedings of International Conference on Machine Learning (ICML), 2018.
+
+Luciano Serafini and Artur d’Avila Garcez. Logic tensor networks: Deep learning and logical reasoning from data and knowledge. arXiv preprint arXiv:1606.04422, 2016.
+
+Lokendra Shastri. Neurally motivated constraints on the working memory capacity of a production system for parallel processing: Implications of a connectionist model based on temporal synchrony. In Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society: July, volume 29, pp. 159, 1992.
+
+Jude W Shavlik and Geoffrey G Towell. An approach to combining explanation-based and neural learning algorithms. In Applications Of Learning And Planning Methods, pp. 71–98. World Scientific, 1991.
+
+Snejana Shegheva and Ashok Goel. The structural affinity method for solving the raven’s progressive matrices test for intelligence. In Proceedings of AAAI Conference on Artificial Intelligence (AAAI), 2018.
+
+Gustav Sourek, Vojtech Aschenbrenner, Filip Zelezny, and Ondrej Kuzelka. Lifted relational neural networks. arXiv preprint arXiv:1508.05128, 2015.
+
+Charles Spearman. The nature of “intelligence” and the principles of cognition. Macmillan, 1923.
+
+Charles Spearman. The abilities of man, volume 6. Macmillan New York, 1927.
+
+Xander Steenbrugge, Sam Leroux, Tim Verbelen, and Bart Dhoedt. Improving generalization for abstract reasoning tasks using disentangled feature representations. arXiv preprint arXiv:1811.04784, 2018.
+
+Geoffrey G Towell and Jude W Shavlik. Knowledge-based artificial neural networks. Artificial intelligence, 70(1-2):119–165, 1994.
+
+Duo Wang, Mateja Jamnik, and Pietro Lio. Abstract diagrammatic reasoning with multiplex graph networks. In International Conference on Learning Representations (ICLR), 2020.
+
+Ke Wang and Zhendong Su. Automatic generation of raven’s progressive matrices. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), 2015.
+
+Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.
+
+Terry Winograd. Procedures as a representation for data in a computer program for understanding natural language. Technical report, MASSACHUSETTS INST OF TECH CAMBRIDGE PROJECT MAC, 1971.
+
+Ludwig Wittgenstein. Philosophical investigations. Philosophische Untersuchungen. Macmillan, 1953.
+
+Jiajun Wu, Joshua B Tenenbaum, and Pushmeet Kohli. Neural scene de-rendering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
+
+Yuhuai Wu, Honghua Dong, Roger Grosse, and Jimmy Ba. The scattering compositional learner: Discovering objects, attributes, relationships in analogical reasoning. arXiv preprint arXiv:2007.04212, 2020.
+
+Kexin Yi, Jiajun Wu, Chuang Gan, Antonio Torralba, Pushmeet Kohli, and Josh Tenenbaum. Neuralsymbolic vqa: Disentangling reasoning from vision and language understanding. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2018.
+
+Kexin Yi, Chuang Gan, Yunzhu Li, Pushmeet Kohli, Jiajun Wu, Antonio Torralba, and Joshua Tenenbaum. Clevrer: Collision events for video representation and reasoning. In International Conference on Learning Representations (ICLR), 2020.
+
+Chi Zhang, Feng Gao, Baoxiong Jia, Yixin Zhu, and Song-Chun Zhu. Raven: A dataset for relational and analogical visual reasoning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019a.
+
+Chi Zhang, Baoxiong Jia, Feng Gao, Yixin Zhu, Hongjing Lu, and Song-Chun Zhu. Learning perceptual inference by contrasting. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019b.
+
+Kecheng Zheng, Zheng-Jun Zha, and Wei Wei. Abstract reasoning with distracting features. In Proceedings of Advances in Neural Information Processing Systems (NeurIPS), 2019.
+
+Song-Chun Zhu, David Mumford, et al. A stochastic grammar of images. Foundations and Trends® in Computer Graphics and Vision, 2(4):259–362, 2007.
+
+# A INDUCING AND EXECUTING OPERATORS
+
+In the main text, we examplify the induction and the execution process using a binary operator. Here, we discuss other details regarding the formulation for all three types of operators, i.e., unary, binary, and ternary.
+
+Unary Operator To induce the unary operator $\mathcal { T } _ { u } ^ { a }$ for an attribute $a$ , we solve the following optimization problem
+
+$$
+\begin{array} { r l } & { T _ { u } ^ { a } = \underset { T } { \operatorname { a r g m i n } } \ell _ { u } ^ { a } ( T ) = 1 / 5 \times \left( \mathbb { E } \left[ \left. M ( b _ { o , 1 } ^ { a } ) T - M ( b _ { o , 2 } ^ { a } ) \right. _ { F } ^ { 2 } \right] + \mathbb { E } \left[ \left. M ( b _ { o , 2 } ^ { a } ) T - M ( b _ { o , 3 } ^ { a } ) \right. _ { F } ^ { 2 } \right] + \right. } \\ & { \qquad \left. \mathbb { E } \left[ \left. M ( b _ { o , 4 } ^ { a } ) T - M ( b _ { o , 5 } ^ { a } ) \right. _ { F } ^ { 2 } \right] + \mathbb { E } \left[ \left. M ( b _ { o , 5 } ^ { a } ) T - M ( b _ { o , 6 } ^ { a } ) \right. _ { F } ^ { 2 } \right] + \right. } \\ & { \qquad \left. \mathbb { E } \left[ \left. M ( b _ { o , 7 } ^ { a } ) T - M ( b _ { o , 8 } ^ { a } ) \right. _ { F } ^ { 2 } \right] \right) + \lambda _ { u } ^ { a } \left. T \right. _ { F } ^ { 2 } , } \end{array}
+$$
+
+where the indexing follows the row / column major. By taking the derivative with respect to $\tau$ and setting it to be 0, we have the following solution,
+
+$$
+\mathcal { T } _ { u } ^ { a } = A ^ { - 1 } B
+$$
+
+where, assuming independence,“
+
+a
+
+$$
+\begin{array} { r l } & { \mathrm { I r s c s , a s s u m m e ~ } _ { \Omega } \mathrm { ~ n u s u s e ~ } _ { P } \mathrm { c u n s e ~ r s m s e , } } \\ & { \qquad A = \mathbb { E } \left[ M ( b _ { o , 1 } ^ { a } ) ^ { T } M ( b _ { o , 1 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 2 } ^ { a } ) ^ { T } M ( b _ { o , 2 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 4 } ^ { a } ) ^ { T } M ( b _ { o , 4 } ^ { a } ) \right] + } \\ & { \qquad \mathbb { E } \left[ M ( b _ { o , 5 } ^ { a } ) ^ { T } M ( b _ { o , 5 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 7 } ^ { a } ) ^ { T } M ( b _ { o , 7 } ^ { a } ) \right] + 5 \lambda _ { u } ^ { a } I } \\ & { \mathrm { I d } } \\ & { \qquad B = \mathbb { E } \left[ M ( b _ { o , 1 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 2 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 2 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 3 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 4 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 5 } ^ { a } ) \right] + } \\ & { \qquad \mathbb { E } \left[ M ( b _ { o , 5 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 6 } ^ { a } ) \right] + \mathbb { E } \left[ M ( b _ { o , 7 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 8 } ^ { a } ) \right] . } \end{array}
+$$
+
+Note that as long as $\lambda _ { u } ^ { a } \ > \ 0$ , $A$ is a symmetric positive definite matrix and hence is invertible. Compared to the binary case, the unary operator can be regarded as a special binary operator where one of the operand is a constant, absorbed into operator learning, and jointly solved.
+
+To predict the answer representation, we solve another optimization problem, i.e.,”› › ı
+
+$$
+\widehat { M _ { u } ^ { a } } = \arg \operatorname* { m i n } _ { M } \ell _ { u } ^ { a } ( M ) = \mathbb { E } \left[ \left\| M ( b _ { o , 8 } ^ { a } ) \mathcal { T } _ { u } ^ { a } - M \right\| _ { F } ^ { 2 } \right] .
+$$
+
+Taking its derivative and setting it to 0, we have“
+
+$$
+\widehat { M _ { u } ^ { a } } = \mathbb { E } \left[ M ( b _ { o , 8 } ^ { a } ) \right] { \mathcal { T } } _ { u } ^ { a } .
+$$
+
+Note that this is exactly the execution of the learned operator.
+
+Binary Operator The optimization problem for the binary case can be expanded as´ ” ı
+
+$$
+\begin{array} { r l } & { \mathcal { T } _ { b } ^ { a } = \mathop { \arg \operatorname* { m i n } } \ell _ { b } ^ { a } ( \mathcal { T } ) = 1 / 2 \times ( \mathbb { E } [ \| M ( b _ { o , 1 } ^ { a } ) \mathcal { T } M ( b _ { o , 2 } ^ { a } ) - M ( b _ { o , 3 } ^ { a } ) \| _ { F } ^ { 2 } ] +  } \\ & { \qquad \mathbb { E } [ \| M ( b _ { o , 4 } ^ { a } ) \mathcal { T } M ( b _ { o , 5 } ^ { a } ) - M ( b _ { o , 6 } ^ { a } ) \| _ { F } ^ { 2 } ] ) + \lambda _ { b } ^ { a } \| \mathcal { T } \| _ { F } ^ { 2 } . } \\ & { \mathop { \gamma _ { \mathrm { e \ t \ o t e \ t h a t , a s s u m i n g ~ i n d e p e n d e n c e , \ t h e \ s o l u t i o n ~ s a t i s f i e s } } } } \\ & { \mathbb { E } [ M ( b _ { o , 1 } ^ { a } ) ^ { T } M ( b _ { o , 1 } ^ { a } ) ] \mathcal { T } \mathbb { E } [ M ( b _ { o , 2 } ^ { a } ) M ( b _ { o , 2 } ^ { a } ) ^ { T } ] + } \\ & { \mathbb { E } [ M ( b _ { o , 4 } ^ { a } ) ^ { T } M ( b _ { o , 4 } ^ { a } ) ] \mathcal { T } \mathbb { E } [ M ( b _ { o , 5 } ^ { a } ) M ( b _ { o , 5 } ^ { a } ) ^ { T } ] + 2 \lambda _ { b } ^ { a } \mathcal { T } } \\ & { = \mathbb { E } [ M ( b _ { o , 1 } ^ { a } ) ^ { T } ] \mathbb { E } [ M ( b _ { o , 2 } ^ { a } ) ] \mathbb { E } [ M ( b _ { o , 5 } ^ { a } ) ^ { T } ] + \mathbb { E } [ M ( b _ { o , 4 } ^ { a } ) ^ { T } ] \mathbb { E } [ M ( b _ { o , \varepsilon } ^ { a } ) ] \mathbb { E } [ M _ { \varepsilon } ^ { a } ] ^ { T } ] + h _ { b } ^ { a } \| \mathcal { T } \| _ { F } ^ { 2 } . } \end{array}
+$$
+
+This is a linear matrix equation and can be turned into a linear equation by vectorization. Using $\operatorname { v e c } ( A T B ) = A \otimes B \operatorname { v e c } ( T )$ (Lancaster, 1970), where $\otimes$ denotes the Kronecker product, we have
+
+$$
+\mathrm { v e c } ( { \mathcal T } _ { b } ^ { a } ) = A ^ { - 1 } B ,
+$$
+
+where
+
+$$
+\begin{array} { r l } & { A = \mathbb { E } \left[ M ( b _ { o , 1 } ^ { a } ) ^ { T } M ( b _ { o , 1 } ^ { a } ) \right] \otimes \mathbb { E } \left[ M ( b _ { o , 2 } ^ { a } ) M ( b _ { o , 2 } ^ { a } ) ^ { T } \right] + } \\ & { \qquad \mathbb { E } \left[ M ( b _ { o , 4 } ^ { a } ) ^ { T } M ( b _ { o , 4 } ^ { a } ) \right] \otimes \mathbb { E } \left[ M ( b _ { o , 5 } ^ { a } ) M ( b _ { o , 5 } ^ { a } ) ^ { T } \right] + 2 \lambda _ { b } ^ { a } I } \end{array}
+$$
+
+and
+
+$$
+\begin{array} { r l } & { B = \mathrm { v e c } \left( { \mathbb E } \left[ M ( b _ { o , 1 } ^ { a } ) ^ { T } \right] { \mathbb E } \left[ M ( b _ { o , 3 } ^ { a } ) \right] { \mathbb E } \left[ M ( b _ { o , 2 } ^ { a } ) ^ { T } \right] \right) + } \\ & { \quad \mathrm { v e c } \left( { \mathbb E } \left[ M ( b _ { o , 4 } ^ { a } ) ^ { T } \right] { \mathbb E } \left[ M ( b _ { o , 6 } ^ { a } ) \right] { \mathbb E } \left[ M ( b _ { o , 5 } ^ { a } ) ^ { T } \right] \right) . } \end{array}
+$$
+
+Note that $A$ is also symmetric positive definite given positive $\lambda _ { b } ^ { a }$ and hence invertible.
+
+The predicted answer representation is given by”
+
+$$
+\widehat { M _ { b } ^ { a } } = \underset { M } { \arg \operatorname* { m i n } } \ell _ { b } ^ { a } ( \bar { M } ) = \mathbb { E } \left[ \left\| M ( b _ { o , 7 } ^ { a } ) \mathcal { T } _ { b } ^ { a } M ( b _ { o , 8 } ^ { a } ) - M \right\| _ { F } ^ { 2 } \right] ,
+$$
+
+which can be solved by executing the induced binary operator $\widehat { M _ { b } ^ { a } } = \mathbb { E } \left[ M ( b _ { o , 7 } ^ { a } ) \right] { \mathcal { T } } _ { b } ^ { a } \mathbb { E } \left[ M ( b _ { o , 8 } ^ { a } ) \right]$
+
+Ternary Operator A ternary operation can be regarded as an unary operation on elements defined on rows $/$ columns. Specifically, we propose to construct the algebraic representation of a row $/$ column by concatenating the algebraic representation of each panel in it, i.e.,
+
+$$
+M ( b _ { o , i } ^ { a } , b _ { o , i + 1 } ^ { a } , b _ { o , i + 2 } ^ { a } ) = [ M ( b _ { o , i } ^ { a } ) ; M ( b _ { o , i + 1 } ^ { a } ) ; M ( b _ { o , i + 2 } ^ { a } ) ] .
+$$
+
+Then the ternary operator can be solved by”
+
+$$
+\mathcal { T } _ { t } ^ { a } = \underset { \mathcal { T } } { \arg \operatorname* { m i n } } \ell _ { t } ^ { a } ( \mathcal { T } ) = \mathbb { E } \left[ \left\| M \big ( b _ { o , 1 } ^ { a } , b _ { o , 2 } ^ { a } , b _ { o , 3 } ^ { a } \big ) \mathcal { T } - M \big ( b _ { o , 4 } ^ { a } , b _ { o , 5 } ^ { a } , b _ { o , 6 } ^ { a } \big ) \right\| _ { F } ^ { 2 } \right] + \lambda _ { t } ^ { a } \left\| \mathcal { T } \right\| _ { F } ^ { 2 } .
+$$
+
+Similar to the unary case discussed above,
+
+$$
+\mathcal { T } _ { t } ^ { a } = A ^ { - 1 } B
+$$
+
+where
+
+$$
+A = \mathbb { E } \left[ M ( b _ { o , 1 } ^ { a } , b _ { o , 2 } ^ { a } , b _ { o , 3 } ^ { a } ) ^ { T } M ( b _ { o , 1 } ^ { a } , b _ { o , 2 } ^ { a } , b _ { o , 3 } ^ { a } ) \right] + \lambda _ { t } ^ { a } I
+$$
+
+and
+
+$$
+B = \mathbb { E } \left[ M ( b _ { o , 1 } ^ { a } , b _ { o , 2 } ^ { a } , b _ { o , 3 } ^ { a } ) ^ { T } \right] \mathbb { E } \left[ M ( b _ { o , 4 } ^ { a } , b _ { o , 5 } ^ { a } , b _ { o , 6 } ^ { a } ) \right] .
+$$
+
+Correspondingly, the answer representation can be obtained by first executing the ternary operator“ ‰ $\mathbb { E } \left[ M ( \mathbf { \dot { \boldsymbol { b } } } _ { o , 4 } ^ { a } , \boldsymbol { b } _ { o , 5 } ^ { a } , \boldsymbol { b } _ { o , 6 } ^ { a } ) \right] \mathcal { T } _ { t } ^ { a }$ and slicing it from the result.
+
+To compute the operator distribution, we model it based on the fitness of each operator type,
+
+$$
+\begin{array} { c } { { P ( T ^ { a } = T _ { u } ^ { a } \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) \propto \exp ( - \ell _ { u } ^ { a } ( T _ { u } ^ { a } ) ) } } \\ { { P ( T ^ { a } = T _ { b } ^ { a } \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) \propto \exp ( - \ell _ { b } ^ { a } ( T _ { b } ^ { a } ) ) } } \\ { { P ( T ^ { a } = T _ { t } ^ { a } \mid \{ I _ { o , i } \} _ { i = 1 } ^ { 8 } ) \propto \exp ( - \ell _ { t } ^ { a } ( T _ { t } ^ { a } ) ) . } } \end{array}
+$$
+
+# B INSTANCES OF OPERATORS
+
+In the original work of Zhang et al. (2019a) and Hu et al. (2020), there are four operators: Constant, Progression, Arithmetic, and Distribute of Three. Progression is parameterized by its step size $( \pm 1 / 2 )$ . Arithmetic includes addition and subtraction. And Distribute of Three is implemented as shifting and can be either a left shift or a right one. Note that Constant can be regarded as special Progression with a step size of 0. In this work, we group all four operators into three types: unary (Constant and Progression), binary (Arithmetic), and ternary (Distribute of Three).
+
+To study systematic generalization in abstract relation learning, we use the RPM generation method proposed in (Zhang et al., 2019a; Hu et al., 2020) and carefully split data into three regimes:
+
+• Systematicity: The training set and the test set contain all three types of operators but disjoint instances. Specifically, the training set has Constant, Progression of $\pm 1$ , addition in Arithmetic, and left shift in Distribute of Three, while in the test set there are Progression of $\pm 2$ , subtraction in Arithmetic, and right shift in Distribute of Three.   
+• Productivity: The training set contains only unary operators and the test set only binary operators. Specifically, the training set has Constant and all instances of Progression, while the test set all instances of Arithmetic.   
+• Localism: The training set contains only binary operators and the test set only unary operators. Specifically, the training set has all instances of Arithmetic and the test set Constant and all instances of Progression.
+
+Please see Figs. S1 to S3 for examples in the three splits.
+
+# C IMPLEMENTATION DETAILS
+
+# C.1 NETWORK ARCHITECTURE
+
+We use a LeNet-like architecture (LeCun et al., 1998) for each branch of the object CNN. See Table S1 for the design. Note that the object CNN consists of four branches, including objectiveness, type, size, and color. The parameters for Convolution denote the output channel size, kernel size, and stride, respectively. A BatchNorm layer is parameterized by the number of channels, whereas a MaxPool layer by its stride. An output size is used to specify a Linear layer’s parameter. $m$ equals 2, 5, 6, 10 for objectiveness, type, size, and color, respectively. For numerical stability, we use LogSoftMax to turn a probability simplex into its log space.
+
+![](images/6a5c109d132e3b49d4d3382f5853893261e640d26bfe8f929b371db6630ba8a0.jpg)  
+Figure S1: A training example (left) and a test example (right) in the systematicity split. Note that in the training example, the arithmetic relation (in number) is addition and the shifting is always a left shift (in type, size, and color). In the test example, the shifting becomes a right shift (in type), the size progression has a step of 2, and color arithmetic becomes subtraction.
+
+![](images/a397ac680e2be2c5dbd1968f992c50c073ebf95f08d03d32f88e2dc78cb850ec.jpg)  
+Figure S2: A training example (left) and a test example (right) in the productivity split. Note that in the training example, the constant rule is applied to the number, type, and size, while the progression rule is applied on color. In the testing example, the arithmetic rule is applied on all attributes.
+
+![](images/c92fa5e0cb2722717b81a61f8fbb2a8f323df1ba7a583809a62122a15ade41be.jpg)  
+Figure S3: A training example (left) and a test example (right) in the localism split. Note that in the training example, the arithmetic rule is on all attributes. In the test example, the progression rule is applied on number and the constant rule on all other attributes.
+
+Table S1: The network architecture used for each branch of the object CNN.   
+
+<table><tr><td>Operator</td><td>Parameters</td></tr><tr><td>Convolution BatchNorm SoftPlus</td><td>[6,5,1] 6</td></tr><tr><td>MaxPool Convolution</td><td>2 [16,5,1]</td></tr><tr><td>BatchNorm SoftPlus</td><td>16</td></tr><tr><td>MaxPool Linear</td><td>2 120</td></tr><tr><td>SoftPlus</td><td></td></tr><tr><td></td><td></td></tr><tr><td>Linear</td><td>84</td></tr><tr><td>SoftPlus</td><td></td></tr><tr><td>Linear LogSoftMax</td><td>m</td></tr></table>
+
+# C.2 OTHER HYPERPARAMETERS
+
+For the inner regularized linear regression, we set different regularization coefficients for different attributes but, for the same attribute, we keep them the same across all three types of operators. For position, $\lambda = 1 0 ^ { - 4 }$ . For number, $\lambda = 1 0 ^ { - 6 }$ . For type, $\lambda = 1 0 ^ { - 6 }$ . For size, $\dot { \lambda } = 1 0 ^ { - 6 }$ . For color, $\mathrm { \bar { \lambda } } = 5 \times 1 0 ^ { - 7 }$ . All of the regularization terms in Eq. (9) in the main text are set to be 1 and $\{ M _ { 0 } ^ { a } \}$ and $\{ M ^ { a } \}$ are initialized as $2 \times 2$ square matrices.
+
+For training, we first train for 10 epochs parameters regarding objectiveness, including the objectiveness branch, and the representation matrices on position and number. We then perform 2 rounds of cyclic training on parameters regarding type, size, and color, each of which experiences 10 epochs of updates in a round. Finally, we fine-tune all parameters for another 10 epochs, totaling up to 80 training epochs. The entire system is optimized using ADAM (Kingma & Ba, 2014) with a learning rate of $\mathrm { \bar { 9 . 5 } \times 1 0 ^ { - 5 } }$ .
+
+# D MARGINALIZATION FOR OTHER ATTRIBUTES
+
+For the attribute of position, we denote its value as $R ^ { o }$ , a binary vector of length $N$ , with each entry corresponding to one of the $N$ windows. Then
+
+$$
+P ( { \mathrm { P o s i t i o n } } = R ^ { o } ) = \prod _ { j = 1 } ^ { N } P ( r _ { j } ^ { o } = R _ { j } ^ { o } ) ,
+$$
+
+where $P ( r _ { j } ^ { o } )$ denotes the $j$ th region’s estimated objectiveness distribution returned by a CNN as in the main text.
+
+For the attribute of type, the panel attribute of type being ¨ $k$ is evaluated as˛
+
+$$
+P ( \mathrm { T y p e } = k ) = \sum _ { R ^ { o } } \left( \prod _ { j , R _ { j } ^ { o } = 1 } ^ { \cdot } P ( r _ { j } ^ { t } = k ) \right) P ( \mathrm { P o s i t i o n } = R ^ { o } ) ,
+$$
+
+where $P ( r _ { j } ^ { t } )$ denotes the $j$ th region’s estimated type distribution returned by a CNN.
+
+The computation for size and color is exactly the same as type, except that we use the region’s estimated size and color distribution returned by a CNN.
+
+# E RELATED WORK ON NEURAL THEOREM PROVING
+
+Combining neural architectures with symbolic reasoning has a long history in the field of theorem proving (Garcez et al., 2012), with early works dated back to propositional rules (Shavlik & Towell, 1991; Towell & Shavlik, 1994; Garcez & Zaverucha, 1999). Later works extend the propositional rules to first-order inference (Shastri, 1992; Ding, 1995; Franc¸a et al., 2014; Sourek et al., 2015; Cohen, 2016). More recent works include the Logic Tensor Networks (Serafini & Garcez, 2016) and the NTP model (Rocktaschel & Riedel, 2017). The former grounds first-order logics and supports func- ¨ tion terms, while the latter is constructed from Prolog’s backward chaining and is related to Komendantskaya (2011); Hiolldobler (1990) but supports function-free terms. DeepProbLog (Manhaeve et al., 2018) further improves on NTP by focusing on tight interactions between a neural component and subsymbolic representation and parameter learning for both the neural and the logic components. Evans & Grefenstette (2018) introduces a differentiable rule induction process, though not integrating the neural and symbolic components. Our work is related to the stream of work on neural theorem proving. However, we formulate the relation induction process as continuous optimization rather than logical induction.
+
+# F MORE ON NEURAL VISUAL PERCEPTION
+
+• Why not train a CNN to predict the position and number of objects? The CNN is trained to predict the type, size, color, and object existence in a window. The object existence in windows is marginalized to be a Number distribution and Position distribution. This is a light-weight method for object detection. Nevertheless, it is also possible to use a Fast-RCNN like method to predict object positions (this implies number) directly. However, in this way, the framework loses the probabilistic interpretation (the object proposal branch is currently still deterministic), and we cannot perform end-to-end learning.
+
+• How does the CNN predict the presence of an object, its type, size, and color given that it is not trained to do that? For each window, the CNN outputs 4 softmaxed vectors, corresponding to the probability distributions of object existence, object type, object size, and object color. The spaces for these attributes are pre-defined. CNN’s weights are then jointly trained in the framework. Such a design follows recent neuro-symbolic methods (Mao et al., 2019; Han et al., 2019) that also rely on the implicitly trained representation. In short, we assign semantics to the implicitly trained representation (probability distributions for attributes), performs marginalization and reasoning as if they are groundtruth attribute distributions, and jointly train using only the problem’s target label.