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+# Semi-Supervised Semantic Segmentation via Adaptive Equalization Learning
+
+Hanzhe $\mathbf { H } \mathbf { u } ^ { 1 , 4 * }$ Fangyun Wei2† Han $\mathbf { H } \mathbf { u } ^ { 2 }$ Qiwei $\mathbf { Y e } ^ { 2 }$ Jinshi Cui1 Liwei Wang1,3†
+
+1Key Laboratory of Machine Perception (MOE), School of EECS, Peking University 2Microsoft Research Asia 3Institute for Artificial Intelligence, Peking University 4Zhejiang Lab huhz@pku.edu.cn {fawe, hanhu, qiwye}@microsoft.com {cjs, wanglw}@cis.pku.edu.cn
+
+# Abstract
+
+Due to the limited and even imbalanced data, semi-supervised semantic segmentation tends to have poor performance on some certain categories, e.g., tailed categories in Cityscapes dataset which exhibits a long-tailed label distribution. Existing approaches almost all neglect this problem, and treat categories equally. Some popular approaches such as consistency regularization or pseudo-labeling may even harm the learning of under-performing categories, that the predictions or pseudo labels of these categories could be too inaccurate to guide the learning on the unlabeled data. In this paper, we look into this problem, and propose a novel framework for semi-supervised semantic segmentation, named adaptive equalization learning (AEL). AEL adaptively balances the training of well and badly performed categories, with a confidence bank to dynamically track category-wise performance during training. The confidence bank is leveraged as an indicator to tilt training towards under-performing categories, instantiated in three strategies: 1) adaptive Copy-Paste and CutMix data augmentation approaches which give more chance for under-performing categories to be copied or cut; 2) an adaptive data sampling approach to encourage pixels from under-performing category to be sampled; 3) a simple yet effective re-weighting method to alleviate the training noise raised by pseudo-labeling. Experimentally, AEL outperforms the state-of-the-art methods by a large margin on the Cityscapes and Pascal VOC benchmarks under various data partition protocols. Code is available at https://github.com/hzhupku/SemiSeg-AEL.
+
+# 1 Introduction
+
+Supervised semantic segmentation requires pixel-level labeling, which is expensive and timeconsuming. This paper is interested in semi-supervised semantic segmentation, which can greatly reduce the efforts of pixel-level annotation, yet may maintain reasonably high accuracy. One problem of common semantic segmentation datasets is that the pixel categories tend to be imbalanced, e.g., the pixel amount of head classes can be hundreds of times larger than that of tailed classes in the widely used Cityscapes dataset [1]. The situation is more serious in the semi-supervised setting where tailed classes may have extremely few samples. We note that recent approaches are mainly dedicated to the design of consistency regularization [2, 3, 4, 5, 6, 7] and pseudo-labeling [8], almost all of which neglect the imbalance problem and treat each category equally, leading to a biased training. These approaches may even harm the learning of tailed classes, as inaccurate predictions or pseudo labels of under-performing categories could falsely guide the learning on unlabeled data.
+
+![](images/84c6174aadda18785e0a8538eb9589ef4d316b175cfc238cddd91ba661a8ef2d.jpg)  
+Figure 1: We count the the training samples of each category on Cityscapes train set under 1/16 and 1/32 data partition protocols, and compare the proposed AEL with a strong semi-supervised learning baseline described in Section 3.2 which treats each category equally. Our method strives to tilt training towards tailed categories which usually tend to be under-performing.
+
+This paper aims to alleviate this biased training problem. We propose a novel Adaptive Equalization Learning (AEL) framework, which adaptively balance the training of different categories as shown in Figure 1. Our design follows two main principles: 1) increasing the proportion of training samples from the under-performing categories; 2) tilting training towards under-performing categories. Concretely, we maintain a confidence bank to dynamically record the category-wise performance at each training step, which indicates the current performance of each category. Following principle 1), we propose two data augmentation approaches named adaptive Copy-Paste and adaptive CutMix, which give more chance for under-performing categories to be copied or cut. Following principle 2), we present an adaptive equalization sampling strategy to encourage pixels from under-performing categories to be sufficiently trained. In addition, we also introduce a simple yet effective re-weighting strategy which takes the model predictions into account to alleviate the issue that semi-supervised learning usually suffers from the training noise.
+
+Experimentally, by using the DeepLabv $^ { 3 + }$ with ResNet-101 backbone, the proposed AEL outperforms state-of-the-art methods by a large margin on the Cityscapes and PASCAL VOC 2012 benchmarks under various data partition protocols. Specifically, it achieves $7 4 . 2 8 \%$ , $7 5 . 8 3 \%$ and $7 7 . 9 0 \%$ on Cityscapes dataset under 1/32, 1/16 and 1/8 protocols, which is $+ 1 6 . 3 9 \%$ , $+ 1 2 . 8 7 \%$ and $+ 8 . 0 9 \%$ better than the supervised baseline. When evaluated on PASCAL VOC 2012 benchmark, it achieves $7 6 . 9 7 \%$ , $7 7 . 2 0 \%$ and $7 7 . 5 7 \%$ under 1/32, 1/16 and 1/8 protocols, which is $+ 6 . 8 3 \%$ , $+ 6 . 6 0 \%$ and $+ 4 . 4 5 \%$ better than the supervised baseline. Moreover, the proposed approach also proves to improve the segmentation model trained on the full Cityscapes train set by $+ 1 . 0 3 \%$ by leveraging $5 , 0 0 0$ images from the Cityscapes coarse set as unlabeled data, achieving $8 1 . 9 5 \%$ .
+
+# 2 Related Work
+
+Semi-Supervised Learning. Recent years have witnessed a significant progress in the SSL field. Most of them can be categorized into consistency regularization, entropy minimization [9] and pseudo-labeling. Consistency regularization [10, 11, 12] enforces consistency in predictions between different views of unlabeled data. Pseudo-labeling [13, 14] trains the model on the unlabeled data with pseudo labels generated from the model’s own predictions. Furthermore, [10, 15, 16, 17, 18] use a low softmax temperature to sharpen the predictions of unlabeled set. Our method refers to Mean Teacher [11] and FixMatch [14] when designing our basic framework.
+
+Semi-Supervised Semantic Segmentation. Existing semi-supervised semantic segmentation methods mainly focus on the design of consistency regularization and pseudo-labeling. Cutmix-Seg [2] applies CutMix augmentation on the unlabeled data. CCT [4] introduces a feature-level perturbation and enforces consistency among the predictions of different decoders. GCT [19] performs network perturbation by using two differently initialized segmentation models and encourages consistency between the predictions from the two models. PseudoSeg [8] focuses on improving the quality of pseudo labels. Though achieving satisfactory improvements over the supervised baseline, none of the aforementioned methods explore the biased learning issue in semi-supervised semantic segmentation.
+
+![](images/42cbc8a37147395065c989b541dfb776a6b6bd21d0bf2f7408ca9772d449ae9a.jpg)  
+Figure 2: Overview of AEL. We adopt the teacher-student architecture as our basic framework. The teacher model is updated by the exponential moving average (EMA) of the student model. Confidence bank is uesd to dynamically record the category-wise performance during training. Adaptive CutMix and adaptive Copy-Paste are applied on the unlabeled and labeled data respectively to provide sufficient training samples from the under-performing categories. Adaptive equalization sampling (AES) encourages the training to involve more samples from the under-performing categories to make the training unbiased. Dynamic re-weighting strategy aims to alleviate the noise of pseudo-labeling.
+
+Class Imbalance in Semi-Supervised Learning. Although SSL has been extensively studied, class imbalance problem in SSL is relatively under-explored, especially for semantic segmentation. Yang et al. [20] demonstrate that leveraging unlabeled data can alleviate imbalance issue. Hyun et al. [21] propose a suppressed consistency loss for class-imbalanced image classification problems. CReST [22] introduces a self-training framework for imbalanced SSL. Our method, though not explicitly targeting at the class imbalance problem, focuses on improving the performance of underperforming categories which are mostly tailed classes. Moreover, we refer to the ideas of resampling [23, 24] and re-weighting [25, 26], which are designed for class imbalance problem.
+
+# 3 Method
+
+Given a labeled set $\mathcal { D } ^ { l } = \{ ( \boldsymbol { \mathbf { \mathit { x } } } _ { i } ^ { l } , \boldsymbol { \mathbf { \mathit { y } } } _ { i } ^ { l } ) \}$ and an unlabeled set $\mathcal { D } ^ { u } = \{ \pmb { x } _ { i } ^ { u } \}$ , the objective of semisupervised semantic segmentation is to learn a segmentation model by efficiently leveraging both labeled and unlabeled data. In this section, we first present an overview of the proposed AEL in Section 3.1. Then we describe our basic framework for semi-supervised semantic segmentation in Section 3.2. Finally, the details of AEL are introduced in Section 3.3.
+
+# 3.1 Overview
+
+Figure 2 displays an overview of AEL, which is a data-efficient framework for semi-supervised semantic segmentation. It is composed of two parts: 1) a basic framework which contains a teacher model for pseudo-labeling and a student model for online learning; 2) dedicated modules which encourages the under-performing categories to be sufficiently trained by effectively leveraging both labeled and unlabeled data. We use the proposed confidence bank to dynamically record the categorywise performance during training, and thus we can easily identify which categories are not sufficiently trained. For those unsatisfactory categories, we present two data augmentation methods to increase their frequency of occurrence in a training batch, namely adaptive CutMix which is applied on the unlabeled data, and adaptive Copy-Paste which is applied on the labeled data. To make the model towards the unbiased learning, we propose the adaptive equalization sampling and dynamic re-weighting strategies to involve enough samples from the under-performing categories into the training, and alleviate the noise raised by pseudo-labeling simultaneously.
+
+# 3.2 Basic Framework
+
+We first set up a basic framework for semi-supervised semantic segmentation. The framework consists of a student model and a teacher model. The teacher model has the same architecture as the student model, but uses a different set of weights which are updated by exponential moving average (EMA) of the student model [11]. Following FixMatch [14], we use the teacher model to generate a set of pseudo labels $\hat { \mathcal { V } } = \{ \hat { y } _ { i } \}$ on the weakly augmented unlabeled data $\mathcal { D } ^ { u }$ . Subsequently, the student model is trained on both labeled data $\mathcal { D } ^ { l }$ (of weak augmentation) with the ground-truth and unlabeled data $\mathcal { D } ^ { u }$ (of strong augmentation) with the generated pseudo labels $\hat { \mathcal { V } }$ . We use standard random resize and random horizontal flip as the weak augmentation. Strong augmentation includes CutMix [27] and all data augmentation strategies used in the weak augmentation.
+
+The overall loss consists of the supervised loss $\mathcal { L } _ { s }$ and the unsupervised loss $\mathcal { L } _ { u }$ :
+
+$$
+\begin{array} { l } { { \displaystyle { \mathcal { L } } _ { s } = \frac { 1 } { N _ { l } } \sum _ { i = 1 } ^ { N _ { l } } \frac { 1 } { W H } \sum _ { j = 1 } ^ { W H } \ell _ { c e } ( y _ { i j } , { p } _ { i j } ) } , } \\ { { \displaystyle { \mathcal { L } } _ { u } = \frac { 1 } { N _ { u } } \sum _ { i = 1 } ^ { N _ { u } } \frac { 1 } { W H } \sum _ { j = 1 } ^ { W H } \ell _ { c e } ( \hat { y } _ { i j } , { p } _ { i j } ) } , } \end{array}
+$$
+
+where $\pmb { p } _ { i j }$ is the prediction of the $j$ -th pixel in the $i$ -th labeled (or unlabeled) image, $N _ { l }$ and $N _ { u }$ denote the number of labeled images and unlabeled images in a training batch, $W$ and $H$ represent the width and height of the input image, and $\ell _ { c e }$ denotes the standard pixel-wise cross-entropy loss. We define the overall loss function as:
+
+$$
+\mathcal { L } = \mathcal { L } _ { s } + \alpha \mathcal { L } _ { u } ,
+$$
+
+where $\alpha$ controls the contribution of the unsupervised loss.
+
+# 3.3 Adaptive Equalization Learning
+
+The baseline framework, though achieving competitive results compared with previous related works, neglects the key issues in semi-supervised semantic segmentation. Due to the limited labeled data, semi-supervised learning tends to have poor performance on some certain categories, e.g., tailed categories in Cityscapes dataset which exhibits a long-tailed label distribution. Insufficient training on these categories introduces more noise of pseudo labels which can disrupt the learning process. The proposed AEL framework aims to alleviate the degradation of under-performing categories during the semi-supervised training. Concretely, we maintain a confidence bank to record the performance of each category during training. The confidence bank enables us to identify the under-performing categories. To improve the performance of these categories and further make the training unbiased, we propose a series of technologies to efficiently leverage both labeled and unlabeled data, namely adaptive CutMix, adaptive Copy-Paste, adaptive equalization sampling and dynamic re-weighting.
+
+Confidence Bank. To tackle the biased training, previous methods [25, 26, 22, 28] always rely on the prior knowledge such as the number of training samples of each category to design the ad hoc sampling and weighting strategies. However, the performance of each category is not always strictly proportional to the number of training samples, because some categories tend to have discriminative features and thus fewer samples are required for training. Inspired by the recent progress [29] which applies active learning on semantic segmentation, we propose to maintain a confidence bank to record the category-wise performance during training. An indicator is needed to assess the performance of each category.
+
+We consider several indicators, namely Confidence, Margin and Entropy. Formally, we define Confidence indicator as:
+
+$$
+\mathrm { C o n f } ^ { c } = \frac { 1 } { N _ { l } } \sum _ { i = 1 } ^ { N _ { l } } \frac { 1 } { N _ { i } ^ { c } } \sum _ { j = 1 } ^ { N _ { i } ^ { c } } p _ { i j } ^ { c } , c \in \{ 1 , \dots , C \}
+$$
+
+where $C$ is the category number, $N _ { i } ^ { c }$ denotes the number of pixels belonging to category $c$ according to its ground-truth ${ \bf { \it y } } _ { i } , { \bf { \it p } } _ { i j } ^ { c }$ denotes the $c$ -th channel prediction of the $j$ -th pixel in the $i$ -th image.
+
+Define Margin indicator as:
+
+$$
+\mathrm { M a r g i n } ^ { c } = \frac { 1 } { N _ { l } } \sum _ { i = 1 } ^ { N _ { l } } \frac { 1 } { N _ { i } ^ { c } } \sum _ { j = 1 } ^ { N _ { i } ^ { c } } ( p _ { i j } ^ { c } - \operatorname * { m a x } _ { c ^ { \prime } \in \{ 1 , \dots , C \} } p _ { i j } ^ { c ^ { \prime } } ) , ~ c \in \{ 1 , \dots , C \}
+$$
+
+where $\mathrm { m a x 2 ( \cdot ) }$ denotes the second largest value operator. At last, we define Entropy indicator as:
+
+$$
+\mathrm { E n t } ^ { c } = - \frac { 1 } { N _ { l } } \sum _ { i = 1 } ^ { N _ { l } } \frac { 1 } { N _ { i } ^ { c } } \sum _ { j = 1 } ^ { N _ { i } ^ { c } } \sum _ { c ^ { \prime } = 1 } ^ { C } p _ { i j } ^ { c ^ { \prime } } \log p _ { i j } ^ { c ^ { \prime } } , c \in \{ 1 , \ldots , C \} .
+$$
+
+For all of the indicators, we only take into account predictions from labeled data. Experimentally, the confidence indicator serves best in our AEL and thus we adopt it by default (see Section 4.3 for the comparison). We use EMA to update the category-wise confidence at each training step:
+
+$$
+\mathrm { C o n f } _ { k } ^ { c } \gets \tau \mathrm { C o n f } _ { k - 1 } ^ { c } + ( 1 - \tau ) \mathrm { C o n f } _ { k } ^ { c } , \ c \in \{ 1 , \ldots , C \} ,
+$$
+
+where $k$ denotes the $k$ -th iteration, $\tau \in [ 0 , 1 )$ is the momentum coefficient which is set to 0.999 experimentally. Through the confidence bank, we can easily identify the under-performing categories for the current model.
+
+Adaptive CutMix. Here we introduce the proposed adaptive CutMix (see Figure 2 for illustration) which is applied on the unlabeled data. It aims to increase the frequency of occurrence of the under-performing samples from the unlabeled data. We first formulate the original CutMix [27] as:
+
+$$
+\begin{array} { r } { \hat { I } = \mathbf { C u t M i x } ( \mathbf { C r o p } ( I _ { 1 } ) , I _ { 2 } ) , } \end{array}
+$$
+
+where $I _ { 1 }$ and $I _ { 2 }$ denote randomly selected unlabeled images, $\hat { I }$ is the augmented image, and Crop(·) represents the random crop operation.
+
+Different from the original CutMix where unlabeled images are randmoly selected, the proposed adaptive CutMix gives under-performing categories a higher sampling probability. Specifically, we first convert the category-wise confidence stored in the confidence bank to the normalized sampling probability $\pmb { r } \in \mathbb { R } ^ { C }$ , which can be formulated as:
+
+$$
+r = \mathrm { S o f t m a x } ( 1 - \mathrm { C o n f } ) .
+$$
+
+According to the sampling probability, we randomly select an unlabeled image containing the sampled category as $I _ { 1 }$ , and another unlabeled image from the training batch is randomly selected as $I _ { 2 }$ . The Crop(·) operation is performed on the region containing the chosen category. After that, we can generate the augmented image by Eq 8. Since the adaptive CutMix is performed on the unlabeled data without any annotations, we use predictions as approximate ground-truth, which works well in practice.
+
+Adaptive Copy-Paste. Copy-Paste [30] is an effective data augmentation strategy for instance segmentation. It yields significant gains on the challenging LVIS benchmark [31], especially for rare object categories. The key idea behind the Copy-Paste augmentation is to paste objects from the source image to the target image. Inspired by this, we further propose the adaptive Copy-Paste (see Figure 2 for illustration) for semi-supervised semantic segmentation. Different from adaptive CutMix, adaptive Copy-Paste augmentation strives for efficiently leveraging the labeled data. Similarly, we involve confidence bank to assess category-wise performance and use $\mathrm { E q } 9$ to compute sampling probability. The under-performing categories have higher probability to be selected for Copy-Paste. Experimentally, the proposed adaptive Copy-Paste augmentation yields slightly better performance in the category level than the instance level. Thus we copy all pixels belonging to the sampled category in the source image and paste them on the target image. Following [30], the augmented image is composed of two randomly selected images from the labeled data and a large scale jittering is applied.
+
+Adaptive Equalization Sampling. As described in Section 1, due to the limited and unbalanced labeled data, the training tends to be biased. To alleviate the training bias, we propose a novel adaptive equalization sampling strategy which focuses training on a sparse set of under-performing samples and prevents the vast number of well-trained samples from overwhelming the model during training. Concretely, we define the sampling rate $s ^ { c }$ for category $c$ as:
+
+$$
+s ^ { c } = \left[ \frac { 1 - \mathrm { C o n f } ^ { c } } { \operatorname* { m a x } _ { c \in \{ 1 , \dots , C \} } \left( 1 - \mathrm { C o n f } ^ { c } \right) } \right] ^ { \beta } , \ c \in \{ 1 , \dots , C \} ,
+$$
+
+where $\beta$ denotes a tunable parameter. Instead of using all pixels to compute the unsupervised loss, for category $c$ with the sampling rate $s ^ { c }$ , we randomly sample a subset of pixels according to their predictions. Then the unsupervised loss in Eq 2 can be reformulated as:
+
+$$
+\mathcal { L } _ { u } = \frac { 1 } { { { N _ { u } } } } { \sum _ { i = 1 } ^ { { N _ { u } } } { \frac { 1 } { { \sum _ { j = 1 } ^ { { W H } } { \mathbb { 1 } _ { i j } } } } \sum _ { j = 1 } ^ { { W H } } { \ell _ { c e } ( { \hat { y } _ { i j } } , { { p _ { i j } } } ) \mathbb { 1 } _ { i j } } } } ,
+$$
+
+where $\mathbb { 1 } _ { i j } = 1$ indicates that the $j$ -th pixel in the $i$ -th image is sampled according to the sampling rate, otherwise $\mathbb { 1 } _ { i j }$ is set to 0, the other terms are the same as in $\operatorname { E q }$ .
+
+Dynamic Re-Weighting. The performance of the model depends on the quality of pseudo labels. Existing methods [2, 4, 19] usually adopt a higher threshold on classification score to filter out most of the pixels with low-confidence. Though this strategy could alleviate the noise raised by pseudolabeling, the strict criteria leads to lower recall for the pixels from under-performing categories, which hinders the training. Another option is to discard the threshold and involve all pixels into the training. However, much more noise is introduced simultaneously. To alleviate this issue, we propose a dynamic re-weighting strategy which adds a modulating factor to the unsupervised loss in the way of semi-supervised learning. On the basis of Eq 11, we formulate our final unsupervised loss as:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { u } = \displaystyle \frac { 1 } { N _ { u } } \sum _ { i = 1 } ^ { N _ { u } } \frac { 1 } { \sum _ { j = 1 } ^ { W H } w _ { i j } } \sum _ { j = 1 } ^ { W H } w _ { i j } \ell _ { c e } ( \hat { \pmb { y } } _ { i j } , { \pmb { p } } _ { i j } ) , } \\ { w _ { i j } = \displaystyle \operatorname* { m a x } _ { c \in \{ 1 , \dots , C \} } ( p _ { i j } ^ { c } ) ^ { \gamma } \mathbb { 1 } _ { i j } , } \end{array}
+$$
+
+where $\gamma$ is the tunable parameter. Different from the Focal Loss [32] where the modulating factor is used for reducing the loss contribution from easy samples, our formulation aims to allocate more contributions for the convincing samples. The combination of adaptive equalization sampling and dynamic re-weighting not only involves more samples from the under-performing categories into the training, but also alleviate the noise raised by pseudo-labeling.
+
+# 4 Experiments
+
+# 4.1 Setup
+
+Datasets. Cityscapes [1] dataset is designed for urban scene understanding. It contains 30 classes and only 19 classes of them are used for scene parsing evaluation. The dataset contains 5, 000 finely annotated images and 20, 000 coarsely annotated images. The finely annotated 5, 000 images are split into 2, 975, 500 and 1, 525 images for training, validation and testing respectively.
+
+PASCAL VOC 2012 [33] dataset is a standard object-centric semantic segmentation dataset. It contains 20 foreground object classes and a background class. The strand training, validation and testing sets consist of 1, 464, 1, 449 and 1, 556 images, respectively. Following common practice, we use the augmented set [34] which contains 10, 582 images as the training set.
+
+ADE20K dataset [35] is a large scale scene parsing benchmark which contains dense labels of 150 stuff/object categories. The dataset includes 20K/2K/3K images for training, validation and testing.
+
+For both Cityscapes and PASCAL VOC 2012 datasets, 1/2, 1/4, 1/8, 1/16 and 1/32 training images are randomly sampled as the labeled training data, and the remaining images are used as the unlabeled data. For each protocol, AEL provides 5 different data folds and the final performance is the average of 5 folds. In addition, we also evaluate our method on the setting where the full Cityscapes train set is used as the labeled data and 1, 000, 3, 000 and 5, 000 images and randomly selected from the Cityscapes coarse set as the unlabeled data.
+
+Evaluation. We use single scale testing and adopt mean of Intersection over Union (mIoU) as the metric to evaluate the performance. We report the results on the Cityscapes val set and PASCAL VOC 2012 val set in comparisons with state-of-the-art methods. All ablation studies are conducted on the Cityscapes val set under 1/16 and 1/32 partition protocols.
+
+Implementation Details. We use ResNet-101 pretrained on ImageNet [36] as our backbone, remove the last two down-sampling operations and employ dilated convolutions in the subsequent convolution layers, making the output stride equal to 8. We use DeepLabv $^ { 3 + }$ [37] as the segmentation head. For
+
+Table 1: Comparison with state-of-the-art methods on the Cityscapes val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone.   
+
+<table><tr><td>Method</td><td>1/32 (93)</td><td>1/16 (186)</td><td>1/8 (372)</td><td>1/4 (744)</td><td>1/2 (1488)</td></tr><tr><td>Supervised</td><td>57.89</td><td>62.96</td><td>69.81</td><td>74.23</td><td>77.46</td></tr><tr><td>MT [11]</td><td>64.07</td><td>68.05</td><td>73.56</td><td>76.66</td><td>78.39</td></tr><tr><td>CCT [4]</td><td>66.35</td><td>69.32</td><td>74.12</td><td>75.99</td><td>78.10</td></tr><tr><td>Cutmix-Seg [2]</td><td>69.11</td><td>72.13</td><td>75.83</td><td>77.24</td><td>78.95</td></tr><tr><td>GCT[19]</td><td>63.21</td><td>66.75</td><td>72.66</td><td>76.11</td><td>78.34</td></tr><tr><td>AEL (Ours)</td><td>74.28</td><td>75.83</td><td>77.90</td><td>79.01</td><td>80.28</td></tr></table>
+
+Table 2: Comparison with state-of-the-art methods on the PASCAL VOC 2012 val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone.   
+
+<table><tr><td rowspan=1 colspan=2>Method</td><td rowspan=1 colspan=1>1/32 (331)</td><td rowspan=1 colspan=3>1/16 (662)</td><td rowspan=1 colspan=1>1/8 (1323)</td><td rowspan=1 colspan=1>1/4 (2646)</td><td rowspan=1 colspan=1>1/2 (5291)</td></tr><tr><td rowspan=1 colspan=2>Supervised</td><td rowspan=1 colspan=1>70.14</td><td rowspan=1 colspan=3>70.60</td><td rowspan=1 colspan=1>73.12</td><td rowspan=1 colspan=1>76.35</td><td rowspan=1 colspan=1>77.21</td></tr><tr><td rowspan=2 colspan=2>MT [11]CCT[4]</td><td rowspan=1 colspan=1>70.56</td><td rowspan=1 colspan=3>71.29</td><td rowspan=2 colspan=1>73.3373.68</td><td rowspan=2 colspan=1>76.6176.51</td><td rowspan=2 colspan=1>78.0877.40</td></tr><tr><td rowspan=3 colspan=2>CCT[4]Cutmix-Seg [2]GCT [19]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>71.22</td><td rowspan=1 colspan=1>71.86</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=2 colspan=1>73.3970.32</td><td rowspan=2 colspan=3>73.5670.90</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>73.96</td><td rowspan=1 colspan=1>77.58</td><td rowspan=1 colspan=1>78.12</td></tr><tr><td rowspan=1 colspan=1>73.29</td><td rowspan=1 colspan=1>76.66</td><td rowspan=1 colspan=1>77.98</td></tr><tr><td rowspan=1 colspan=2>AEL (Ours)</td><td rowspan=1 colspan=1>76.97</td><td rowspan=1 colspan=3>77.20</td><td rowspan=1 colspan=1>77.57</td><td rowspan=1 colspan=1>78.06</td><td rowspan=1 colspan=1>80.29</td></tr></table>
+
+Cityscapes dataset, we use stochastic gradient descent (SGD) optimizer with initial learning rate 0.01, weight decay 0.0005 and momentum 0.9. Moreover, we adopt the ‘poly’ learning rate policy, where the initial learning rate is multiplied by $\begin{array} { r } { ( 1 - \frac { \mathrm { i t e r } } { \mathrm { m a x i t e r } } ) ^ { 0 . 9 } } \end{array}$ . We adopt the crop size as $7 6 9 \times 7 6 9$ , batch size as 16 and training iterations as $1 8 \mathrm { k }$ . For PASCAL VOC 2012 dataset, we set the initial learning rate as 0.001, weight decay as 0.0001, crop size as $5 1 3 \times 5 1 3$ , batch size as 16 and training iterations as $3 0 \mathrm { k }$ . We use random horizontal flip and random resize as the default data augmentation if not specified. All the supervised baselines are trained on the labeled data.
+
+# 4.2 Comparison with State-of-the-Art Methods
+
+We compare our method with recent semi-supervised semantic segmentation methods, including Mean Teacher (MT) [11], Cross-Consistency Training (CCT) [4], Guided Collaborative Training (GCT) [19] and Cutmix-Seg [2]. For a fair comparison, we re-implement all above methods and adopt the same network architecture (DeepLabv $^ { 3 + }$ with ResNet-101 backbone).
+
+Results on Cityscapes Dataset. Table 1 compares AEL with state-of-the-art methods on the Cityscapes val set. Without leveraging any unlabeled data, the performance of the supervised baseline is unsatisfactory under various data partition protocols, especially for the fewer data settings, e.g., 1/32 and 1/16 protocols. Our method consistently promotes the baseline, achieving the improvements of $+ 1 6 . 4 \%$ , $+ 1 2 . 9 \%$ , $+ 8 . 1 \%$ , $+ 4 . 8 \%$ and $+ 2 . 8 \%$ under 1/32, 1/16, 1/8, 1/4 and 1/2 partition protocols respectively. Our method also significantly outperforms the existing state-of-the-art methods by a large margin under all data partition protocols. In particular, AEL outperforms the existing best method Cutmix-Seg by $+ 5 . 2 \%$ under extremely few data setting (1/32 protocol), and surpasses Cutmix-Seg by $+ 1 . 3 \%$ under the $1 / 2$ protocol.
+
+Results on PASCAL VOC 2012 Dataset. Table 2 shows comparison with state-of-the-art methods on the PASCAL VOC 2012 val dataset. AEL achieves consistent performance gains over the supervised baseline, obtaining an improvements of $+ 6 . 8 \%$ , $+ 7 . 0 \%$ , $+ 4 . 1 \%$ , $+ 1 . 7 \%$ and $+ 3 . 1 \%$ under 1/32, 1/16, 1/8, 1/4 and $1 / 2$ partition protocols respectively. We can see that over all protocols, AEL outperforms the state-of-the-art methods. For example, our method outperforms the previous best method by $+ 3 . 6 \%$ and $+ 2 . 2 \%$ under the 1/32 and $1 / 2$ partition protocols.
+
+Table 3: Ablation study on the effectiveness of different components: Dynamic Re-weighting (DR), Adaptive Equalization Sampling(AES), Adaptive CutMix (ACM), Adaptive Copy-Paste (ACP).   
+
+<table><tr><td rowspan=1 colspan=1>DR</td><td rowspan=1 colspan=1>AES</td><td rowspan=1 colspan=1>ACM</td><td rowspan=1 colspan=2>ACP</td><td rowspan=1 colspan=1>1/32 (93)</td><td rowspan=1 colspan=1>1/16 (186)</td></tr><tr><td rowspan=7 colspan=1>√√√√</td><td rowspan=7 colspan=1>厂√厂√</td><td rowspan=6 colspan=1>4√</td><td rowspan=5 colspan=2>√</td><td rowspan=1 colspan=1>69.11</td><td rowspan=1 colspan=1>72.13</td></tr><tr><td rowspan=1 colspan=1>70.27</td><td rowspan=1 colspan=1>73.85</td></tr><tr><td rowspan=1 colspan=1>71.65</td><td rowspan=2 colspan=1>74.1273.8972.64</td></tr><tr><td rowspan=1 colspan=1>70.4969.69</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>72.5173.43</td><td rowspan=2 colspan=1>74.3975.12</td></tr><tr><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=2>√</td><td rowspan=1 colspan=1>74.28</td><td rowspan=1 colspan=1>75.83</td></tr></table>
+
+# 4.3 Ablation Study
+
+To further understand the advantages of AEL, we conduct a series of ablation studies that examine the effectiveness of different components and different hyper-parameters. All experiments are conducted on the validation set of Cityscapes dataset.
+
+The Effectiveness of Different Components. We ablate each component of AEL step by step. Table 3 reports the studies. We use the basic framework described in Section 3.2 as our baseline, which achieves $6 9 . 1 1 \%$ and $7 2 . 1 3 \%$ under 1/32 and 1/16 protocols respectively. We first evaluate the effectiveness of each single component. As shown in the table, Dynamic Re-weighting (DR) improves the baseline by $+ 1 . 1 \%$ and $+ 1 . 7 \%$ under 1/32 and 1/16 partition protocols. Adaptive Equalization Sampling (AES) alleviates the biased training issue, achieving the improvements of $+ 2 . 5 \%$ and $+ 2 . 0 \%$ over the baseline. Adaptive CutMix (ACM) and Adaptive Copy-Paste (ACP) data augmentation approaches give more chance for under-performing categories to be sampled, and bring the improvements of $+ 1 . 3 \% / + 1 . 7 \%$ and $+ 0 . 5 \% / + 0 . 5 \%$ respectively. Furthermore, we present the performance gains in a progressive manner. On top of the DR, by leveraging AES strategy on the unsupervised loss, our method obtains improvements of $+ 2 . 3 \%$ and $+ 0 . 5 \%$ under 1/32 and 1/16 protocols. The two proposed data augmentation approaches further boost the performance to $7 4 . 2 8 \%$ and $7 5 . 8 3 \%$ , demonstrating the effectiveness of our adaptive learning.
+
+Ablation Study on Hyper-Parameters. Table 5 ablates the tunable parameter $\gamma$ in dynamic reweighting (in Eq 13), where $\gamma = 2$ yields slightly better performance. Dynamic re-weighting is found to be insensitive to $\gamma$ .
+
+Table 6 ablates the influence of different indicators, including Confidence (in Eq 4), Margin (in Eq 5), and Entropy (in Eq 6). We use the Confidence as the default indicator to assess the category-wise performance during training due to its best performance.
+
+Adaptive CutMix requires a criteria to identify whether an unlabeled image contains a certain class. We use the ratio between pseudo labels of a certain category and total pixels of the input image as the criteria. Table 7 ablates different ratios.
+
+Table 8 studies the number of sampled categories $K$ in the Adaptive Copy-Paste. We find that $K = 3$ achieves the best performance. One potential reason is that a smaller $K$ provides less training samples from the under-performing categories while a larger $K$ may increase the difficulty for training.
+
+Table 9 ablates the loss weight $\alpha$ which is used to balance the supervised loss and unsupervised loss as shown in Eq 3. As illustrated in the table, $\alpha = 1$ achieves the best performance. We use $\alpha = 1$ in our approach for all the experiments.
+
+# 4.4 Per-class Results
+
+Since the class imbalance problem is severe in the Cityscapes dataset, we provide per-class results under 1/32 data partition protocol in Table 4. We choose 9 classes with the least training samples in the Cityscapes dataset as tail classes, i.e. wall, traffic light, traffic sign, rider, truck, bus, train, motorcycle and bicycle. As shown in the table, our method not only achieves the best overall mIoU, but also obtains significant improvements on tail classes. In particular, Our method outperforms the existing best method Cutmix-Seg by $+ 5 . 2 \%$ in overall mIoU and $+ 9 . 2 \%$ in mIoU for tail classes under 1/32 partition protocol.
+
+Table 4: Per-class results on Cityscapes val set under 1/32 data partition protocol. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone.   
+
+<table><tr><td></td><td></td><td></td><td></td><td></td><td>Head Classes</td><td></td><td></td><td></td><td colspan="10">Tail Classes</td></tr><tr><td>Methods</td><td></td><td></td><td>meno </td><td>seeaara Buping </td><td>Vegeee </td><td>Eirllrn 灵</td><td>uosiad</td><td>3u</td><td></td><td>igre</td><td></td><td>rs grgen</td><td></td><td></td><td></td><td></td><td>meroreite</td><td>eaelbir</td></tr><tr><td>Supervised</td><td></td><td>57.9</td><td>39.8 94.6</td><td>72.5 87.4</td><td>42.4 51.6</td><td>88.3 49.8</td><td>91.1</td><td>74.5</td><td>89.4</td><td>21.7</td><td>47.7</td><td>59.1</td><td>33.7</td><td>43.3</td><td>37.2</td><td></td><td>11.4 42.1</td><td>62.2</td></tr><tr><td>GCT[19]</td><td>63.2</td><td>48.1</td><td>96.9</td><td>75.8 89.8</td><td>40.3 57.5 91.1</td><td>53.5</td><td>93.1 78.1</td><td>91.6</td><td></td><td>23.6 58.9</td><td></td><td>70.1</td><td>43.4</td><td>25.8</td><td>45.7</td><td>49.2</td><td>45.0</td><td>71.4</td></tr><tr><td>MT [11]</td><td>64.1</td><td>50.4</td><td>96.7</td><td>75.6 89.5</td><td>40.0 57.3 91.0</td><td>53.2</td><td>92.80 77.9</td><td>91.3</td><td></td><td>26.2 61.1</td><td></td><td>72.3</td><td>45.8</td><td>28.0</td><td>48.1</td><td>51.6</td><td>47.1</td><td>73.8</td></tr><tr><td>CCT [4]</td><td>66.4</td><td>54.2</td><td>95.7</td><td>77.2 88.6</td><td>46.5 58.5 90.1</td><td>55.5</td><td>91.5</td><td>77.9 91.8</td><td></td><td>27.9</td><td>60.5</td><td>71.8</td><td>48.0</td><td>44.5</td><td>61.4</td><td>50.7</td><td>52.0</td><td>70.5</td></tr><tr><td>Cutmix-Seg [2]</td><td>69.1</td><td>58.7</td><td>97.2</td><td>78.6 90.1</td><td>48.1 60.1 91.5</td><td>57.2</td><td>93.0 79.6</td><td>93.3</td><td></td><td>32.4</td><td>64.8</td><td>76.5</td><td>52.3</td><td>49.4</td><td>66.0</td><td>54.8</td><td>56.7</td><td>75.1</td></tr><tr><td>AEL (Ours)</td><td>74.3</td><td>67.9</td><td>97.1</td><td>78.7 90.3</td><td>52.3 62.0 91.7</td><td>59.2</td><td>93.8</td><td>81.6 94.0</td><td></td><td>37.3</td><td>67.9</td><td>77.6</td><td>60.5</td><td>65.6</td><td>83.8</td><td>74.3</td><td>66.9</td><td>77.0</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 5: Study on $\gamma$ of dynamic re-weighting.   
+
+<table><tr><td>Y</td><td>1/32</td><td>1/16</td></tr><tr><td>0</td><td>69.11</td><td>72.13</td></tr><tr><td>0.5</td><td>69.74</td><td>73.28</td></tr><tr><td>1</td><td>69.35</td><td>73.67</td></tr><tr><td>2</td><td>70.27</td><td>73.85</td></tr><tr><td>3</td><td>70.26</td><td>73.40</td></tr></table>
+
+Table 6: Study on different indicators for AES.   
+
+<table><tr><td>Indicator</td><td>1/32</td><td>1/16</td></tr><tr><td>None</td><td>70.27</td><td>73.85</td></tr><tr><td>Ent</td><td>71.38</td><td>73.21</td></tr><tr><td>Conf</td><td>72.51</td><td>74.39</td></tr><tr><td>Margin</td><td>70.86</td><td>73.05</td></tr></table>
+
+Table 7: Study on different ratios in ACM.   
+
+<table><tr><td>Ratio</td><td>1/32</td><td>1/16</td></tr><tr><td>0.001</td><td>73.27</td><td>74.28</td></tr><tr><td>0.003</td><td>73.29</td><td>74.36</td></tr><tr><td>0.005</td><td>73.43</td><td>75.12</td></tr><tr><td>0.01</td><td>72.78</td><td>73.66</td></tr></table>
+
+# 4.5 Performance on the Full Labeled Set
+
+We conduct experiments where the full Cityscapes train set is used as the labeled dataset and the Cityscapes coarse set is used as the unlabeled dataset. We do not leverage any annotations from the coarse set though it provides coarsely annotated ground-truth. We randomly sample 1,000, 3,000 and 5,000 images from the coarse set to verify the proposed method. As shown in Table 10, the proposed AEL can still improve the supervised baselines by leveraging the unlabeled data though a large amount of labeled data is provided.
+
+# 4.6 Results on ADE20K Dataset
+
+We further provide results on the ADE20K dataset [35]. Since no previous methods in semi-supervised segmentation conducted experiments on ADE20K dataset, we compare our method with supervised baseline and existing best method Cutmix-Seg on the dataset. As shown in Table 11, our method consistently promotes the supervised baseline by $6 . 3 6 \%$ , $5 . 7 0 \%$ , $5 . 6 7 \%$ , $3 . 1 8 \%$ and $1 . 4 5 \%$ , and outperforms the Cutmix-Seg by $2 . 2 5 \%$ , $3 . 3 8 \%$ , $2 . 4 8 \%$ , $1 . 3 1 \%$ and $1 . 2 6 \%$ under 1/32, 1/16, 1/8, 1/4 and 1/2 partition protocols, respectively.
+
+# 4.7 Qualitative Results
+
+Figure 3 shows the visualization results of different methods evaluated on the Cityscapes val set. We compare the proposed AEL with ground-truth, supervised baseline and our basic framework described in Section 3.2. Benefiting from a series of technologies designed for the balanced training, AEL achieves great performance on not only head categories (e.g. Road), but also tailed categories (e.g. Rider and Bicycle).
+
+Table 8: Study on number of sampled categories $K$ in ACP.   
+
+<table><tr><td>K</td><td>1/32</td><td>1/16</td></tr><tr><td>1</td><td>72.18</td><td>74.85</td></tr><tr><td>2</td><td>72.84</td><td>74.95</td></tr><tr><td>3</td><td>74.28</td><td>75.83</td></tr><tr><td>4</td><td>73.43</td><td>74.10</td></tr></table>
+
+Table 9: Study on loss weight $\alpha$ .   
+
+<table><tr><td>α</td><td>1/32</td><td>1/16</td></tr><tr><td>0.5</td><td>71.85</td><td>74.61</td></tr><tr><td>1.0</td><td>74.28</td><td>75.83</td></tr><tr><td>1.5</td><td>74.10</td><td>73.44</td></tr><tr><td>2.0</td><td>73.79</td><td>72.86</td></tr></table>
+
+Table 10: Performance on the full Cityscapes train set.   
+
+<table><tr><td rowspan=1 colspan=1>Number</td><td rowspan=1 colspan=1>Baseline</td><td rowspan=1 colspan=1>AEL</td></tr><tr><td rowspan=1 colspan=1>0</td><td rowspan=2 colspan=1>80.1680.22</td><td rowspan=2 colspan=1>80.28</td></tr><tr><td rowspan=1 colspan=1>1000</td></tr><tr><td rowspan=1 colspan=1>3000</td><td rowspan=1 colspan=1>80.55</td><td rowspan=1 colspan=1>81.36</td></tr><tr><td rowspan=1 colspan=1>5000</td><td rowspan=1 colspan=1>80.92</td><td rowspan=1 colspan=1>81.95</td></tr></table>
+
+Table 11: Comparison with supervised baseline and Cutmix-Seg on the ADE20K val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone.   
+
+<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=1>1/32 (631)</td><td rowspan=1 colspan=1>1/16 (1263)</td><td rowspan=1 colspan=1>1/8 (2526)</td><td rowspan=1 colspan=1>1/4 (5052)</td><td rowspan=1 colspan=1>1/2 (10105)</td></tr><tr><td rowspan=1 colspan=1>Supervised</td><td rowspan=1 colspan=1>22.04</td><td rowspan=1 colspan=1>27.52</td><td rowspan=1 colspan=1>32.36</td><td rowspan=1 colspan=1>36.39</td><td rowspan=1 colspan=1>41.97</td></tr><tr><td rowspan=1 colspan=1>Cutmix-Seg [2]</td><td rowspan=1 colspan=1>26.15    一</td><td rowspan=1 colspan=1>29.84</td><td rowspan=1 colspan=1>35.55</td><td rowspan=1 colspan=1>38.26</td><td rowspan=1 colspan=1>42.16</td></tr><tr><td rowspan=1 colspan=1>AEL (Ours)</td><td rowspan=1 colspan=1>28.40</td><td rowspan=1 colspan=1>33.22</td><td rowspan=1 colspan=1>38.03</td><td rowspan=1 colspan=1>39.57</td><td rowspan=1 colspan=1>43.42</td></tr></table>
+
+![](images/1dfaed8e0950061c019275aed03487718cd0bfa80cf10041a6a93e28cc20fec6.jpg)  
+Figure 3: Qualitative results on the Cityscapes val set. From left to right: input image, ground-truth, predictions of the supervised baseline, predictions of our basic framework and predictions of the proposed AEL. Orange rectangles highlight the unsatisfactory segmentation results.
+
+# 5 Conclusion
+
+In this paper, we propose a novel Adaptive Equalization Learning (AEL) framework for semisupervised semantic segmentation. Different from the existing methods dedicating to the design of consistency regularization or pseudo-labeling, AEL aims to adaptively balance the training based on the fact that pixel categories in common semantic segmentation datasets tend to be imbalanced. We introduce a confidence bank to dynamically record the category-wise performance at each training step, which enables us to identify the under-performing categories and adaptively tilt training towards these categories. Several technologies are proposed to make the training unbiased, namely adaptive Copy-Paste and CutMix, adaptive equalization sampling and dynamic re-weighting. Through the adaptive design, AEL outperforms the state-of-the-art methods by a large margin on the Cityscapes and Pascal VOC benchmarks under various data partition protocols.
+
+# Acknowledgment
+
+This work was supported by the National Key R&D Program of China under grant 2017YFB1002804 and National Natural Science Foundation of China (No. 31771230).
+
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+[36] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25:1097– 1105, 2012.   
+[37] Liang-Chieh Chen, Yukun Zhu, George Papandreou, Florian Schroff, and Hartwig Adam. Encoder-decoder with atrous separable convolution for semantic image segmentation. In Proceedings of the European conference on computer vision (ECCV), pages 801–818, 2018.

parse/train/5CGPY2VeEGb/5CGPY2VeEGb_content_list.json

@@ -0,0 +1,1385 @@
+[
+    {
+        "type": "text",
+        "text": "Semi-Supervised Semantic Segmentation via Adaptive Equalization Learning ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Hanzhe $\\mathbf { H } \\mathbf { u } ^ { 1 , 4 * }$ Fangyun Wei2† Han $\\mathbf { H } \\mathbf { u } ^ { 2 }$ Qiwei $\\mathbf { Y e } ^ { 2 }$ Jinshi Cui1 Liwei Wang1,3† ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1Key Laboratory of Machine Perception (MOE), School of EECS, Peking University 2Microsoft Research Asia 3Institute for Artificial Intelligence, Peking University 4Zhejiang Lab huhz@pku.edu.cn {fawe, hanhu, qiwye}@microsoft.com {cjs, wanglw}@cis.pku.edu.cn ",
+        "bbox": [
+            223,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            362,
+            535,
+            378
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Due to the limited and even imbalanced data, semi-supervised semantic segmentation tends to have poor performance on some certain categories, e.g., tailed categories in Cityscapes dataset which exhibits a long-tailed label distribution. Existing approaches almost all neglect this problem, and treat categories equally. Some popular approaches such as consistency regularization or pseudo-labeling may even harm the learning of under-performing categories, that the predictions or pseudo labels of these categories could be too inaccurate to guide the learning on the unlabeled data. In this paper, we look into this problem, and propose a novel framework for semi-supervised semantic segmentation, named adaptive equalization learning (AEL). AEL adaptively balances the training of well and badly performed categories, with a confidence bank to dynamically track category-wise performance during training. The confidence bank is leveraged as an indicator to tilt training towards under-performing categories, instantiated in three strategies: 1) adaptive Copy-Paste and CutMix data augmentation approaches which give more chance for under-performing categories to be copied or cut; 2) an adaptive data sampling approach to encourage pixels from under-performing category to be sampled; 3) a simple yet effective re-weighting method to alleviate the training noise raised by pseudo-labeling. Experimentally, AEL outperforms the state-of-the-art methods by a large margin on the Cityscapes and Pascal VOC benchmarks under various data partition protocols. Code is available at https://github.com/hzhupku/SemiSeg-AEL. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Supervised semantic segmentation requires pixel-level labeling, which is expensive and timeconsuming. This paper is interested in semi-supervised semantic segmentation, which can greatly reduce the efforts of pixel-level annotation, yet may maintain reasonably high accuracy. One problem of common semantic segmentation datasets is that the pixel categories tend to be imbalanced, e.g., the pixel amount of head classes can be hundreds of times larger than that of tailed classes in the widely used Cityscapes dataset [1]. The situation is more serious in the semi-supervised setting where tailed classes may have extremely few samples. We note that recent approaches are mainly dedicated to the design of consistency regularization [2, 3, 4, 5, 6, 7] and pseudo-labeling [8], almost all of which neglect the imbalance problem and treat each category equally, leading to a biased training. These approaches may even harm the learning of tailed classes, as inaccurate predictions or pseudo labels of under-performing categories could falsely guide the learning on unlabeled data. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/84c6174aadda18785e0a8538eb9589ef4d316b175cfc238cddd91ba661a8ef2d.jpg",
+        "image_caption": [
+            "Figure 1: We count the the training samples of each category on Cityscapes train set under 1/16 and 1/32 data partition protocols, and compare the proposed AEL with a strong semi-supervised learning baseline described in Section 3.2 which treats each category equally. Our method strives to tilt training towards tailed categories which usually tend to be under-performing. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This paper aims to alleviate this biased training problem. We propose a novel Adaptive Equalization Learning (AEL) framework, which adaptively balance the training of different categories as shown in Figure 1. Our design follows two main principles: 1) increasing the proportion of training samples from the under-performing categories; 2) tilting training towards under-performing categories. Concretely, we maintain a confidence bank to dynamically record the category-wise performance at each training step, which indicates the current performance of each category. Following principle 1), we propose two data augmentation approaches named adaptive Copy-Paste and adaptive CutMix, which give more chance for under-performing categories to be copied or cut. Following principle 2), we present an adaptive equalization sampling strategy to encourage pixels from under-performing categories to be sufficiently trained. In addition, we also introduce a simple yet effective re-weighting strategy which takes the model predictions into account to alleviate the issue that semi-supervised learning usually suffers from the training noise. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Experimentally, by using the DeepLabv $^ { 3 + }$ with ResNet-101 backbone, the proposed AEL outperforms state-of-the-art methods by a large margin on the Cityscapes and PASCAL VOC 2012 benchmarks under various data partition protocols. Specifically, it achieves $7 4 . 2 8 \\%$ , $7 5 . 8 3 \\%$ and $7 7 . 9 0 \\%$ on Cityscapes dataset under 1/32, 1/16 and 1/8 protocols, which is $+ 1 6 . 3 9 \\%$ , $+ 1 2 . 8 7 \\%$ and $+ 8 . 0 9 \\%$ better than the supervised baseline. When evaluated on PASCAL VOC 2012 benchmark, it achieves $7 6 . 9 7 \\%$ , $7 7 . 2 0 \\%$ and $7 7 . 5 7 \\%$ under 1/32, 1/16 and 1/8 protocols, which is $+ 6 . 8 3 \\%$ , $+ 6 . 6 0 \\%$ and $+ 4 . 4 5 \\%$ better than the supervised baseline. Moreover, the proposed approach also proves to improve the segmentation model trained on the full Cityscapes train set by $+ 1 . 0 3 \\%$ by leveraging $5 , 0 0 0$ images from the Cityscapes coarse set as unlabeled data, achieving $8 1 . 9 5 \\%$ . ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Semi-Supervised Learning. Recent years have witnessed a significant progress in the SSL field. Most of them can be categorized into consistency regularization, entropy minimization [9] and pseudo-labeling. Consistency regularization [10, 11, 12] enforces consistency in predictions between different views of unlabeled data. Pseudo-labeling [13, 14] trains the model on the unlabeled data with pseudo labels generated from the model’s own predictions. Furthermore, [10, 15, 16, 17, 18] use a low softmax temperature to sharpen the predictions of unlabeled set. Our method refers to Mean Teacher [11] and FixMatch [14] when designing our basic framework. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Semi-Supervised Semantic Segmentation. Existing semi-supervised semantic segmentation methods mainly focus on the design of consistency regularization and pseudo-labeling. Cutmix-Seg [2] applies CutMix augmentation on the unlabeled data. CCT [4] introduces a feature-level perturbation and enforces consistency among the predictions of different decoders. GCT [19] performs network perturbation by using two differently initialized segmentation models and encourages consistency between the predictions from the two models. PseudoSeg [8] focuses on improving the quality of pseudo labels. Though achieving satisfactory improvements over the supervised baseline, none of the aforementioned methods explore the biased learning issue in semi-supervised semantic segmentation. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/42cbc8a37147395065c989b541dfb776a6b6bd21d0bf2f7408ca9772d449ae9a.jpg",
+        "image_caption": [
+            "Figure 2: Overview of AEL. We adopt the teacher-student architecture as our basic framework. The teacher model is updated by the exponential moving average (EMA) of the student model. Confidence bank is uesd to dynamically record the category-wise performance during training. Adaptive CutMix and adaptive Copy-Paste are applied on the unlabeled and labeled data respectively to provide sufficient training samples from the under-performing categories. Adaptive equalization sampling (AES) encourages the training to involve more samples from the under-performing categories to make the training unbiased. Dynamic re-weighting strategy aims to alleviate the noise of pseudo-labeling. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Class Imbalance in Semi-Supervised Learning. Although SSL has been extensively studied, class imbalance problem in SSL is relatively under-explored, especially for semantic segmentation. Yang et al. [20] demonstrate that leveraging unlabeled data can alleviate imbalance issue. Hyun et al. [21] propose a suppressed consistency loss for class-imbalanced image classification problems. CReST [22] introduces a self-training framework for imbalanced SSL. Our method, though not explicitly targeting at the class imbalance problem, focuses on improving the performance of underperforming categories which are mostly tailed classes. Moreover, we refer to the ideas of resampling [23, 24] and re-weighting [25, 26], which are designed for class imbalance problem. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Method ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a labeled set $\\mathcal { D } ^ { l } = \\{ ( \\boldsymbol { \\mathbf { \\mathit { x } } } _ { i } ^ { l } , \\boldsymbol { \\mathbf { \\mathit { y } } } _ { i } ^ { l } ) \\}$ and an unlabeled set $\\mathcal { D } ^ { u } = \\{ \\pmb { x } _ { i } ^ { u } \\}$ , the objective of semisupervised semantic segmentation is to learn a segmentation model by efficiently leveraging both labeled and unlabeled data. In this section, we first present an overview of the proposed AEL in Section 3.1. Then we describe our basic framework for semi-supervised semantic segmentation in Section 3.2. Finally, the details of AEL are introduced in Section 3.3. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Overview ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure 2 displays an overview of AEL, which is a data-efficient framework for semi-supervised semantic segmentation. It is composed of two parts: 1) a basic framework which contains a teacher model for pseudo-labeling and a student model for online learning; 2) dedicated modules which encourages the under-performing categories to be sufficiently trained by effectively leveraging both labeled and unlabeled data. We use the proposed confidence bank to dynamically record the categorywise performance during training, and thus we can easily identify which categories are not sufficiently trained. For those unsatisfactory categories, we present two data augmentation methods to increase their frequency of occurrence in a training batch, namely adaptive CutMix which is applied on the unlabeled data, and adaptive Copy-Paste which is applied on the labeled data. To make the model towards the unbiased learning, we propose the adaptive equalization sampling and dynamic re-weighting strategies to involve enough samples from the under-performing categories into the training, and alleviate the noise raised by pseudo-labeling simultaneously. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 Basic Framework ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            90,
+            336,
+            106
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We first set up a basic framework for semi-supervised semantic segmentation. The framework consists of a student model and a teacher model. The teacher model has the same architecture as the student model, but uses a different set of weights which are updated by exponential moving average (EMA) of the student model [11]. Following FixMatch [14], we use the teacher model to generate a set of pseudo labels $\\hat { \\mathcal { V } } = \\{ \\hat { y } _ { i } \\}$ on the weakly augmented unlabeled data $\\mathcal { D } ^ { u }$ . Subsequently, the student model is trained on both labeled data $\\mathcal { D } ^ { l }$ (of weak augmentation) with the ground-truth and unlabeled data $\\mathcal { D } ^ { u }$ (of strong augmentation) with the generated pseudo labels $\\hat { \\mathcal { V } }$ . We use standard random resize and random horizontal flip as the weak augmentation. Strong augmentation includes CutMix [27] and all data augmentation strategies used in the weak augmentation. ",
+        "bbox": [
+            173,
+            116,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The overall loss consists of the supervised loss $\\mathcal { L } _ { s }$ and the unsupervised loss $\\mathcal { L } _ { u }$ : ",
+        "bbox": [
+            173,
+            252,
+            700,
+            267
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/904fa3d968d65556a0076dc248d32d8f0b60978bed3f97ae8c557f39855cf05e.jpg",
+        "text": "$$\n\\begin{array} { l } { { \\displaystyle { \\mathcal { L } } _ { s } = \\frac { 1 } { N _ { l } } \\sum _ { i = 1 } ^ { N _ { l } } \\frac { 1 } { W H } \\sum _ { j = 1 } ^ { W H } \\ell _ { c e } ( y _ { i j } , { p } _ { i j } ) } , } \\\\ { { \\displaystyle { \\mathcal { L } } _ { u } = \\frac { 1 } { N _ { u } } \\sum _ { i = 1 } ^ { N _ { u } } \\frac { 1 } { W H } \\sum _ { j = 1 } ^ { W H } \\ell _ { c e } ( \\hat { y } _ { i j } , { p } _ { i j } ) } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            273,
+            607,
+            366
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\pmb { p } _ { i j }$ is the prediction of the $j$ -th pixel in the $i$ -th labeled (or unlabeled) image, $N _ { l }$ and $N _ { u }$ denote the number of labeled images and unlabeled images in a training batch, $W$ and $H$ represent the width and height of the input image, and $\\ell _ { c e }$ denotes the standard pixel-wise cross-entropy loss. We define the overall loss function as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a0bb52e7bd8b4bb1f0073536eb66e130989221b3a4c96a186fe839963854da7e.jpg",
+        "text": "$$\n\\mathcal { L } = \\mathcal { L } _ { s } + \\alpha \\mathcal { L } _ { u } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            444,
+            438,
+            552,
+            453
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\alpha$ controls the contribution of the unsupervised loss. ",
+        "bbox": [
+            173,
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+            481
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 Adaptive Equalization Learning ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            497,
+            437,
+            512
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The baseline framework, though achieving competitive results compared with previous related works, neglects the key issues in semi-supervised semantic segmentation. Due to the limited labeled data, semi-supervised learning tends to have poor performance on some certain categories, e.g., tailed categories in Cityscapes dataset which exhibits a long-tailed label distribution. Insufficient training on these categories introduces more noise of pseudo labels which can disrupt the learning process. The proposed AEL framework aims to alleviate the degradation of under-performing categories during the semi-supervised training. Concretely, we maintain a confidence bank to record the performance of each category during training. The confidence bank enables us to identify the under-performing categories. To improve the performance of these categories and further make the training unbiased, we propose a series of technologies to efficiently leverage both labeled and unlabeled data, namely adaptive CutMix, adaptive Copy-Paste, adaptive equalization sampling and dynamic re-weighting. ",
+        "bbox": [
+            173,
+            521,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Confidence Bank. To tackle the biased training, previous methods [25, 26, 22, 28] always rely on the prior knowledge such as the number of training samples of each category to design the ad hoc sampling and weighting strategies. However, the performance of each category is not always strictly proportional to the number of training samples, because some categories tend to have discriminative features and thus fewer samples are required for training. Inspired by the recent progress [29] which applies active learning on semantic segmentation, we propose to maintain a confidence bank to record the category-wise performance during training. An indicator is needed to assess the performance of each category. ",
+        "bbox": [
+            173,
+            680,
+            825,
+            792
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We consider several indicators, namely Confidence, Margin and Entropy. Formally, we define Confidence indicator as: ",
+        "bbox": [
+            176,
+            796,
+            823,
+            827
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b3d8981a14bb398effbfc8603fe8de7be40629254636fb105c92c9227cb42848.jpg",
+        "text": "$$\n\\mathrm { C o n f } ^ { c } = \\frac { 1 } { N _ { l } } \\sum _ { i = 1 } ^ { N _ { l } } \\frac { 1 } { N _ { i } ^ { c } } \\sum _ { j = 1 } ^ { N _ { i } ^ { c } } p _ { i j } ^ { c } , c \\in \\{ 1 , \\dots , C \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            832,
+            651,
+            878
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $C$ is the category number, $N _ { i } ^ { c }$ denotes the number of pixels belonging to category $c$ according to its ground-truth ${ \\bf { \\it y } } _ { i } , { \\bf { \\it p } } _ { i j } ^ { c }$ denotes the $c$ -th channel prediction of the $j$ -th pixel in the $i$ -th image. ",
+        "bbox": [
+            171,
+            883,
+            828,
+            912
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Define Margin indicator as: ",
+        "bbox": [
+            174,
+            92,
+            356,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/88fdfcf4c952a4f12b3e4d2463bf496b4ee371e36985422118046f976b1070ef.jpg",
+        "text": "$$\n\\mathrm { M a r g i n } ^ { c } = \\frac { 1 } { N _ { l } } \\sum _ { i = 1 } ^ { N _ { l } } \\frac { 1 } { N _ { i } ^ { c } } \\sum _ { j = 1 } ^ { N _ { i } ^ { c } } ( p _ { i j } ^ { c } - \\operatorname * { m a x } _ { c ^ { \\prime } \\in \\{ 1 , \\dots , C \\} } p _ { i j } ^ { c ^ { \\prime } } ) , ~ c \\in \\{ 1 , \\dots , C \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            277,
+            111,
+            720,
+            156
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathrm { m a x 2 ( \\cdot ) }$ denotes the second largest value operator. At last, we define Entropy indicator as: ",
+        "bbox": [
+            169,
+            161,
+            807,
+            176
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/746d3e7e478360513b6a45e12b8ac4b0137f487b3b4daec2be40d571b201adf1.jpg",
+        "text": "$$\n\\mathrm { E n t } ^ { c } = - \\frac { 1 } { N _ { l } } \\sum _ { i = 1 } ^ { N _ { l } } \\frac { 1 } { N _ { i } ^ { c } } \\sum _ { j = 1 } ^ { N _ { i } ^ { c } } \\sum _ { c ^ { \\prime } = 1 } ^ { C } p _ { i j } ^ { c ^ { \\prime } } \\log p _ { i j } ^ { c ^ { \\prime } } , c \\in \\{ 1 , \\ldots , C \\} .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            180,
+            692,
+            227
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For all of the indicators, we only take into account predictions from labeled data. Experimentally, the confidence indicator serves best in our AEL and thus we adopt it by default (see Section 4.3 for the comparison). We use EMA to update the category-wise confidence at each training step: ",
+        "bbox": [
+            173,
+            237,
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+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5a41cf5d5ca2387eb73473e8c14fc1133c3fa5eb1c12ccb661b7e3584ffd0b29.jpg",
+        "text": "$$\n\\mathrm { C o n f } _ { k } ^ { c } \\gets \\tau \\mathrm { C o n f } _ { k - 1 } ^ { c } + ( 1 - \\tau ) \\mathrm { C o n f } _ { k } ^ { c } , \\ c \\in \\{ 1 , \\ldots , C \\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            284,
+            679,
+            301
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $k$ denotes the $k$ -th iteration, $\\tau \\in [ 0 , 1 )$ is the momentum coefficient which is set to 0.999 experimentally. Through the confidence bank, we can easily identify the under-performing categories for the current model. ",
+        "bbox": [
+            176,
+            304,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adaptive CutMix. Here we introduce the proposed adaptive CutMix (see Figure 2 for illustration) which is applied on the unlabeled data. It aims to increase the frequency of occurrence of the under-performing samples from the unlabeled data. We first formulate the original CutMix [27] as: ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e7a4acf9408bf4cce7260b2a79848a2d230bcede95c9cf39023188b1fd508ccf.jpg",
+        "text": "$$\n\\begin{array} { r } { \\hat { I } = \\mathbf { C u t M i x } ( \\mathbf { C r o p } ( I _ { 1 } ) , I _ { 2 } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            400,
+            589,
+            419
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $I _ { 1 }$ and $I _ { 2 }$ denote randomly selected unlabeled images, $\\hat { I }$ is the augmented image, and Crop(·) represents the random crop operation. ",
+        "bbox": [
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+            425,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Different from the original CutMix where unlabeled images are randmoly selected, the proposed adaptive CutMix gives under-performing categories a higher sampling probability. Specifically, we first convert the category-wise confidence stored in the confidence bank to the normalized sampling probability $\\pmb { r } \\in \\mathbb { R } ^ { C }$ , which can be formulated as: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a3981b5a05697f107532cd3b12980be4864deda7b311907243468d43a5a19aab.jpg",
+        "text": "$$\nr = \\mathrm { S o f t m a x } ( 1 - \\mathrm { C o n f } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            413,
+            520,
+            584,
+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "According to the sampling probability, we randomly select an unlabeled image containing the sampled category as $I _ { 1 }$ , and another unlabeled image from the training batch is randomly selected as $I _ { 2 }$ . The Crop(·) operation is performed on the region containing the chosen category. After that, we can generate the augmented image by Eq 8. Since the adaptive CutMix is performed on the unlabeled data without any annotations, we use predictions as approximate ground-truth, which works well in practice. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adaptive Copy-Paste. Copy-Paste [30] is an effective data augmentation strategy for instance segmentation. It yields significant gains on the challenging LVIS benchmark [31], especially for rare object categories. The key idea behind the Copy-Paste augmentation is to paste objects from the source image to the target image. Inspired by this, we further propose the adaptive Copy-Paste (see Figure 2 for illustration) for semi-supervised semantic segmentation. Different from adaptive CutMix, adaptive Copy-Paste augmentation strives for efficiently leveraging the labeled data. Similarly, we involve confidence bank to assess category-wise performance and use $\\mathrm { E q } 9$ to compute sampling probability. The under-performing categories have higher probability to be selected for Copy-Paste. Experimentally, the proposed adaptive Copy-Paste augmentation yields slightly better performance in the category level than the instance level. Thus we copy all pixels belonging to the sampled category in the source image and paste them on the target image. Following [30], the augmented image is composed of two randomly selected images from the labeled data and a large scale jittering is applied. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adaptive Equalization Sampling. As described in Section 1, due to the limited and unbalanced labeled data, the training tends to be biased. To alleviate the training bias, we propose a novel adaptive equalization sampling strategy which focuses training on a sparse set of under-performing samples and prevents the vast number of well-trained samples from overwhelming the model during training. Concretely, we define the sampling rate $s ^ { c }$ for category $c$ as: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1eb7fcdedabfa98384053cc54532fb89fbf00f73c7516a5bf4b06a3db4297157.jpg",
+        "text": "$$\ns ^ { c } = \\left[ \\frac { 1 - \\mathrm { C o n f } ^ { c } } { \\operatorname* { m a x } _ { c \\in \\{ 1 , \\dots , C \\} } \\left( 1 - \\mathrm { C o n f } ^ { c } \\right) } \\right] ^ { \\beta } , \\ c \\in \\{ 1 , \\dots , C \\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            877,
+            679,
+            916
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\beta$ denotes a tunable parameter. Instead of using all pixels to compute the unsupervised loss, for category $c$ with the sampling rate $s ^ { c }$ , we randomly sample a subset of pixels according to their predictions. Then the unsupervised loss in Eq 2 can be reformulated as: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a5c2388530964df62124b8b02f28d37587992f88764122df5fbcf964d5fdf202.jpg",
+        "text": "$$\n\\mathcal { L } _ { u } = \\frac { 1 } { { { N _ { u } } } } { \\sum _ { i = 1 } ^ { { N _ { u } } } { \\frac { 1 } { { \\sum _ { j = 1 } ^ { { W H } } { \\mathbb { 1 } _ { i j } } } } \\sum _ { j = 1 } ^ { { W H } } { \\ell _ { c e } ( { \\hat { y } _ { i j } } , { { p _ { i j } } } ) \\mathbb { 1 } _ { i j } } } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            138,
+            653,
+            183
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbb { 1 } _ { i j } = 1$ indicates that the $j$ -th pixel in the $i$ -th image is sampled according to the sampling rate, otherwise $\\mathbb { 1 } _ { i j }$ is set to 0, the other terms are the same as in $\\operatorname { E q }$ . ",
+        "bbox": [
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+            188,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Dynamic Re-Weighting. The performance of the model depends on the quality of pseudo labels. Existing methods [2, 4, 19] usually adopt a higher threshold on classification score to filter out most of the pixels with low-confidence. Though this strategy could alleviate the noise raised by pseudolabeling, the strict criteria leads to lower recall for the pixels from under-performing categories, which hinders the training. Another option is to discard the threshold and involve all pixels into the training. However, much more noise is introduced simultaneously. To alleviate this issue, we propose a dynamic re-weighting strategy which adds a modulating factor to the unsupervised loss in the way of semi-supervised learning. On the basis of Eq 11, we formulate our final unsupervised loss as: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/03f1bd74b40695ef6c4a50a20d9d4f8b97bfb451f21262df873a945ac6e10fac.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { u } = \\displaystyle \\frac { 1 } { N _ { u } } \\sum _ { i = 1 } ^ { N _ { u } } \\frac { 1 } { \\sum _ { j = 1 } ^ { W H } w _ { i j } } \\sum _ { j = 1 } ^ { W H } w _ { i j } \\ell _ { c e } ( \\hat { \\pmb { y } } _ { i j } , { \\pmb { p } } _ { i j } ) , } \\\\ { w _ { i j } = \\displaystyle \\operatorname* { m a x } _ { c \\in \\{ 1 , \\dots , C \\} } ( p _ { i j } ^ { c } ) ^ { \\gamma } \\mathbb { 1 } _ { i j } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            338,
+            655,
+            411
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\gamma$ is the tunable parameter. Different from the Focal Loss [32] where the modulating factor is used for reducing the loss contribution from easy samples, our formulation aims to allocate more contributions for the convincing samples. The combination of adaptive equalization sampling and dynamic re-weighting not only involves more samples from the under-performing categories into the training, but also alleviate the noise raised by pseudo-labeling. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Cityscapes [1] dataset is designed for urban scene understanding. It contains 30 classes and only 19 classes of them are used for scene parsing evaluation. The dataset contains 5, 000 finely annotated images and 20, 000 coarsely annotated images. The finely annotated 5, 000 images are split into 2, 975, 500 and 1, 525 images for training, validation and testing respectively. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "PASCAL VOC 2012 [33] dataset is a standard object-centric semantic segmentation dataset. It contains 20 foreground object classes and a background class. The strand training, validation and testing sets consist of 1, 464, 1, 449 and 1, 556 images, respectively. Following common practice, we use the augmented set [34] which contains 10, 582 images as the training set. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ADE20K dataset [35] is a large scale scene parsing benchmark which contains dense labels of 150 stuff/object categories. The dataset includes 20K/2K/3K images for training, validation and testing. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For both Cityscapes and PASCAL VOC 2012 datasets, 1/2, 1/4, 1/8, 1/16 and 1/32 training images are randomly sampled as the labeled training data, and the remaining images are used as the unlabeled data. For each protocol, AEL provides 5 different data folds and the final performance is the average of 5 folds. In addition, we also evaluate our method on the setting where the full Cityscapes train set is used as the labeled data and 1, 000, 3, 000 and 5, 000 images and randomly selected from the Cityscapes coarse set as the unlabeled data. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. We use single scale testing and adopt mean of Intersection over Union (mIoU) as the metric to evaluate the performance. We report the results on the Cityscapes val set and PASCAL VOC 2012 val set in comparisons with state-of-the-art methods. All ablation studies are conducted on the Cityscapes val set under 1/16 and 1/32 partition protocols. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We use ResNet-101 pretrained on ImageNet [36] as our backbone, remove the last two down-sampling operations and employ dilated convolutions in the subsequent convolution layers, making the output stride equal to 8. We use DeepLabv $^ { 3 + }$ [37] as the segmentation head. For ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1cd0ec48207f480b6efdbe129efdbda4bb1dfa1b50249188fd20589e5bee068c.jpg",
+        "table_caption": [
+            "Table 1: Comparison with state-of-the-art methods on the Cityscapes val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>1/32 (93)</td><td>1/16 (186)</td><td>1/8 (372)</td><td>1/4 (744)</td><td>1/2 (1488)</td></tr><tr><td>Supervised</td><td>57.89</td><td>62.96</td><td>69.81</td><td>74.23</td><td>77.46</td></tr><tr><td>MT [11]</td><td>64.07</td><td>68.05</td><td>73.56</td><td>76.66</td><td>78.39</td></tr><tr><td>CCT [4]</td><td>66.35</td><td>69.32</td><td>74.12</td><td>75.99</td><td>78.10</td></tr><tr><td>Cutmix-Seg [2]</td><td>69.11</td><td>72.13</td><td>75.83</td><td>77.24</td><td>78.95</td></tr><tr><td>GCT[19]</td><td>63.21</td><td>66.75</td><td>72.66</td><td>76.11</td><td>78.34</td></tr><tr><td>AEL (Ours)</td><td>74.28</td><td>75.83</td><td>77.90</td><td>79.01</td><td>80.28</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/87eb4317b3e2cfe3f0d2693f388a5a5fe71dcf9364352a67846427f173b6d829.jpg",
+        "table_caption": [
+            "Table 2: Comparison with state-of-the-art methods on the PASCAL VOC 2012 val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=2>Method</td><td rowspan=1 colspan=1>1/32 (331)</td><td rowspan=1 colspan=3>1/16 (662)</td><td rowspan=1 colspan=1>1/8 (1323)</td><td rowspan=1 colspan=1>1/4 (2646)</td><td rowspan=1 colspan=1>1/2 (5291)</td></tr><tr><td rowspan=1 colspan=2>Supervised</td><td rowspan=1 colspan=1>70.14</td><td rowspan=1 colspan=3>70.60</td><td rowspan=1 colspan=1>73.12</td><td rowspan=1 colspan=1>76.35</td><td rowspan=1 colspan=1>77.21</td></tr><tr><td rowspan=2 colspan=2>MT [11]CCT[4]</td><td rowspan=1 colspan=1>70.56</td><td rowspan=1 colspan=3>71.29</td><td rowspan=2 colspan=1>73.3373.68</td><td rowspan=2 colspan=1>76.6176.51</td><td rowspan=2 colspan=1>78.0877.40</td></tr><tr><td rowspan=3 colspan=2>CCT[4]Cutmix-Seg [2]GCT [19]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>71.22</td><td rowspan=1 colspan=1>71.86</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=2 colspan=1>73.3970.32</td><td rowspan=2 colspan=3>73.5670.90</td><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1>73.96</td><td rowspan=1 colspan=1>77.58</td><td rowspan=1 colspan=1>78.12</td></tr><tr><td rowspan=1 colspan=1>73.29</td><td rowspan=1 colspan=1>76.66</td><td rowspan=1 colspan=1>77.98</td></tr><tr><td rowspan=1 colspan=2>AEL (Ours)</td><td rowspan=1 colspan=1>76.97</td><td rowspan=1 colspan=3>77.20</td><td rowspan=1 colspan=1>77.57</td><td rowspan=1 colspan=1>78.06</td><td rowspan=1 colspan=1>80.29</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Cityscapes dataset, we use stochastic gradient descent (SGD) optimizer with initial learning rate 0.01, weight decay 0.0005 and momentum 0.9. Moreover, we adopt the ‘poly’ learning rate policy, where the initial learning rate is multiplied by $\\begin{array} { r } { ( 1 - \\frac { \\mathrm { i t e r } } { \\mathrm { m a x i t e r } } ) ^ { 0 . 9 } } \\end{array}$ . We adopt the crop size as $7 6 9 \\times 7 6 9$ , batch size as 16 and training iterations as $1 8 \\mathrm { k }$ . For PASCAL VOC 2012 dataset, we set the initial learning rate as 0.001, weight decay as 0.0001, crop size as $5 1 3 \\times 5 1 3$ , batch size as 16 and training iterations as $3 0 \\mathrm { k }$ . We use random horizontal flip and random resize as the default data augmentation if not specified. All the supervised baselines are trained on the labeled data. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 Comparison with State-of-the-Art Methods ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            608,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare our method with recent semi-supervised semantic segmentation methods, including Mean Teacher (MT) [11], Cross-Consistency Training (CCT) [4], Guided Collaborative Training (GCT) [19] and Cutmix-Seg [2]. For a fair comparison, we re-implement all above methods and adopt the same network architecture (DeepLabv $^ { 3 + }$ with ResNet-101 backbone). ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results on Cityscapes Dataset. Table 1 compares AEL with state-of-the-art methods on the Cityscapes val set. Without leveraging any unlabeled data, the performance of the supervised baseline is unsatisfactory under various data partition protocols, especially for the fewer data settings, e.g., 1/32 and 1/16 protocols. Our method consistently promotes the baseline, achieving the improvements of $+ 1 6 . 4 \\%$ , $+ 1 2 . 9 \\%$ , $+ 8 . 1 \\%$ , $+ 4 . 8 \\%$ and $+ 2 . 8 \\%$ under 1/32, 1/16, 1/8, 1/4 and 1/2 partition protocols respectively. Our method also significantly outperforms the existing state-of-the-art methods by a large margin under all data partition protocols. In particular, AEL outperforms the existing best method Cutmix-Seg by $+ 5 . 2 \\%$ under extremely few data setting (1/32 protocol), and surpasses Cutmix-Seg by $+ 1 . 3 \\%$ under the $1 / 2$ protocol. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results on PASCAL VOC 2012 Dataset. Table 2 shows comparison with state-of-the-art methods on the PASCAL VOC 2012 val dataset. AEL achieves consistent performance gains over the supervised baseline, obtaining an improvements of $+ 6 . 8 \\%$ , $+ 7 . 0 \\%$ , $+ 4 . 1 \\%$ , $+ 1 . 7 \\%$ and $+ 3 . 1 \\%$ under 1/32, 1/16, 1/8, 1/4 and $1 / 2$ partition protocols respectively. We can see that over all protocols, AEL outperforms the state-of-the-art methods. For example, our method outperforms the previous best method by $+ 3 . 6 \\%$ and $+ 2 . 2 \\%$ under the 1/32 and $1 / 2$ partition protocols. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b8437025ffab8b0c0973549a35dc1f6e9b8f24b0b74addb7318b157e711ccdec.jpg",
+        "table_caption": [
+            "Table 3: Ablation study on the effectiveness of different components: Dynamic Re-weighting (DR), Adaptive Equalization Sampling(AES), Adaptive CutMix (ACM), Adaptive Copy-Paste (ACP). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>DR</td><td rowspan=1 colspan=1>AES</td><td rowspan=1 colspan=1>ACM</td><td rowspan=1 colspan=2>ACP</td><td rowspan=1 colspan=1>1/32 (93)</td><td rowspan=1 colspan=1>1/16 (186)</td></tr><tr><td rowspan=7 colspan=1>√√√√</td><td rowspan=7 colspan=1>厂√厂√</td><td rowspan=6 colspan=1>4√</td><td rowspan=5 colspan=2>√</td><td rowspan=1 colspan=1>69.11</td><td rowspan=1 colspan=1>72.13</td></tr><tr><td rowspan=1 colspan=1>70.27</td><td rowspan=1 colspan=1>73.85</td></tr><tr><td rowspan=1 colspan=1>71.65</td><td rowspan=2 colspan=1>74.1273.8972.64</td></tr><tr><td rowspan=1 colspan=1>70.4969.69</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>72.5173.43</td><td rowspan=2 colspan=1>74.3975.12</td></tr><tr><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=2>√</td><td rowspan=1 colspan=1>74.28</td><td rowspan=1 colspan=1>75.83</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 Ablation Study ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            313,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To further understand the advantages of AEL, we conduct a series of ablation studies that examine the effectiveness of different components and different hyper-parameters. All experiments are conducted on the validation set of Cityscapes dataset. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The Effectiveness of Different Components. We ablate each component of AEL step by step. Table 3 reports the studies. We use the basic framework described in Section 3.2 as our baseline, which achieves $6 9 . 1 1 \\%$ and $7 2 . 1 3 \\%$ under 1/32 and 1/16 protocols respectively. We first evaluate the effectiveness of each single component. As shown in the table, Dynamic Re-weighting (DR) improves the baseline by $+ 1 . 1 \\%$ and $+ 1 . 7 \\%$ under 1/32 and 1/16 partition protocols. Adaptive Equalization Sampling (AES) alleviates the biased training issue, achieving the improvements of $+ 2 . 5 \\%$ and $+ 2 . 0 \\%$ over the baseline. Adaptive CutMix (ACM) and Adaptive Copy-Paste (ACP) data augmentation approaches give more chance for under-performing categories to be sampled, and bring the improvements of $+ 1 . 3 \\% / + 1 . 7 \\%$ and $+ 0 . 5 \\% / + 0 . 5 \\%$ respectively. Furthermore, we present the performance gains in a progressive manner. On top of the DR, by leveraging AES strategy on the unsupervised loss, our method obtains improvements of $+ 2 . 3 \\%$ and $+ 0 . 5 \\%$ under 1/32 and 1/16 protocols. The two proposed data augmentation approaches further boost the performance to $7 4 . 2 8 \\%$ and $7 5 . 8 3 \\%$ , demonstrating the effectiveness of our adaptive learning. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study on Hyper-Parameters. Table 5 ablates the tunable parameter $\\gamma$ in dynamic reweighting (in Eq 13), where $\\gamma = 2$ yields slightly better performance. Dynamic re-weighting is found to be insensitive to $\\gamma$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6 ablates the influence of different indicators, including Confidence (in Eq 4), Margin (in Eq 5), and Entropy (in Eq 6). We use the Confidence as the default indicator to assess the category-wise performance during training due to its best performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Adaptive CutMix requires a criteria to identify whether an unlabeled image contains a certain class. We use the ratio between pseudo labels of a certain category and total pixels of the input image as the criteria. Table 7 ablates different ratios. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 8 studies the number of sampled categories $K$ in the Adaptive Copy-Paste. We find that $K = 3$ achieves the best performance. One potential reason is that a smaller $K$ provides less training samples from the under-performing categories while a larger $K$ may increase the difficulty for training. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 9 ablates the loss weight $\\alpha$ which is used to balance the supervised loss and unsupervised loss as shown in Eq 3. As illustrated in the table, $\\alpha = 1$ achieves the best performance. We use $\\alpha = 1$ in our approach for all the experiments. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 Per-class Results ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Since the class imbalance problem is severe in the Cityscapes dataset, we provide per-class results under 1/32 data partition protocol in Table 4. We choose 9 classes with the least training samples in the Cityscapes dataset as tail classes, i.e. wall, traffic light, traffic sign, rider, truck, bus, train, motorcycle and bicycle. As shown in the table, our method not only achieves the best overall mIoU, but also obtains significant improvements on tail classes. In particular, Our method outperforms the existing best method Cutmix-Seg by $+ 5 . 2 \\%$ in overall mIoU and $+ 9 . 2 \\%$ in mIoU for tail classes under 1/32 partition protocol. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5c694b589e79e829be31f5c9c39d8fd4acbd4b61118ed4a57376f9e0db0b4cfa.jpg",
+        "table_caption": [
+            "Table 4: Per-class results on Cityscapes val set under 1/32 data partition protocol. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td></td><td></td><td></td><td>Head Classes</td><td></td><td></td><td></td><td colspan=\"10\">Tail Classes</td></tr><tr><td>Methods</td><td></td><td></td><td>meno </td><td>seeaara Buping </td><td>Vegeee </td><td>Eirllrn 灵</td><td>uosiad</td><td>3u</td><td></td><td>igre</td><td></td><td>rs grgen</td><td></td><td></td><td></td><td></td><td>meroreite</td><td>eaelbir</td></tr><tr><td>Supervised</td><td></td><td>57.9</td><td>39.8 94.6</td><td>72.5 87.4</td><td>42.4 51.6</td><td>88.3 49.8</td><td>91.1</td><td>74.5</td><td>89.4</td><td>21.7</td><td>47.7</td><td>59.1</td><td>33.7</td><td>43.3</td><td>37.2</td><td></td><td>11.4 42.1</td><td>62.2</td></tr><tr><td>GCT[19]</td><td>63.2</td><td>48.1</td><td>96.9</td><td>75.8 89.8</td><td>40.3 57.5 91.1</td><td>53.5</td><td>93.1 78.1</td><td>91.6</td><td></td><td>23.6 58.9</td><td></td><td>70.1</td><td>43.4</td><td>25.8</td><td>45.7</td><td>49.2</td><td>45.0</td><td>71.4</td></tr><tr><td>MT [11]</td><td>64.1</td><td>50.4</td><td>96.7</td><td>75.6 89.5</td><td>40.0 57.3 91.0</td><td>53.2</td><td>92.80 77.9</td><td>91.3</td><td></td><td>26.2 61.1</td><td></td><td>72.3</td><td>45.8</td><td>28.0</td><td>48.1</td><td>51.6</td><td>47.1</td><td>73.8</td></tr><tr><td>CCT [4]</td><td>66.4</td><td>54.2</td><td>95.7</td><td>77.2 88.6</td><td>46.5 58.5 90.1</td><td>55.5</td><td>91.5</td><td>77.9 91.8</td><td></td><td>27.9</td><td>60.5</td><td>71.8</td><td>48.0</td><td>44.5</td><td>61.4</td><td>50.7</td><td>52.0</td><td>70.5</td></tr><tr><td>Cutmix-Seg [2]</td><td>69.1</td><td>58.7</td><td>97.2</td><td>78.6 90.1</td><td>48.1 60.1 91.5</td><td>57.2</td><td>93.0 79.6</td><td>93.3</td><td></td><td>32.4</td><td>64.8</td><td>76.5</td><td>52.3</td><td>49.4</td><td>66.0</td><td>54.8</td><td>56.7</td><td>75.1</td></tr><tr><td>AEL (Ours)</td><td>74.3</td><td>67.9</td><td>97.1</td><td>78.7 90.3</td><td>52.3 62.0 91.7</td><td>59.2</td><td>93.8</td><td>81.6 94.0</td><td></td><td>37.3</td><td>67.9</td><td>77.6</td><td>60.5</td><td>65.6</td><td>83.8</td><td>74.3</td><td>66.9</td><td>77.0</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/225f9d7a55b61fee6c7a572d9876080e27e60f7c6a6101101285f696c22271af.jpg",
+        "table_caption": [
+            "Table 5: Study on $\\gamma$ of dynamic re-weighting. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Y</td><td>1/32</td><td>1/16</td></tr><tr><td>0</td><td>69.11</td><td>72.13</td></tr><tr><td>0.5</td><td>69.74</td><td>73.28</td></tr><tr><td>1</td><td>69.35</td><td>73.67</td></tr><tr><td>2</td><td>70.27</td><td>73.85</td></tr><tr><td>3</td><td>70.26</td><td>73.40</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/ed9198751b599a08e740dbcc849f70510eddc1a706f925c82fdbd91646939ffa.jpg",
+        "table_caption": [
+            "Table 6: Study on different indicators for AES. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Indicator</td><td>1/32</td><td>1/16</td></tr><tr><td>None</td><td>70.27</td><td>73.85</td></tr><tr><td>Ent</td><td>71.38</td><td>73.21</td></tr><tr><td>Conf</td><td>72.51</td><td>74.39</td></tr><tr><td>Margin</td><td>70.86</td><td>73.05</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/c4e383cc00c32bdc681cbb7df0965b2783a019964e241fea687c03662063c837.jpg",
+        "table_caption": [
+            "Table 7: Study on different ratios in ACM. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ratio</td><td>1/32</td><td>1/16</td></tr><tr><td>0.001</td><td>73.27</td><td>74.28</td></tr><tr><td>0.003</td><td>73.29</td><td>74.36</td></tr><tr><td>0.005</td><td>73.43</td><td>75.12</td></tr><tr><td>0.01</td><td>72.78</td><td>73.66</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.5 Performance on the Full Labeled Set ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments where the full Cityscapes train set is used as the labeled dataset and the Cityscapes coarse set is used as the unlabeled dataset. We do not leverage any annotations from the coarse set though it provides coarsely annotated ground-truth. We randomly sample 1,000, 3,000 and 5,000 images from the coarse set to verify the proposed method. As shown in Table 10, the proposed AEL can still improve the supervised baselines by leveraging the unlabeled data though a large amount of labeled data is provided. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.6 Results on ADE20K Dataset ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We further provide results on the ADE20K dataset [35]. Since no previous methods in semi-supervised segmentation conducted experiments on ADE20K dataset, we compare our method with supervised baseline and existing best method Cutmix-Seg on the dataset. As shown in Table 11, our method consistently promotes the supervised baseline by $6 . 3 6 \\%$ , $5 . 7 0 \\%$ , $5 . 6 7 \\%$ , $3 . 1 8 \\%$ and $1 . 4 5 \\%$ , and outperforms the Cutmix-Seg by $2 . 2 5 \\%$ , $3 . 3 8 \\%$ , $2 . 4 8 \\%$ , $1 . 3 1 \\%$ and $1 . 2 6 \\%$ under 1/32, 1/16, 1/8, 1/4 and 1/2 partition protocols, respectively. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.7 Qualitative Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            814,
+            344,
+            829
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 shows the visualization results of different methods evaluated on the Cityscapes val set. We compare the proposed AEL with ground-truth, supervised baseline and our basic framework described in Section 3.2. Benefiting from a series of technologies designed for the balanced training, AEL achieves great performance on not only head categories (e.g. Road), but also tailed categories (e.g. Rider and Bicycle). ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/4442df744d82afa537af7dfc670e86f3728222d633a4a03ecf9f2a0197d9ea68.jpg",
+        "table_caption": [
+            "Table 8: Study on number of sampled categories $K$ in ACP. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>K</td><td>1/32</td><td>1/16</td></tr><tr><td>1</td><td>72.18</td><td>74.85</td></tr><tr><td>2</td><td>72.84</td><td>74.95</td></tr><tr><td>3</td><td>74.28</td><td>75.83</td></tr><tr><td>4</td><td>73.43</td><td>74.10</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/d6e0570d702a1fdfb01066d60e363a9d22949d879236c65702f580602821b73d.jpg",
+        "table_caption": [
+            "Table 9: Study on loss weight $\\alpha$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>α</td><td>1/32</td><td>1/16</td></tr><tr><td>0.5</td><td>71.85</td><td>74.61</td></tr><tr><td>1.0</td><td>74.28</td><td>75.83</td></tr><tr><td>1.5</td><td>74.10</td><td>73.44</td></tr><tr><td>2.0</td><td>73.79</td><td>72.86</td></tr></table>",
+        "bbox": [
+            400,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/d9082c6212c0ba7b18f24c0136109717e9334a84f4fca2b2892414b593562873.jpg",
+        "table_caption": [
+            "Table 10: Performance on the full Cityscapes train set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Number</td><td rowspan=1 colspan=1>Baseline</td><td rowspan=1 colspan=1>AEL</td></tr><tr><td rowspan=1 colspan=1>0</td><td rowspan=2 colspan=1>80.1680.22</td><td rowspan=2 colspan=1>80.28</td></tr><tr><td rowspan=1 colspan=1>1000</td></tr><tr><td rowspan=1 colspan=1>3000</td><td rowspan=1 colspan=1>80.55</td><td rowspan=1 colspan=1>81.36</td></tr><tr><td rowspan=1 colspan=1>5000</td><td rowspan=1 colspan=1>80.92</td><td rowspan=1 colspan=1>81.95</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/e38da7803cef615c9e4c1dc63b866fb57f30cad54092794f61a8cf6d19863b5b.jpg",
+        "table_caption": [
+            "Table 11: Comparison with supervised baseline and Cutmix-Seg on the ADE20K val set under different partition protocols. All the methods are based on DeepLabv $^ { 3 + }$ with ResNet-101 backbone. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=1>1/32 (631)</td><td rowspan=1 colspan=1>1/16 (1263)</td><td rowspan=1 colspan=1>1/8 (2526)</td><td rowspan=1 colspan=1>1/4 (5052)</td><td rowspan=1 colspan=1>1/2 (10105)</td></tr><tr><td rowspan=1 colspan=1>Supervised</td><td rowspan=1 colspan=1>22.04</td><td rowspan=1 colspan=1>27.52</td><td rowspan=1 colspan=1>32.36</td><td rowspan=1 colspan=1>36.39</td><td rowspan=1 colspan=1>41.97</td></tr><tr><td rowspan=1 colspan=1>Cutmix-Seg [2]</td><td rowspan=1 colspan=1>26.15    一</td><td rowspan=1 colspan=1>29.84</td><td rowspan=1 colspan=1>35.55</td><td rowspan=1 colspan=1>38.26</td><td rowspan=1 colspan=1>42.16</td></tr><tr><td rowspan=1 colspan=1>AEL (Ours)</td><td rowspan=1 colspan=1>28.40</td><td rowspan=1 colspan=1>33.22</td><td rowspan=1 colspan=1>38.03</td><td rowspan=1 colspan=1>39.57</td><td rowspan=1 colspan=1>43.42</td></tr></table>",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/1dfaed8e0950061c019275aed03487718cd0bfa80cf10041a6a93e28cc20fec6.jpg",
+        "image_caption": [
+            "Figure 3: Qualitative results on the Cityscapes val set. From left to right: input image, ground-truth, predictions of the supervised baseline, predictions of our basic framework and predictions of the proposed AEL. Orange rectangles highlight the unsatisfactory segmentation results. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel Adaptive Equalization Learning (AEL) framework for semisupervised semantic segmentation. Different from the existing methods dedicating to the design of consistency regularization or pseudo-labeling, AEL aims to adaptively balance the training based on the fact that pixel categories in common semantic segmentation datasets tend to be imbalanced. We introduce a confidence bank to dynamically record the category-wise performance at each training step, which enables us to identify the under-performing categories and adaptively tilt training towards these categories. Several technologies are proposed to make the training unbiased, namely adaptive Copy-Paste and CutMix, adaptive equalization sampling and dynamic re-weighting. Through the adaptive design, AEL outperforms the state-of-the-art methods by a large margin on the Cityscapes and Pascal VOC benchmarks under various data partition protocols. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported by the National Key R&D Program of China under grant 2017YFB1002804 and National Natural Science Foundation of China (No. 31771230). ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References   \n[1] Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes dataset for semantic urban scene understanding. In 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, NV, USA, June 27-30, 2016, pages 3213–3223. IEEE Computer Society, 2016.   \n[2] Geoffrey French, Samuli Laine, Timo Aila, Michal Mackiewicz, and Graham D. Finlayson. Semi-supervised semantic segmentation needs strong, varied perturbations. In 31st British Machine Vision Conference 2020, BMVC 2020, Virtual Event, UK, September 7-10, 2020. BMVA Press, 2020.   \n[3] Jongmok Kim, Jooyoung Jang, and Hyunwoo Park. Structured consistency loss for semisupervised semantic segmentation. CoRR, abs/2001.04647, 2020.   \n[4] Yassine Ouali, Céline Hudelot, and Myriam Tami. Semi-supervised semantic segmentation with cross-consistency training. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pages 12671–12681. IEEE, 2020.   \n[5] Zhanghan Ke, Daoye Wang, Qiong Yan, Jimmy S. J. Ren, and Rynson W. H. Lau. Dual student: Breaking the limits of the teacher in semi-supervised learning. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 6727–6735. IEEE, 2019.   \n[6] Jianlong Yuan, Yifan Liu, Chunhua Shen, Zhibin Wang, and Hao Li. A simple baseline for semi-supervised semantic segmentation with strong data augmentation. arXiv preprint arXiv:2104.07256, 2021.   \n[7] Xiaokang Chen, Yuhui Yuan, Gang Zeng, and Jingdong Wang. Semi-supervised semantic segmentation with cross pseudo supervision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2613–2622, 2021.   \n[8] Yuliang Zou, Zizhao Zhang, Han Zhang, Chun-Liang Li, Xiao Bian, Jia-Bin Huang, and Tomas Pfister. Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020.   \n[9] Yves Grandvalet, Yoshua Bengio, et al. Semi-supervised learning by entropy minimization. In CAP, pages 281–296, 2005.   \n[10] Samuli Laine and Timo Aila. Temporal ensembling for semi-supervised learning. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.   \n[11] Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. In Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pages 1195–1204, 2017.   \n[12] Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, and Shin Ishii. Virtual adversarial training: A regularization method for supervised and semi-supervised learning. IEEE Trans. Pattern Anal. Mach. Intell., 41(8):1979–1993, 2019.   \n[13] Dong-Hyun Lee et al. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on challenges in representation learning, ICML, volume 3, 2013.   \n[14] Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin Raffel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying semisupervised learning with consistency and confidence. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020. ",
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parse/train/S1AG8zYeg/S1AG8zYeg.md

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+# SENTENCE ORDERING USING RECURRENT NEURAL NETWORKS
+
+Lajanugen Logeswaran, Honglak Lee & Dragomir Radev
+
+Department of EECS   
+University of Michigan   
+Ann Arbor, MI 48109, USA   
+{llajan,honglak,radev}@umich.edu
+
+# ABSTRACT
+
+Modeling the structure of coherent texts is a task of great importance in NLP. The task of organizing a given set of sentences into a coherent order has been commonly used to build and evaluate models that understand such structure. In this work we propose an end-to-end neural approach based on the recently proposed set to sequence mapping framework to address the sentence ordering problem. Our model achieves state-of-the-art performance in the order discrimination task on two datasets widely used in the literature. We also consider a new interesting task of ordering abstracts from conference papers and research proposals and demonstrate strong performance against recent methods. Visualizing the sentence representations learned by the model shows that the model has captured high level logical structure in these paragraphs. The model also learns rich semantic sentence representations by learning to order texts, performing comparably to recent unsupervised representation learning methods in the sentence similarity and paraphrase detection tasks.
+
+# 1 INTRODUCTION
+
+Modeling the structure of coherent texts is one of the central problems in NLP. A well written piece of text has a particular high level logical and topical structure to it. The actual word and sentence choices as well as their transitions come together to convey the purpose of the text. Our overarching goal is to build models that can learn such structure by learning to arrange a given set of sentences to make coherent text.
+
+The sentence ordering task finds several applications. Multi-document Summarization (MDS) and retrieval based question answering involve extracting information from multiple source documents and organizing the content into a coherent summary. Since the relative ordering about sentences that come from different sources can be unclear, being able to automatically evaluate a particular order and/or finding the optimal order is essential. Barzilay and Elhadad (2002) discuss the importance of an explicit ordering component in MDS systems. Their experiments show that finding an acceptable ordering can enhance user comprehension.
+
+Models that learn to order text fragments can also be used as models of coherence. Automated essay scoring (Miltsakaki and Kukich, 2004; Burstein et al., 2010) is an application that can benefit from such a coherence model. Coherence is one of the key elements on which student essays are evaluated in standardized writing tests such as GRE (ETS). Apart from its importance and applications, our motivation to address this problem also stems from its stimulating nature. It can be considered as a jigsaw puzzle of sorts in the language domain.
+
+Our approach to the problem of modeling coherence is driven by recent successes in 1) capturing semantics using distributed representations and 2) using RNNs for sequence modeling tasks.
+
+Success in unsupervised approaches for learning embeddings for textual entities from large text corpora altered the way NLP problems are studied today. These embeddings have been shown to capture syntactic and semantic information as well as higher level analogical structure. These methods have been adopted to learn vector representations of sentences, paragraphs and entire documents. Embedding based approaches allow models to be trained end-to-end from scratch with no handcrafting.
+
+Recurrent Neural Networks (RNNs) have become the de facto approach to sequence learning and mapping problems in recent times. The Sequence to sequence mapping framework (Sutskever et al., 2014), as well as several of its variants have fuelled RNN based approaches to a wide variety of problems including language modeling, language generation, machine translation, question answering and many others.
+
+Vinyals et al. (2015a) recently showed that the order in which tokens of the input sequence are fed to seq2seq models has a significant impact on the performance of the model. In particular, for problems such as sorting which involve a source set (as opposed to a sequence), the optimal order to feed the tokens is not clear. They introduce an attention mechanism over the input tokens which allows the model to learn a soft input order. This is called the read, process and write (or set to sequence) framework. The read block maps the input tokens to a fixed length vector representation. The process block is an RNN encoder which, at each time step, attends to the input token embeddings and computes an attention readout, appending it to the current hidden state. The write block is an RNN which produces the target sequence conditioned on the representation produced by the process block.
+
+In this work we propose an RNN based approach to the sentence ordering problem which exploits the set to sequence framework. A word level RNN encoder produces sentence embeddings. A sentence level set encoder RNN iteratively attends to these embeddings (process block above) and constructs a representation of the context. Initialized with this representation, a sentence level pointer network RNN points to the next sentence candidates.
+
+The most widely studied task relevant to sentence ordering and coherence modeling in the literature is the order discrimination task. Given a document and a permuted version of it, the task involves identifying the more coherent ordering of the two. Our proposed model achieves state of the art performance on two benchmark datasets for this task, outperforming several classical approaches and more recent data-driven approaches.
+
+Addressing the more challenging task of ordering a given collection of sentences, we consider the novel and interesting task of ordering sentences from abstracts of conference papers and research grants. Our model strongly outperforms previous work on this task. We visualize the learned sentence representations and show that our model captures high level discourse structure. We provide visualizations that aid understanding what information in the sentences the model uses to identify the next sentence. We also study the quality of the sentence representations learned by the model by training the model on a large text corpus and show that these embeddings are comparable to recent unsupervised methods in capturing semantics.
+
+In summary our key contributions are as follows,
+
+• We propose an end to end trainable model based on the set to sequence framework to address the challenging problem of organizing a given collection of sentences in a coherent order. • We consider the novel task of understanding structure in abstract paragraphs and demonstrate state of the art results in order discrimination and sentence ordering tasks. • We demonstrate that the proposed model is capable of learning semantic representations of sentences that are comparable to recently proposed methods for learning such representations.
+
+# 2 RELATED WORK
+
+Coherence modeling and sentence ordering The coherence modeling and sentence ordering tasks have been approached by closely related techniques. Most approaches propose a measure of coherence and formulate the ordering problem as finding an order with maximal coherence. Recurring themes from prior work include linguistic features, centering theory, local and global coherence.
+
+Local coherence has been modeled by considering properties of a local window of sentences such as sentence similarity and sentence transition structure. Foltz et al. (1998) represent words using vectors of co-occurent counts and sentences as a mean of these word vectors. Sentence similarity is defined as the cosine distance between sentence vectors and text coherence is modeled as a normalized sum of similarity scores of adjacent sentences. Lapata (2003) represents sentences by vectors of linguistic features and learn the transition probabilities from one set of features to another in adjacent sentences. A popular model of coherence is the Entity-Grid model Barzilay and Lapata (2008) which captures local coherence by modeling patterns of entity distributions in the discourse. Sentences are represented by the syntactic roles of entities appearing in the document and entity transition frequencies in successive sentences are treated as features that are are used to train a ranking SVM. These two approaches find motivation from ideas in centering theory (Grosz et al., 1995) which state that nouns and entities in coherent discourses exhibit certain patterns.
+
+Global models of coherence typically use an HMM to model document structure. The content model proposed by Barzilay and Lee (2004) represents topics in a particular domain as states in an HMM. State transitions capture possible presentation orderings within the domain. Words of a sentence are modeled using a topic-specific language model. The content model has inspired several subsequent work to combine the strengths of local and global models. Elsner et al. (2007) combine the entity model and the content model using a non-parametric HMM. Soricut and Marcu (2006) use several models as feature functions and define a log linear model to assign probability to a given text. Louis and Nenkova (2012) attempt to capture the intentional structure in documents using syntax as a proxy for the communicative goal of a sentence. Syntax features such as parse tree production rules and constituency tags at a particular tree depth were used.
+
+Unlike previous approaches, we do not employ any handcrafted features and adopt an embedding based approach. Local coherence is taken into account by having a next sentence prediction component in the model and global dependencies are naturally captured by an RNN. We demonstrate that our model is able to capture both logical and topical structure by evaluating its performance on different types of data.
+
+Data-driven approaches Neural approaches have gained attention more recently. Li and Hovy (2014) model sentences as embeddings derived from recurrent/recursive neural nets and train a feedforward neural network that takes an input window of sentence embeddings and outputs a probability which represents the coherence of the sentence window. Coherence evaluation is performed by sliding the window over the text and aggregating the score. Li and Jurafsky (2016) study the same model in a larger scale task and also consider a sequence to sequence approach where the model is trained to generate the next sentence given the current sentence and vice versa. Chen et al. (2016) also propose a sentence embedding based approach where they model the probability that one sentence should come before another and define coherence based on the likelihood of the relative order of every pair of sentences. We believe these models are limited by the fact that they are local in nature and our experiments show that exploiting larger contexts can be very beneficial.
+
+Hierarchical RNNs for document modeling Word level and sentence level RNNs have been used in a hierarchical fashion for modeling documents in prior work. Li et al. (2015b) proposed a hierarchical document autoencoder which has potential to be used in generation and summarization applications. More relevant to our work is a similar model (but without an encoder) considered by Lin et al. (2015). A sentence level RNN predicts the bag of words in the next sentence given the previous sentences and a word level RNN predicts the word sequence conditioned on the sentence level RNN hidden state. The model has a structure similar to the content model of Barzilay and Lee (2004) with RNNs playing the roles of the HMM and the bigram language model. Our model has a hierarchical nature in that a sentence level RNN operates over words of a sentence and a document level RNN operates over sentence embeddings.
+
+Combinatorial optimization with RNNs Vinyals et al. (2015a) equip sequence to sequence models with the capability to handle input and output sets, and discuss experiments on sorting, language modeling and parsing. Their goal is to show that input and output orderings can matter in these tasks, which is demonstrated using several small scale experiments. Our work exploits this framework to address the challenging problem of modeling logical and hierarchical structure in text. Vinyals et al. (2015b) proposed pointer-networks, aimed at combinatorial optimization problems where the output dictionary size depends on the number of input elements. We use a pointer-network that points to each of the next sentence candidates as the decoder.
+
+![](images/f18d10cb155fa62453b415d7b0cafee130c5a7b60bdf362f040e430f538f2a9f.jpg)  
+Figure 1: Model Overview: Illustration of the sentence encoder and single time-step computations in encoder and decoder. $s _ { i }$ ’s represent sentence embeddings derived from the sentence encoder. Attention weights are computed for the sentences based on their embeddings and the current hidden state. In the encoder an attention readout is concatenated with the LSTM output to form the next hidden state. The decoder uses the attention weights for prediction.
+
+# 3 APPROACH
+
+Our proposed model is inspired by the way a human would solve this task. First, the model attempts to read the sentences to capture the semantics of the sentences as well as the general context of the paragraph. Given this knowledge, the model attempts to pick the sentences one by one sequentially till exhaustion.
+
+Our model is based on the read, process and write framework proposed by Vinyals et al. (2015a) briefly discussed in section 1. We use the encoder-decoder terminology that is more common in the literature in the following discussion.
+
+The model is comprised of a sentence encoder RNN, an encoder RNN and a decoder RNN (figure 1). An RNN sentence encoder takes as input the words of a sentence $s$ sequentially and computes an embedding representation of the sentence (Figure 1a). Henceforth, we shall use $s$ to refer to a sentence or its embedding interchangeably. The embeddings $\{ s _ { 1 } , s _ { 2 } , . . . , s _ { n } \}$ of a given set of $n$ sentences constitute the sentence memory, available to be accessed by subsequent components.
+
+The encoder is identical to the originally proposed process block and is defined by equations 1-5 (See Figure 1b). Following the regular LSTM hidden state $( h _ { \mathrm { e n c } } ^ { t - 1 } , c _ { \mathrm { e n c } } ^ { t - 1 } )$ update, the hidden state is concatenated with an attention readout vector $s _ { \mathrm { a t t } } ^ { t }$ , and this concatenated vector is treated as the hidden state for the next time step (Equation 5). Attention probabilities are computed by composing the hidden state with embeddings of the candidate sentences through a scoring function $f$ and taking the softmax (Equations 2, 3). This process is iterated for a number of times, called the number of read cycles. As described in Vinyals et al. (2015a) the encoder has the desirable property of being invariant to the order in which the sentence embeddings reside in the memory. The LSTM used here does not take any inputs (input is clamped to zero).
+
+$$
+\begin{array} { r l } & { \tilde { h } _ { \mathrm { e n c } } ^ { t } , c _ { \mathrm { e n c } } ^ { t } = \mathrm { L S T M } ( h _ { \mathrm { e n c } } ^ { t - 1 } , c _ { \mathrm { e n c } } ^ { t - 1 } ) } \\ & { \qquad e _ { \mathrm { e n c } } ^ { t , i } = f ( s _ { i } , \tilde { h } _ { \mathrm { e n c } } ^ { t } ) ; i \in \{ 1 , . . . , n \} } \\ & { \qquad a _ { \mathrm { e n c } } ^ { t } = \mathrm { S o f t m a x } ( e _ { \mathrm { e n c } } ^ { t } ) } \\ & { \qquad s _ { \mathrm { a t t } } ^ { t } = \displaystyle \sum _ { i = 1 } ^ { n } a _ { \mathrm { e n c } } ^ { t , i } s _ { i } } \\ & { \qquad k _ { \mathrm { e n c } } ^ { t } = \widetilde { [ h } _ { \mathrm { e n c } } ^ { t } , ~ s _ { \mathrm { a t t } } ^ { t } ] } \end{array}
+$$
+
+The decoder is a pointer network that takes a similar form with a few differences (equations 6-8, Figure 1c). The LSTM takes the embedding of the previous sentence also as input: At training time the correct order of sentences $( s _ { o _ { 1 } } , s _ { o _ { 2 } } , . . . , \bar { s } _ { o _ { n } } ) = ( \bar { x } ^ { 1 } , x ^ { 2 } , . . . , x ^ { n } )$ is known $\scriptstyle { \dot { o } }$ represents the correct order) and $x ^ { t - 1 }$ is used as the input. At test time the predicted assignment $\hat { x } ^ { t - 1 }$ is used instead. This makes concatenating the attention readout to the hidden state somewhat redundant (verified empirically), and hence it is omitted. The attention computation is identical to that of the encoder. The initial state of the decoder LSTM is initialized with the final hidden state of the encoder as in sequence to sequence models.1 $x ^ { 0 }$ is a vector of zeros. Figure 1 illustrates the single time-step computation in the encoder and decoder.
+
+$$
+\begin{array} { r l } & { h _ { \mathrm { d e c } } ^ { t } , c _ { \mathrm { d e c } } ^ { t } = \mathrm { L S T M } ( h _ { \mathrm { d e c } } ^ { t - 1 } , c _ { \mathrm { d e c } } ^ { t - 1 } , x ^ { t - 1 } ) } \\ & { ~ e _ { \mathrm { d e c } } ^ { t , i } = f ( s _ { i } , h _ { \mathrm { d e c } } ^ { t } ) ; i \in \{ 1 , . . . , n \} ~ } \\ & { ~ a _ { \mathrm { d e c } } ^ { t } = \mathrm { S o f t m a x } ( e _ { \mathrm { d e c } } ^ { t } ) } \end{array}
+$$
+
+The attention probability $a _ { \mathrm { d e c } } ^ { t , i }$ is interpreted as the probability for $s _ { i }$ being the correct sentence choice at position $t$ , conditioned on the previous sentence assignments $p ( S _ { t } = s _ { i } | S _ { 1 } , . . . , S _ { t - 1 } )$ .
+
+# 3.1 SCORING FUNCTION
+
+We consider two choices for the scoring functions $f$ in our experiments. The first one is a single hidden layer feed-forward net that takes $s , h$ as inputs and outputs a score
+
+$$
+f ( s , h ) = W ^ { \prime } { \operatorname { t a n h } } ( W [ s ; h ] + b ) + b ^ { \prime }
+$$
+
+where $W , b , W ^ { \prime } , b ^ { \prime }$ are learnable parameters. This scoring function takes a discriminative approach in classifying the next sentence. Note that the structure of this scoring function is similar to the window network in Li and Hovy (2014). While they used a local window of sentences to capture context, this scoring function exploits the RNN hidden state to score sentence candidates.
+
+We also consider a bilinear scoring function
+
+$$
+f ( s , h ) = s ^ { T } ( W h + b )
+$$
+
+Compared to the previous scoring function, this takes a generative approach of trying to regress the next sentence given the current hidden state $\left( W h + b \right)$ and enforcing that it be most similar to the correct next sentence. We observed that this scoring function led to learning better sentence representations (section 4.4).
+
+# 3.2 TRAINING OBJECTIVE
+
+The model is trained with the maximum likelihood objective:
+
+$$
+\operatorname* { m a x } \sum _ { x \in D } \sum _ { t = 1 } ^ { | x | } \log p ( x ^ { t } | x ^ { 1 } , . . . , x ^ { t - 1 } )
+$$
+
+where $D$ denotes the training set and each training instance is given by an ordered document of sentences $x = ( x ^ { 1 } , . . . , x ^ { | x | } )$ . We also considered an alternative structured margin loss which imposes less penalty for assigning high scores to sentence candidates that are close to the correct sentence in the source document instead of uniformly penalizing all incorrect sentence candidates. However, the softmax output with cross entropy loss consistently performed better.
+
+# 3.3 COHERENCE MODELING
+
+We define the coherence score of an arbitrary partial/complete assignment $( s _ { p _ { 1 } } , . . . , s _ { p _ { k } } )$ to the first $k$ sentence positions as
+
+$$
+\sum _ { i = 1 } ^ { k } \log p ( S _ { i } = s _ { p _ { i } } | S _ { 1 } = s _ { p _ { 1 } } , . . . , S _ { i - 1 } = s _ { p _ { i - 1 } } )
+$$
+
+where $S _ { 1 } , . . , S _ { k }$ are random variables representing the sentence assignment to positions 1 through $k$ . The conditional probabilities are derived from the network. This is our measure of comparing the coherence of different renderings of a document. It is also used as a heuristic during decoding.
+
+Table 1: Statistics of data used in our experiments. For the first two datasets, the test set size\* is the number of permutation pairs used for order discrimination experiments.   
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="4">Length Statistics</td><td colspan="3">Data Split</td><td rowspan="2">Types</td></tr><tr><td>Min</td><td>Mode</td><td>Mean</td><td>Max</td><td>Train</td><td>Val</td><td>Test</td></tr><tr><td>Accidents</td><td>6</td><td>11</td><td>11.6</td><td>19</td><td>100</td><td>-</td><td>1986*</td><td>5,140</td></tr><tr><td>Earthquakes</td><td>3</td><td>7</td><td>10.4</td><td>31</td><td>100</td><td>1</td><td>1956*</td><td>3,775</td></tr><tr><td>NIPS abstracts</td><td>2</td><td>7</td><td>6</td><td>15</td><td>2448</td><td>409</td><td>402</td><td>18,696</td></tr><tr><td>AAN abstracts</td><td>1</td><td>4</td><td>5</td><td>20</td><td>8569</td><td>962</td><td>2626</td><td>40,288</td></tr><tr><td>NSF abstracts</td><td>2</td><td>7</td><td>8.9</td><td>40</td><td>96070</td><td>10185</td><td>21580</td><td>373,909</td></tr></table>
+
+# 4 EXPERIMENTAL RESULTS
+
+# 4.1 MODEL TRAINING
+
+For all tasks discussed in this section we train the model with the same objective (equation 11) on the training data relevant to the task. We used the single hidden layer MLP scoring function for the order discrimination and sentence ordering tasks. Models are trained end-to-end.
+
+Model parameters. We use pre-trained 300 dimensional GloVe word embeddings (Pennington et al., 2014). All LSTMs use a hidden layer size of 1000 and the MLP in section 9 has a hidden layer size of 500. The number of read cycles in the encoder is set to 10. The same model architecture is used across all experiments.
+
+Preprocessing. The nltk sentence tokenizer was used for word tokenization. The GloVe vocabulary was used as the reference vocabulary. Any word not in the vocabulary is checked for a case insensitive match. If a token is hyphenated, we check if the constituent words are in the vocabulary. In the AAN abstracts data (section 4.3.1), some words tend to have a hyphen in the middle because of word hyphenation across lines in the original document. Hence we also check if stripping hyphens produces a vocabulary word. If all checks fail, and a token appears in the training set above a certain frequency, it is added to the vocabulary.
+
+Learning . We used a batch size of 10 and the Adam optimizer (Kingma and Ba, 2014) with a base learning rate of 5e-4 for all experiments. Early stopping is used for regularization.
+
+# 4.2 ORDER DISCRIMINATION
+
+Finding the optimal ordering is a difficult problem when a large number of sentences are required to be rearranged or when there is inherent ambiguity in the ordering of the sentences. For this reason, the ordering problem is commonly formulated as the following binary classification task. Given a reference paragraph and a permuted version of it, the more coherently organized one needs to be identified (Barzilay and Lapata, 2008).
+
+# 4.2.1 DATA
+
+We consider data from two different domains that have been widely used for this task in previous work since Barzilay and Lee (2004); Barzilay and Lapata (2008). The ACCIDENTS data (aka AIRPLANE data) is a set of aviation accident reports from the National Transportation Safety Board’s database. The EARTHQUAKES data comprises newspaper articles from the North American News Text Corpus. In each of the above datasets the training and test sets include 100 articles as well as approximately 20 permutations of each article. Further statistics about the data are shown in table 1.
+
+# 4.2.2 RESULTS
+
+Table 2 compares the performance of our model against prior approaches. We compare results against traditional approaches in the literature as well as some recent data-driven approaches (See section 2 for more details). The entity grid model provides a strong baseline on the ACCIDENTS dataset, only outperformed by our model and Li and Jurafsky (2016) . On the EARTHQUAKE data the window approach of Li and Hovy (2014) and Li and Jurafsky (2016) perform strongly. Our approach outperforms prior models on both datasets, achieving near perfect performance on the Earthquakes dataset.
+
+Table 2: Mean Accuracy comparison on the Accidents and Earthquakes data for the order discrimination task. Reference results obtained from the respective publications.   
+
+<table><tr><td>Methods</td><td>ACCIDENTS</td><td>EARTHQUAKES</td></tr><tr><td>Barzilay and Lapata (2008)</td><td>0.904</td><td>0.872</td></tr><tr><td>Louis and Nenkova (2012)</td><td>0.842</td><td>0.957</td></tr><tr><td>Guinaudeau and Strube (2013)</td><td>0.846</td><td>0.635</td></tr><tr><td>Liand Hovy (2014) -Recurrent</td><td>0.840</td><td>0.951</td></tr><tr><td>Li and Hovy (2014) - Recursive</td><td>0.864</td><td>0.976</td></tr><tr><td>Li and Jurafsky (2016)</td><td>0.930</td><td>0.992</td></tr><tr><td>Ours</td><td>0.944</td><td>0.997</td></tr></table>
+
+While these datasets have been widely used in the literature, they are quite formulaic in nature and are no longer challenging. We hence turn to the more challenging task of ordering a given collection of sentences to make a coherent document.
+
+# 4.3 SENTENCE ORDERING
+
+In this task we directly address the ordering problem. We do not assume the availability of a set of candidate orderings to choose from and instead attempt to find a good ordering from all possible permutations of the sentences.
+
+The difficulty of the ordering problem depends on the nature of the text as well as the length of paragraphs considered. Evaluation on text from arbitrary text sources makes it difficult to interpret the results, since it may not be clear whether to attribute the observed performance to a deficient model or ambiguity in next sentence choices due to many plausible orderings.
+
+Text summaries are a suitable source of data for this task. They often exhibit a clear flow of ideas and have minimal redundancy. We specifically look at abstracts of conference papers and NSF research proposals. This data has several favorable properties. Abstracts usually have a particular high level format - They start out with a brief introduction, a description of the problem addressed and proposed approach and conclude with performance remarks. This would allow us to identify if the model is capable of capturing high level logical structure. Second, abstracts have an average length of about 10, making the ordering task more accessible. Furthermore, this also gives us a significant amount of data to train and test our models.
+
+# 4.3.1 DATA
+
+NIPS Abstracts. We consider abstracts from NIPS papers in the past 10 years. We parsed 3280 abstracts from paper pdfs and obtained 3259 abstracts after omitting erroneous extracts. The dataset was split into years 2005-2013 for training and years 2014, 2015 respectively for validation and testing2.
+
+ACL Abstracts. A second source of abstracts we consider are papers from the ACL Anthology Network (AAN) corpus (Radev et al., 2009) of ACL papers. At the time of retrieval, the corpus had publications up to year 2013. We extracted abstracts from the text parses using simple keyword matching for the strings ‘Abstract’ and ‘Introduction’. Our extraction is successful for 12,157 articles. Most of the failures occur for older papers due to improper formatting and OCR issues. We use all extracts of papers published up to year 2010 for training, year 2011 for validation and years 2012-2013 for testing. We additionally merge words hyphenated at the edges of paragraph boundaries.
+
+NSF Abstracts. We also evaluate our model on the NSF Research Award Abstracts dataset (Lichman, 2013). This dataset comprises abstracts from a diverse set of scientific areas in contrast to the previous two sources of data and the abstracts are also lengthier, making this dataset more challenging. Years 1990-1999 were used for training, 2000 for validation and 2001-2003 for testing. We capped the parses of the abstracts to a maximum length of 40 sentences. Unsuccessful parses and parses of excessive length were discarded. Further details about the datasets are provided in table 1.
+
+Table 3: Comparison against prior methods on the abstracts data.   
+
+<table><tr><td rowspan="2"></td><td colspan="2">NIPS Abstracts</td><td colspan="2">AAN Abstracts</td><td colspan="2">NSF Abstracts</td></tr><tr><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td></tr><tr><td>Random</td><td>15.59</td><td>0</td><td>19.36</td><td>0</td><td>9.46</td><td>0</td></tr><tr><td>Entity Grid (Barzilay and Lapata, 2008)</td><td>20.10</td><td>0.09</td><td>21.82</td><td>0.10</td><td>1</td><td>-</td></tr><tr><td>Seq2seq (Uni) (Li and Jurafsky,2016)</td><td>27.18</td><td>0.27</td><td>36.62</td><td>0.40</td><td>13.68</td><td>0.10</td></tr><tr><td>Window network (Li and Hovy,2014)</td><td>41.76</td><td>0.59</td><td>50.87</td><td>0.65</td><td>18.67</td><td>0.28</td></tr><tr><td>RNN Decoder</td><td>48.22</td><td>0.67</td><td>52.06</td><td>0.66</td><td>25.79</td><td>0.48</td></tr><tr><td>Proposed model</td><td>51.55</td><td>0.72</td><td>58.06</td><td>0.73</td><td>28.33</td><td>0.51</td></tr></table>
+
+# 4.3.2 METRICS
+
+We use the following metrics to evaluate performance on this task. Accuracy measures how often the absolute position of a sentence was correctly predicted. Being a too stringent measure, it penalizes correctly predicted subsequences that are shifted. Another metric widely used in the literature is Kendall’s tau $\left( \tau \right)$ , computed as $1 - 2 \times$ (number of inversions)/ $\binom { n } { 2 }$ , where the number of inversions is the number of pairs in the predicted sequence with incorrect relative order and $n$ is the length of the sequence. Lapata (2006) discusses that this metric reliably correlates with human judgements.
+
+# 4.3.3 BASELINES
+
+Entity Grid. Our first baseline is the Entity Grid model of Barzilay and Lapata (2008). We use the Stanford parser (Klein and Manning, 2003) to get constituency trees for all sentences in our datasets. We derive entity grid representations for the parsed sentences using the Brown Coherence Toolkit.3 A ranking SVM is trained to score correct orderings higher than incorrect orderings as in the original work. We used 20 permutations per document as training data. Since the entity grid representation only provides a means of feature extraction we evaluate the model in the ordering setting as follows. We choose 1000 random permutations for each document, one of them being the correct order, and pick the order with maximum coherence. We experimented with transitions of length at most 3 in the entity-grid.
+
+Sequence to sequence. The second baseline we consider is a sequence to sequence model which is trained to predict the next sentence given the current sentence. Li and Jurafsky (2016) consider similar methods and our model is same as the uni-directional model in their work. These methods were shown to yield sentence embeddings that have competitive performance in several semantic tasks in Kiros et al. (2015).
+
+Window Network. We consider the window approach of Li and Hovy (2014) and Li and Jurafsky (2016) which demonstrated strong performance in the order discrimination task as our third baseline. We adopt the same coherence score interpretation considered by the authors in the above work. In both the above models we consider a special embedding vector which is padded at the beginning of a paragraph and learned during training. This vector allows us to identify the initial few sentences during greedy decoding.
+
+RNN Decoder. Another baseline we consider is our proposed model without the encoder. The decoder hidden state is initialized with zeros. We observed that using a special start symbol as for the other baselines helped obtain better performance with this model. However, a start symbol did not help when the model is equipped with an encoder as the hidden state initialization alone was good enough.
+
+We do not place emphasis on the particular search algorithm in this work and thus use beam search using the coherence score heuristic for all models. A beam size of 100 was used. During decoding, sentence candidates that have been already chosen are pruned from the beam. All RNNs use a hidden layer size of 1000. For the window network we used a window size of 3 and a hidden layer size of 2000. We initialize all models with pre-trained GloVe word embeddings.
+
+![](images/e53d4ba67148ca85ebcb090221c5785b3890a9ea64b01607ca07a2f3792adf2a.jpg)  
+Figure 2: t-SNE embeddings of representations learned by the model for sentences from the test set. The embeddings are color coded by the position of the sentence in the document it appears.
+
+# 4.3.4 RESULTS
+
+We assess the performance of our model against baseline methods in table 3. The window network performs strongly compared to the other baselines. Our model does better by a significant margin by exploiting global context, demonstrating that global context is important to be successful in this task.
+
+While the Entity-Grid model has been fairly successful for the order discrimination task in the past we observe that it fails to discriminate between a large number of candidates. One reason could be that the feature representation is fairly less sensitive to local changes in sentence order (such as swapping adjacent sentences). We did not use coreference resolution for computing the entity-grids due to the computational overhead. This could potentially improve results by a few percentage points. The computational expense of obtaining parse trees and constructing grids on a large amount of data prohibited us from experimenting with this model on the NSF abstracts data.
+
+The sequence to sequence model falls short of the window network in performance. Interestingly, Li and Jurafsky (2016) observe that the seq2seq model outperforms the window network in an order discrimination task on wikipedia data. However, the wikipedia data considered in their work has an order of magnitude more data that the datasets considered here, and that could have potentially helped the generative model. These models are also expensive during inference since they involve computing and sampling from word distributions.
+
+In Figure 3 we attempt to visualize the sentence representations learned by the sentence encoder in our model. The figure shows 2-dimensional t-SNE embeddings of test set sentences from each of the datasets color coded by their positions in the source abstract. This shows that the model learns high-level structure in the documents, generalizing well to unseen documents. The structure is less apparent in the NSF data which we presume is because of the data diversity and longer documents. While approaches based on the content model of Barzilay and Lee (2004) attempt to explicitly capture topics by discovering clusters in sentences, we observe that the neural approach implicitly discovers such structure.
+
+# 4.4 LEARNED SENTENCE REPRESENTATIONS
+
+One of the original motivations for this work is the question whether we can learn high quality sentence representations by learning to model text coherence. To address this question we trained our model on a large dataset of paragraphs. We chose the BookCorpus dataset (Kiros et al., 2015) for this purpose. We trained the model with two key changes from the models trained on the abstracts data - 1) In addition to the sentences in the paragraph being considered, we added more contrastive sentences from other paragraphs as well. 2) We use the bilinear scoring function. These techniques helped obtain better representations when training on large amounts of data.
+
+To evaluate the quality of the sentence embeddings derived from the model, we use the evaluation pipeline of Kiros et al. (2015) for tasks that involve understanding sentence semantics. These evaluations are performed by training a classifier on top of the embeddings derived from the model so that the performance is indicative of the quality of sentence representations. We consider the semantic relatedness and paraphrase detection tasks. Our results are presented in tables 4a, 4b. Results for only uni-directional versions of different models are discussed here for a reasonable comparison.
+
+Table 4: Performance comparison for the semantic similarity (SICK dataset) and paraphrase detection (MSR paraphrase corpus) tasks. In each table the first section shows some best performing supervised methods in the literature. The second section shows models relevant to the skip-thought model. The third section shows our models.   
+(a) Sentence similarity   
+
+<table><tr><td>Method</td><td>r</td><td>p</td><td>MSE</td></tr><tr><td colspan="4">Purely supervised methods</td></tr><tr><td>DT-RNN (Tai et al., 2015)</td><td>0.792</td><td>0.732</td><td>0.382</td></tr><tr><td>LSTM (Tai et al.,2015)</td><td>0.853</td><td>0.791</td><td>0.283</td></tr><tr><td>DT-LSTM (Tai et al.,2015)</td><td>0.868</td><td>0.808</td><td>0.253</td></tr><tr><td colspan="4">Classifier trained on sentence embeddings</td></tr><tr><td>skip-bow (Kiros et al.,2015)</td><td>0.782</td><td>0.724</td><td>0.398</td></tr><tr><td>uni-skip (Kiros et al., 2015)</td><td>0.848</td><td>0.778</td><td>0.287</td></tr><tr><td>Ordering model</td><td>0.807</td><td>0.742</td><td>0.356</td></tr><tr><td>+BoW</td><td>0.842</td><td>0.775</td><td>0.299</td></tr><tr><td>+ uni-skip</td><td>0.860</td><td>0.795</td><td>0.270</td></tr></table>
+
+(b) Paraphrase detection   
+
+<table><tr><td>Method</td><td>Acc F1</td></tr><tr><td>Purely supervised methods</td><td>83.6</td></tr><tr><td>Socher et al. (2011) Madnani et al. (2012) Ji and Eisenstein (2013)</td><td>76.8 77.4 84.1 80.4</td></tr><tr><td> Classifier trained on sentence embeddings</td><td>86.0</td></tr><tr><td>skip-bow (Kiros et al., 2015) uni-skip (Kiros et al., 2015)</td><td>67.8 80.3 73.0 81.9</td></tr><tr><td>Ordering model</td><td>72.3</td></tr><tr><td>+BoW + uni-skip</td><td>81.0 74.0 81.9 74.9 82.5</td></tr></table>
+
+Skip-thought vectors are learned by predicting both the previous and next sentences given the current sentence. Following suit, we train two models - one predicting the correct order in the forward direction and another in the backward direction. Note that the sentence level RNN is still unidirectional in both cases. The numbers shown for the ordering model were obtained by concatenating the representations obtained from the two models.
+
+Concatenating the above representation with the bag of words representation (using the fine-tuned word embeddings) of the sentence further improves performance4. We believe the reason to be that the ordering model can choose to pay less attention to specific lexical information and instead focus on the high level document structure. Hence the two representations can be seen as capturing complementary semantics. Adding the skip-thought embedding features as well improves performance further.
+
+Our model has several key advantages over the skip-thought model. The skip-thought model has a word-level reconstruction objective and requires training with large softmax output layers. This limits the size of the vocabulary and makes training very time consuming (they use a vocabulary size of $2 0 \mathrm { k }$ and report 2 weeks of training). Our model achieves comparable performance and does not have such a word reconstruction component. We are able to train with a large vocabulary of $4 0 0 \mathrm { k }$ words and the above results were obtained with a training time of 2 days.
+
+A conceptual issue surrounding word-level reconstruction is that it forces the model to predict both the meaning and syntax of the target sentence. This makes learning difficult since there are numerous ways of expressing the same idea in syntax. In our model we instead let the model discover features from a sentence which are both predictive (of the next sentence) and predictable (from the previous sentences) and interpret these set of features as a meaning representation. We believe this is an important distinction and hope to study these models further in the context of learning syntax independent semantic representations of sentences.
+
+# 5 CONCLUSION
+
+In this work we considered the challenging problem of coherently organizing a given set of sentences. Our RNN based model performs strongly compared to baseline methods as well as prior work on sentence ordering and order discrimination tasks. We further demonstrated that the model captures high level document structure and learns useful sentence representations when trained on large amounts of data. Our approach to the ordering problem deviates from most prior work that use handcrafted features. However, exploiting linguistic features for next sentence classification can potentially further improve performance on the task. Entity distribution patterns can provide useful features about named entities that are treated as out of vocabulary words. The ordering problem can be further studied at higher level discourse units such as paragraphs, sections and chapters.
+
+# REFERENCES
+
+Automated scoring of writing quality. URL https://www.ets.org/research/topics/ as_nlp/writing_quality. Accessed: 2016-11-1.
+
+R. Barzilay and N. Elhadad. Inferring strategies for sentence ordering in multidocument news summarization. Journal of Artificial Intelligence Research, pages 35–55, 2002.
+
+R. Barzilay and M. Lapata. Modeling local coherence: An entity-based approach. Computational Linguistics, 34(1):1–34, 2008.
+
+R. Barzilay and L. Lee. Catching the drift: Probabilistic content models, with applications to generation and summarization. arXiv preprint cs/0405039, 2004.
+
+J. Burstein, J. Tetreault, and S. Andreyev. Using entity-based features to model coherence in student essays. In Human language technologies: The 2010 annual conference of the North American chapter of the Association for Computational Linguistics, pages 681–684. Association for Computational Linguistics, 2010.
+
+X. Chen, X. Qiu, and X. Huang. Neural sentence ordering. arXiv preprint arXiv:1607.06952, 2016.
+
+M. Elsner, J. L. Austerweil, and E. Charniak. A unified local and global model for discourse coherence. In HLT-NAACL, pages 436–443, 2007.
+
+P. W. Foltz, W. Kintsch, and T. K. Landauer. The measurement of textual coherence with latent semantic analysis. Discourse processes, 25(2-3):285–307, 1998.
+
+B. J. Grosz, S. Weinstein, and A. K. Joshi. Centering: A framework for modeling the local coherence of discourse. Computational linguistics, 21(2):203–225, 1995.
+
+C. Guinaudeau and M. Strube. Graph-based local coherence modeling. In ACL (1), pages 93–103, 2013.
+
+Y. Ji and J. Eisenstein. Discriminative improvements to distributional sentence similarity. In EMNLP, pages 891–896, 2013.
+
+Y. Ji, T. Cohn, L. Kong, C. Dyer, and J. Eisenstein. Document context language models. In International Conference on Learning Representations, Poster Paper, volume abs/1511.03962, 2015.
+
+D. Kingma and J. Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
+
+R. Kiros, Y. Zhu, R. R. Salakhutdinov, R. Zemel, R. Urtasun, A. Torralba, and S. Fidler. Skip-thought vectors. In Advances in Neural Information Processing Systems, pages 3276–3284, 2015.
+
+D. Klein and C. D. Manning. Accurate unlexicalized parsing. In Proceedings of the 41st Annual Meeting on Association for Computational Linguistics-Volume 1, pages 423–430. Association for Computational Linguistics, 2003.
+
+M. Lapata. Probabilistic text structuring: Experiments with sentence ordering. In Proceedings of the 41st Annual Meeting on Association for Computational Linguistics-Volume 1, pages 545–552. Association for Computational Linguistics, 2003.
+
+M. Lapata. Automatic evaluation of information ordering: Kendall’s tau. Computational Linguistics, 32(4):471–484, 2006.
+
+J. Li and E. H. Hovy. A model of coherence based on distributed sentence representation. In EMNLP, pages 2039–2048, 2014.
+
+J. Li and D. Jurafsky. Neural net models for open-domain discourse coherence. arXiv preprint arXiv:1606.01545, 2016.   
+J. Li, X. Chen, E. Hovy, and D. Jurafsky. Visualizing and understanding neural models in nlp. arXiv preprint arXiv:1506.01066, 2015a.   
+J. Li, M.-T. Luong, and D. Jurafsky. A hierarchical neural autoencoder for paragraphs and documents. arXiv preprint arXiv:1506.01057, 2015b.   
+M. Lichman. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ ml.   
+R. Lin, S. Liu, M. Yang, M. Li, M. Zhou, and S. Li. Hierarchical recurrent neural network for document modeling. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 899–907, 2015.   
+A. Louis and A. Nenkova. A coherence model based on syntactic patterns. In Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pages 1157–1168. Association for Computational Linguistics, 2012.   
+N. Madnani, J. Tetreault, and M. Chodorow. Re-examining machine translation metrics for paraphrase identification. In Proceedings of the 2012 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 182–190. Association for Computational Linguistics, 2012.   
+E. Miltsakaki and K. Kukich. Evaluation of text coherence for electronic essay scoring systems. Natural Language Engineering, 10(01):25–55, 2004.   
+J. Pennington, R. Socher, and C. D. Manning. Glove: Global vectors for word representation. In EMNLP, volume 14, pages 1532–43, 2014.   
+D. R. Radev, M. T. Joseph, B. Gibson, and P. Muthukrishnan. A Bibliometric and Network Analysis of the field of Computational Linguistics. Journal of the American Society for Information Science and Technology, 2009.   
+R. Socher, E. H. Huang, J. Pennin, C. D. Manning, and A. Y. Ng. Dynamic pooling and unfolding recursive autoencoders for paraphrase detection. In Advances in Neural Information Processing Systems, pages 801–809, 2011.   
+R. Soricut and D. Marcu. Discourse generation using utility-trained coherence models. In Proceedings of the COLING/ACL on Main conference poster sessions, pages 803–810. Association for Computational Linguistics, 2006.   
+I. Sutskever, O. Vinyals, and Q. V. Le. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pages 3104–3112, 2014.   
+K. S. Tai, R. Socher, and C. D. Manning. Improved semantic representations from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.   
+O. Vinyals, S. Bengio, and M. Kudlur. Order matters: Sequence to sequence for sets. arXiv preprint arXiv:1511.06391, 2015a.   
+O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In Advances in Neural Information Processing Systems, pages 2674–2682, 2015b.
+
+Table 5: Visualizing salient words.   
+
+<table><tr><td>In this paper,we propose a new method for semantic class induction . First ,we introduce a generative model of sentences ,based on dependency trees and which takes into account homonymy Our model can thus be seen as a generalization of Brown clustering . Second , we describe an efficient algorithm to perform inference and learning in this model . Third ,we apply our proposed method on two large datasets （108 tokens ,105 words types ）,and demonstrate that classes induced by our algorithm improve performance over Brown clustering on the task of semisupervised supersense tagging and named entity recognition .</td></tr><tr><td>Representation learning is a promising technique for discovering features that allow supervised classifiers to generalize from a source domain dataset to arbitrary new domains We present a novel, formal statement of the representation learning task . We argue that because the task is computationally intractable in general,it is important for arepresentation learner to be able to incorporate expert knowledge during its search for helpful features . Leveraging the Posterior Regularization framework ,we develop an architecture for incorporating biases into</td></tr><tr><td>learners identify significantly better sets offeatures than unbiased learners,resulting inarelative reduction in error of more than 16% forboth tasks ,with respect to existing state-of-the-art representation learning techniques. We present an approach for detecting salient (important）dates in texts in order to automatically build event timelines from a search query（e.g . the name of an event or person,etc .）. This work was carried out on a corpus of newswire texts in English provided by the Agence France Presse</td></tr><tr><td>(AFP). In order to extract salient dates that warrant inclusion in an event timeline ,we first recognize and normalize temporal expressons in texts and then use a machine-learning approach to extract salient dates that relate to a particular topic . We focused only on extracting the dates and not the events to which they are related . The paper aims to come up with a system that examines the degree of semantic equivalence between two</td></tr><tr><td>sentences. At the core of the paper is the attempt to grade the similarity of two sentences by finding the maximal weighted bipartite match between the tokens of the two sentences . The tokens include single words,or multiwords in case of Named Entitites ，adjectivally and numerically modified words. Two token similarity measures are used for the task -WordNet based similarity,and a statistical word similarity</td></tr></table>
+
+# A WORD INFLUENCE
+
+We attempt to understand what text level clues the model captures to perform the ordering task. Some techniques for visualizing neural network models in the context of text applications are discussed in Li et al. (2015a). Drawing inspiration from this work, we use gradients of prediction decisions with respect to the words of the correct sentence as a proxy for the salience of each word.
+
+For each time step during decoding we do the following. Assume the sentence assignments for all previous time steps have been correct. let $h$ be the current hidden state in this setting and $s = ( w _ { 1 } , . . . , w _ { n } )$ be the correct next sentence candidate, the $w _ { i }$ being its words. The score for this sentence is defined as $e = f ( s , h )$ (See equation 7). The importance of word $w _ { i }$ in predicting $s$ as the correct next sentence is interpreted as $\big | \big | \frac { \partial e } { \partial w _ { i } } \big | \big |$ . We assume $h$ to be fixed and only backpropagate gradients through the sentence encoder.
+
+Table 5 shows visualizations of a few selected abstracts. Words expressed in darker shades correspond to higher gradient norms. In the first example the model seems to be using the word clues ‘first’, ‘second’ and ‘third’. A similar observation was made by Chen et al. (2016) in their experiments. In the second example we observe that the model has paid attention to phrases such as ‘We present’, ‘We argue’ which are typical of abstract texts. The model has also focused on the word ‘representation’
+
+![](images/adad558c7205bc48c9fabf9b69b0c9378dffcd77969ecbe41c7f2faafcc2571f.jpg)  
+(b) Accuracy of predicting the correct sentence at a given position.
+
+![](images/e81e192d491a4ec3d3ee35f9f997b4da73575cf61465110ee3b4df1540c5e875.jpg)  
+Figure 3: Performance with respect to paragraph length and sentence position - NIPS abstracts test data.
+
+(a) $\tau$ scores of order predictions on paragraphs of a given length.
+
+appearing in the first two sentences. Similarly in the third example, the words ‘salient’ and ‘dates’ have been attended to. In the last example, the words ‘token’, ‘tokens’, ‘tokenization’ have received attention. We believe that these observations link to ideas from centering theory which state that entity distributions in coherent discourses adhere to certain patterns. The model has implicitly learned learned these patterns with no syntax annotations or handcrafted features.
+
+# B PERFORMANCE ANALYSIS
+
+Figure 3a shows the average $\tau$ for the models on the NIPS abstracts test set for a given paragraph length. The performance of local approaches dies down fairly quickly as we can expect and face difficulties handling lengthy paragraphs. Our model attempts to maintain consistent performance with increasing paragraph size with a more gradual decline in performance.
+
+Figure 3b compares the average prediction accuracy for a given sentence position in the test set. It is interesting to observe that all models fair well in predicting the first sentence. The greedy decoding procedure also contributes to the decline in performance as we move right. Our model remains more robust compared to the other two methods.
+
+Another trend to be observed is that as the context size increases (2 for next sentence generation, 3 for window network, complete sentential history for our model) the performance decline is more gradual.
+
+(a) Classify 1 of 2 - Accuracy   
+
+<table><tr><td></td><td>NIPS</td><td>AAN</td><td>NSF</td></tr><tr><td>Entity Grid</td><td>0.712</td><td>0.660</td><td>=</td></tr><tr><td>Seq2seq (Uni)</td><td>0.890</td><td>0.888</td><td></td></tr><tr><td>Window network</td><td>0.944</td><td>0.942</td><td>0.936</td></tr><tr><td>RNNDecoder</td><td>0.964</td><td>0.952</td><td>0.972</td></tr><tr><td>Proposed model</td><td>0.970</td><td>0.955</td><td>0.982</td></tr></table>
+
+(b) Classify 1 of 100 - Accuracy   
+
+<table><tr><td></td><td>NIPS</td><td>AAN</td><td>NSF</td></tr><tr><td>Entity Grid</td><td>0.070</td><td>0.102</td><td>=</td></tr><tr><td>Seq2seq (Uni)</td><td>0.171</td><td>0.290</td><td>=</td></tr><tr><td>Window network</td><td>0.385</td><td>0.470</td><td>0.300</td></tr><tr><td>RNN Decoder</td><td>0.516</td><td>0.541</td><td>0.647</td></tr><tr><td>Proposed model</td><td>0.566</td><td>0.581</td><td>0.710</td></tr></table>
+
+Table 7: Accuracy (of predicting sentence position) and $\tau$ metrics for the 1 of 100 classification task.   
+
+<table><tr><td rowspan="2"></td><td colspan="2">NIPS Abstracts</td><td colspan="2">AAN Abstracts</td><td colspan="2">NSF Abstracts</td></tr><tr><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td></tr><tr><td>Entity Grid</td><td>21.30</td><td>0.12</td><td>23.22</td><td>0.11</td><td></td><td></td></tr><tr><td>Seq2seq (Uni)</td><td>38.36</td><td>0.40</td><td>48.47</td><td>0.50</td><td>=</td><td>=</td></tr><tr><td>Window network</td><td>59.20</td><td>0.67</td><td>64.02</td><td>0.71</td><td>44.65</td><td>0.46</td></tr><tr><td>RNN Decoder</td><td>67.05</td><td>0.73</td><td>68.54</td><td>0.74</td><td>79.01</td><td>0.76</td></tr><tr><td>Proposed model</td><td>72.25</td><td>0.79</td><td>72.25</td><td>0.77</td><td>83.85</td><td>0.81</td></tr></table>
+
+# C ADDITIONAL EXPERIMENTAL RESULTS
+
+# C.1 CLASSIFICATION EXPERIMENTS FOR ABSTRACTS DATA
+
+Classify 1 of 2 (Pairwise ranking). We create a random permutation for each document (different from the correct order) and compute the pairwise classification accuracy. The mean result over 100 such experiments is reported in table 6a.
+
+Classify 1 of N. In this experiment we consider a pool of $\Nu = 1 0 0$ permutations where one of them is the correct order and the rest are random permutations. We compute coherence scores of all orderings in the pool and pick the best one. Table 6b reports how accurately each model identified the correct order. Table 7 computes the same metrics in table 3 for the orders that were chosen by the model.
+
+The performance gaps are not significant for the first experiment. However, they are more pronounced in the second experiment. The reason is because in the binary classification setting, a majority of the permutations will be very different from the correct order, and the models can discriminate well for these cases. However, when choosing from a large set of permutations the models need to be sensitive to permutations which deviate from the correct ordering by a small amount (Eg: only two sentences out of place from correct order). Models incapable of discriminating at this finer level perform tend to perform poorly.
+
+Note that the second experiment is closer to the practical task of finding an appropriate presentation ordering for a given collection of sentences, while taking the decoding algorithm out of the picture.
+
+# C.2 ORDER DISCRIMINATION - PENN TREEBANK DATASET
+
+We perform order discrimination experiments on the Penn Treebank dataset. The experimental protocol is identical to that of Ji et al. (2015). The standard train, dev, test split was used. The vocabulary comprises the most 10,000 frequent words and an additional special symbol representing low frequency words. A bootstrapping procedure is used for evaluation - 1000 test sets are generated by randomly sampling with replacement 155 documents from the test set and constructing a random permutation different from the correct order for each sampled document. We used the same model hyperparameters described in section 4.1. We did not use pre-trained word embeddings for fair comparison with the reference method. Performance statistics are computed over the 1000 bootstrapped test sets. Table 8 shows a performance comparison.
+
+A key difference of this dataset compared to the other datasets is that the documents are more open domain and they are significantly longer. Our model performs strongly despite these differences.
+
+Table 8: Order discrimination on PTB dataset. Reference results re-printed from Ji et al. (2015).   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Accuracy</td></tr><tr><td>Mean (%)</td><td>Standard deviation (%)</td></tr><tr><td>Hierarchical RNNLM (Lin et al., 2015)</td><td>75.32</td><td>4.42</td></tr><tr><td>DCLM (Ji et al., 2015)</td><td>83.26</td><td>3.77</td></tr><tr><td>Proposed model</td><td>90.25</td><td>2.38</td></tr></table>
+
+Table 9: Impact of using contrastive sentences and the bilinear scoring function for learning sentence representations.   
+
+<table><tr><td rowspan="2">Contrastive Sentences</td><td rowspan="2">Scoring Function</td><td colspan="3">Semantic Relatedness</td><td colspan="2">Paraphrase detection</td></tr><tr><td>r</td><td>p</td><td>MSE</td><td>Acc</td><td>F1</td></tr><tr><td>No</td><td>MLP</td><td>0.631</td><td>0.568</td><td>0.613</td><td>0.687</td><td>0.791</td></tr><tr><td>No</td><td>Bilinear</td><td>0.650</td><td>0.609</td><td>0.588</td><td>0.681</td><td>0.785</td></tr><tr><td>Yes</td><td>MLP</td><td>0.718</td><td>0.648</td><td>0.494</td><td>0.689</td><td>0.785</td></tr><tr><td>Yes</td><td>Bilinear</td><td>0.787</td><td>0.727</td><td>0.387</td><td>0.712</td><td>0.804</td></tr></table>
+
+# C.3 SENTENCE REPRESENTATION LEARNING TASK
+
+We briefly discussed two techniques in section 4.4 that helped obtain better sentence representations.
+
+• Adding contrastive sentence candidates for the decoder • The bilinear scoring function
+
+Table 9 shows results of ablative experiments which demonstrate the effect of these ideas. Each experimental setting indicates whether or not contrastive sentences were used and the type of scoring function employed. Note that these models were trained to predict the correct order of sentences only in the forward direction (as opposed to the results reported in table 4 where two models were trained to predict the order in the forward and backward directions and the representations were concatenated). Models were chosen using the validation set of the relevant task.
+
+We observe the trend that adding contrastive sentences or switching from the MLP to the bilinear scoring function produces a sharp improvement in the result for the semantic relatedness task. Although the performance differences are less significant in the paraphrase detection task when the individual factors are changed, we observe an overall performance gain by using contrastive sentences and the bilinear scoring function.
+
+This confirms our intuition that adding contrastive sentences makes the task more challenging and leads to better representations being learned. Similarly, the bilinear scoring function takes a generative approach of trying to regress the next sentence as opposed to the MLP scoring function which treats the prediction task as purely discriminative, and hence encourages the learning of better representations.
+
+# D MODEL DETAILS
+
+The LSTM update in equation 1 of the paper
+
+$$
+h _ { t } , c _ { t } = L S T M ( h _ { t - 1 } , c _ { t - 1 } )
+$$
+
+is as follows.
+
+$$
+\begin{array} { r l } & { i _ { t } = \sigma \big ( W _ { i } h _ { t - 1 } + b _ { i } \big ) } \\ & { f _ { t } = \sigma \big ( W _ { f } h _ { t - 1 } + b _ { f } \big ) } \\ & { o _ { t } = \sigma \big ( W _ { o } h _ { t - 1 } + b _ { o } \big ) } \\ & { \hat { c } _ { t } = \mathrm { t a n h } \big ( W _ { c } h _ { t - 1 } + b _ { c } \big ) } \\ & { c _ { t } = f _ { t } \odot c _ { t - 1 } + i _ { t } \odot \hat { c } _ { t } } \\ & { h _ { t } = o _ { t } \odot \mathrm { t a n h } \big ( c _ { t } \big ) } \end{array}
+$$
+
+where $W _ { \{ i , f , o , c \} } , b _ { \{ i , f , o , c \} }$ are learnable parameters.
+
+The LSTM update in equation 6
+
+is given by the following.
+
+$$
+h _ { t } , c _ { t } = L S T M ( h _ { t - 1 } , c _ { t - 1 } , x _ { t - 1 } )
+$$
+
+$$
+\begin{array} { r l } & { i _ { t } = \sigma \big ( W _ { h i } h _ { t - 1 } + W _ { x i } x _ { t - 1 } + b _ { i } \big ) } \\ & { f _ { t } = \sigma \big ( W _ { h f } h _ { t - 1 } + W _ { x f } x _ { t - 1 } + b _ { f } \big ) } \\ & { o _ { t } = \sigma \big ( W _ { h o } h _ { t - 1 } + W _ { x o } x _ { t - 1 } + b _ { o } \big ) } \\ & { \hat { c } _ { t } = \mathrm { t a n h } \big ( W _ { h c } h _ { t - 1 } + W _ { x c } x _ { t - 1 } + b _ { c } \big ) } \\ & { c _ { t } = f _ { t } \odot c _ { t - 1 } + i _ { t } \odot \hat { c } _ { t } } \\ & { h _ { t } = o _ { t } \odot \mathrm { t a n h } \big ( c _ { t } \big ) } \end{array}
+$$
+
+where $W _ { \{ h i , h f , h o , h c \} } , W _ { \{ x i , x f , x o , x c \} } , b _ { \{ i , f , o , c \} }$ are learnable parameters.

parse/train/S1AG8zYeg/S1AG8zYeg_content_list.json

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+    {
+        "type": "text",
+        "text": "SENTENCE ORDERING USING RECURRENT NEURAL NETWORKS ",
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+        "type": "text",
+        "text": "Lajanugen Logeswaran, Honglak Lee & Dragomir Radev ",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Department of EECS   \nUniversity of Michigan   \nAnn Arbor, MI 48109, USA   \n{llajan,honglak,radev}@umich.edu ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            276,
+            544,
+            291
+        ],
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+        "type": "text",
+        "text": "Modeling the structure of coherent texts is a task of great importance in NLP. The task of organizing a given set of sentences into a coherent order has been commonly used to build and evaluate models that understand such structure. In this work we propose an end-to-end neural approach based on the recently proposed set to sequence mapping framework to address the sentence ordering problem. Our model achieves state-of-the-art performance in the order discrimination task on two datasets widely used in the literature. We also consider a new interesting task of ordering abstracts from conference papers and research proposals and demonstrate strong performance against recent methods. Visualizing the sentence representations learned by the model shows that the model has captured high level logical structure in these paragraphs. The model also learns rich semantic sentence representations by learning to order texts, performing comparably to recent unsupervised representation learning methods in the sentence similarity and paraphrase detection tasks. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+            527,
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+            544
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Modeling the structure of coherent texts is one of the central problems in NLP. A well written piece of text has a particular high level logical and topical structure to it. The actual word and sentence choices as well as their transitions come together to convey the purpose of the text. Our overarching goal is to build models that can learn such structure by learning to arrange a given set of sentences to make coherent text. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The sentence ordering task finds several applications. Multi-document Summarization (MDS) and retrieval based question answering involve extracting information from multiple source documents and organizing the content into a coherent summary. Since the relative ordering about sentences that come from different sources can be unclear, being able to automatically evaluate a particular order and/or finding the optimal order is essential. Barzilay and Elhadad (2002) discuss the importance of an explicit ordering component in MDS systems. Their experiments show that finding an acceptable ordering can enhance user comprehension. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Models that learn to order text fragments can also be used as models of coherence. Automated essay scoring (Miltsakaki and Kukich, 2004; Burstein et al., 2010) is an application that can benefit from such a coherence model. Coherence is one of the key elements on which student essays are evaluated in standardized writing tests such as GRE (ETS). Apart from its importance and applications, our motivation to address this problem also stems from its stimulating nature. It can be considered as a jigsaw puzzle of sorts in the language domain. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Our approach to the problem of modeling coherence is driven by recent successes in 1) capturing semantics using distributed representations and 2) using RNNs for sequence modeling tasks. ",
+        "bbox": [
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+            833,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Success in unsupervised approaches for learning embeddings for textual entities from large text corpora altered the way NLP problems are studied today. These embeddings have been shown to capture syntactic and semantic information as well as higher level analogical structure. These methods have been adopted to learn vector representations of sentences, paragraphs and entire documents. Embedding based approaches allow models to be trained end-to-end from scratch with no handcrafting. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recurrent Neural Networks (RNNs) have become the de facto approach to sequence learning and mapping problems in recent times. The Sequence to sequence mapping framework (Sutskever et al., 2014), as well as several of its variants have fuelled RNN based approaches to a wide variety of problems including language modeling, language generation, machine translation, question answering and many others. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Vinyals et al. (2015a) recently showed that the order in which tokens of the input sequence are fed to seq2seq models has a significant impact on the performance of the model. In particular, for problems such as sorting which involve a source set (as opposed to a sequence), the optimal order to feed the tokens is not clear. They introduce an attention mechanism over the input tokens which allows the model to learn a soft input order. This is called the read, process and write (or set to sequence) framework. The read block maps the input tokens to a fixed length vector representation. The process block is an RNN encoder which, at each time step, attends to the input token embeddings and computes an attention readout, appending it to the current hidden state. The write block is an RNN which produces the target sequence conditioned on the representation produced by the process block. ",
+        "bbox": [
+            174,
+            215,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work we propose an RNN based approach to the sentence ordering problem which exploits the set to sequence framework. A word level RNN encoder produces sentence embeddings. A sentence level set encoder RNN iteratively attends to these embeddings (process block above) and constructs a representation of the context. Initialized with this representation, a sentence level pointer network RNN points to the next sentence candidates. ",
+        "bbox": [
+            174,
+            348,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The most widely studied task relevant to sentence ordering and coherence modeling in the literature is the order discrimination task. Given a document and a permuted version of it, the task involves identifying the more coherent ordering of the two. Our proposed model achieves state of the art performance on two benchmark datasets for this task, outperforming several classical approaches and more recent data-driven approaches. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Addressing the more challenging task of ordering a given collection of sentences, we consider the novel and interesting task of ordering sentences from abstracts of conference papers and research grants. Our model strongly outperforms previous work on this task. We visualize the learned sentence representations and show that our model captures high level discourse structure. We provide visualizations that aid understanding what information in the sentences the model uses to identify the next sentence. We also study the quality of the sentence representations learned by the model by training the model on a large text corpus and show that these embeddings are comparable to recent unsupervised methods in capturing semantics. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In summary our key contributions are as follows, ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "• We propose an end to end trainable model based on the set to sequence framework to address the challenging problem of organizing a given collection of sentences in a coherent order. • We consider the novel task of understanding structure in abstract paragraphs and demonstrate state of the art results in order discrimination and sentence ordering tasks. • We demonstrate that the proposed model is capable of learning semantic representations of sentences that are comparable to recently proposed methods for learning such representations. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            758,
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+            775
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Coherence modeling and sentence ordering The coherence modeling and sentence ordering tasks have been approached by closely related techniques. Most approaches propose a measure of coherence and formulate the ordering problem as finding an order with maximal coherence. Recurring themes from prior work include linguistic features, centering theory, local and global coherence. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Local coherence has been modeled by considering properties of a local window of sentences such as sentence similarity and sentence transition structure. Foltz et al. (1998) represent words using vectors of co-occurent counts and sentences as a mean of these word vectors. Sentence similarity is defined as the cosine distance between sentence vectors and text coherence is modeled as a normalized sum of similarity scores of adjacent sentences. Lapata (2003) represents sentences by vectors of linguistic features and learn the transition probabilities from one set of features to another in adjacent sentences. A popular model of coherence is the Entity-Grid model Barzilay and Lapata (2008) which captures local coherence by modeling patterns of entity distributions in the discourse. Sentences are represented by the syntactic roles of entities appearing in the document and entity transition frequencies in successive sentences are treated as features that are are used to train a ranking SVM. These two approaches find motivation from ideas in centering theory (Grosz et al., 1995) which state that nouns and entities in coherent discourses exhibit certain patterns. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Global models of coherence typically use an HMM to model document structure. The content model proposed by Barzilay and Lee (2004) represents topics in a particular domain as states in an HMM. State transitions capture possible presentation orderings within the domain. Words of a sentence are modeled using a topic-specific language model. The content model has inspired several subsequent work to combine the strengths of local and global models. Elsner et al. (2007) combine the entity model and the content model using a non-parametric HMM. Soricut and Marcu (2006) use several models as feature functions and define a log linear model to assign probability to a given text. Louis and Nenkova (2012) attempt to capture the intentional structure in documents using syntax as a proxy for the communicative goal of a sentence. Syntax features such as parse tree production rules and constituency tags at a particular tree depth were used. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Unlike previous approaches, we do not employ any handcrafted features and adopt an embedding based approach. Local coherence is taken into account by having a next sentence prediction component in the model and global dependencies are naturally captured by an RNN. We demonstrate that our model is able to capture both logical and topical structure by evaluating its performance on different types of data. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Data-driven approaches Neural approaches have gained attention more recently. Li and Hovy (2014) model sentences as embeddings derived from recurrent/recursive neural nets and train a feedforward neural network that takes an input window of sentence embeddings and outputs a probability which represents the coherence of the sentence window. Coherence evaluation is performed by sliding the window over the text and aggregating the score. Li and Jurafsky (2016) study the same model in a larger scale task and also consider a sequence to sequence approach where the model is trained to generate the next sentence given the current sentence and vice versa. Chen et al. (2016) also propose a sentence embedding based approach where they model the probability that one sentence should come before another and define coherence based on the likelihood of the relative order of every pair of sentences. We believe these models are limited by the fact that they are local in nature and our experiments show that exploiting larger contexts can be very beneficial. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Hierarchical RNNs for document modeling Word level and sentence level RNNs have been used in a hierarchical fashion for modeling documents in prior work. Li et al. (2015b) proposed a hierarchical document autoencoder which has potential to be used in generation and summarization applications. More relevant to our work is a similar model (but without an encoder) considered by Lin et al. (2015). A sentence level RNN predicts the bag of words in the next sentence given the previous sentences and a word level RNN predicts the word sequence conditioned on the sentence level RNN hidden state. The model has a structure similar to the content model of Barzilay and Lee (2004) with RNNs playing the roles of the HMM and the bigram language model. Our model has a hierarchical nature in that a sentence level RNN operates over words of a sentence and a document level RNN operates over sentence embeddings. ",
+        "bbox": [
+            174,
+            590,
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+            729
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Combinatorial optimization with RNNs Vinyals et al. (2015a) equip sequence to sequence models with the capability to handle input and output sets, and discuss experiments on sorting, language modeling and parsing. Their goal is to show that input and output orderings can matter in these tasks, which is demonstrated using several small scale experiments. Our work exploits this framework to address the challenging problem of modeling logical and hierarchical structure in text. Vinyals et al. (2015b) proposed pointer-networks, aimed at combinatorial optimization problems where the output dictionary size depends on the number of input elements. We use a pointer-network that points to each of the next sentence candidates as the decoder. ",
+        "bbox": [
+            174,
+            736,
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+            848
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/f18d10cb155fa62453b415d7b0cafee130c5a7b60bdf362f040e430f538f2a9f.jpg",
+        "image_caption": [
+            "Figure 1: Model Overview: Illustration of the sentence encoder and single time-step computations in encoder and decoder. $s _ { i }$ ’s represent sentence embeddings derived from the sentence encoder. Attention weights are computed for the sentences based on their embeddings and the current hidden state. In the encoder an attention readout is concatenated with the LSTM output to form the next hidden state. The decoder uses the attention weights for prediction. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 APPROACH",
+        "text_level": 1,
+        "bbox": [
+            174,
+            367,
+            299,
+            382
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our proposed model is inspired by the way a human would solve this task. First, the model attempts to read the sentences to capture the semantics of the sentences as well as the general context of the paragraph. Given this knowledge, the model attempts to pick the sentences one by one sequentially till exhaustion. ",
+        "bbox": [
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+            398,
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+            454
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our model is based on the read, process and write framework proposed by Vinyals et al. (2015a) briefly discussed in section 1. We use the encoder-decoder terminology that is more common in the literature in the following discussion. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The model is comprised of a sentence encoder RNN, an encoder RNN and a decoder RNN (figure 1). An RNN sentence encoder takes as input the words of a sentence $s$ sequentially and computes an embedding representation of the sentence (Figure 1a). Henceforth, we shall use $s$ to refer to a sentence or its embedding interchangeably. The embeddings $\\{ s _ { 1 } , s _ { 2 } , . . . , s _ { n } \\}$ of a given set of $n$ sentences constitute the sentence memory, available to be accessed by subsequent components. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The encoder is identical to the originally proposed process block and is defined by equations 1-5 (See Figure 1b). Following the regular LSTM hidden state $( h _ { \\mathrm { e n c } } ^ { t - 1 } , c _ { \\mathrm { e n c } } ^ { t - 1 } )$ update, the hidden state is concatenated with an attention readout vector $s _ { \\mathrm { a t t } } ^ { t }$ , and this concatenated vector is treated as the hidden state for the next time step (Equation 5). Attention probabilities are computed by composing the hidden state with embeddings of the candidate sentences through a scoring function $f$ and taking the softmax (Equations 2, 3). This process is iterated for a number of times, called the number of read cycles. As described in Vinyals et al. (2015a) the encoder has the desirable property of being invariant to the order in which the sentence embeddings reside in the memory. The LSTM used here does not take any inputs (input is clamped to zero). ",
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+        "img_path": "images/cd7b8ecc06e1b8333bfbb6977fdc70cfca441dd5db81459b564bebde0a1157a1.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { h } _ { \\mathrm { e n c } } ^ { t } , c _ { \\mathrm { e n c } } ^ { t } = \\mathrm { L S T M } ( h _ { \\mathrm { e n c } } ^ { t - 1 } , c _ { \\mathrm { e n c } } ^ { t - 1 } ) } \\\\ & { \\qquad e _ { \\mathrm { e n c } } ^ { t , i } = f ( s _ { i } , \\tilde { h } _ { \\mathrm { e n c } } ^ { t } ) ; i \\in \\{ 1 , . . . , n \\} } \\\\ & { \\qquad a _ { \\mathrm { e n c } } ^ { t } = \\mathrm { S o f t m a x } ( e _ { \\mathrm { e n c } } ^ { t } ) } \\\\ & { \\qquad s _ { \\mathrm { a t t } } ^ { t } = \\displaystyle \\sum _ { i = 1 } ^ { n } a _ { \\mathrm { e n c } } ^ { t , i } s _ { i } } \\\\ & { \\qquad k _ { \\mathrm { e n c } } ^ { t } = \\widetilde { [ h } _ { \\mathrm { e n c } } ^ { t } , ~ s _ { \\mathrm { a t t } } ^ { t } ] } \\end{array}\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "The decoder is a pointer network that takes a similar form with a few differences (equations 6-8, Figure 1c). The LSTM takes the embedding of the previous sentence also as input: At training time the correct order of sentences $( s _ { o _ { 1 } } , s _ { o _ { 2 } } , . . . , \\bar { s } _ { o _ { n } } ) = ( \\bar { x } ^ { 1 } , x ^ { 2 } , . . . , x ^ { n } )$ is known $\\scriptstyle { \\dot { o } }$ represents the correct order) and $x ^ { t - 1 }$ is used as the input. At test time the predicted assignment $\\hat { x } ^ { t - 1 }$ is used instead. This makes concatenating the attention readout to the hidden state somewhat redundant (verified empirically), and hence it is omitted. The attention computation is identical to that of the encoder. The initial state of the decoder LSTM is initialized with the final hidden state of the encoder as in sequence to sequence models.1 $x ^ { 0 }$ is a vector of zeros. Figure 1 illustrates the single time-step computation in the encoder and decoder. ",
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+        "text": "$$\n\\begin{array} { r l } & { h _ { \\mathrm { d e c } } ^ { t } , c _ { \\mathrm { d e c } } ^ { t } = \\mathrm { L S T M } ( h _ { \\mathrm { d e c } } ^ { t - 1 } , c _ { \\mathrm { d e c } } ^ { t - 1 } , x ^ { t - 1 } ) } \\\\ & { ~ e _ { \\mathrm { d e c } } ^ { t , i } = f ( s _ { i } , h _ { \\mathrm { d e c } } ^ { t } ) ; i \\in \\{ 1 , . . . , n \\} ~ } \\\\ & { ~ a _ { \\mathrm { d e c } } ^ { t } = \\mathrm { S o f t m a x } ( e _ { \\mathrm { d e c } } ^ { t } ) } \\end{array}\n$$",
+        "text_format": "latex",
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+        "text": "The attention probability $a _ { \\mathrm { d e c } } ^ { t , i }$ is interpreted as the probability for $s _ { i }$ being the correct sentence choice at position $t$ , conditioned on the previous sentence assignments $p ( S _ { t } = s _ { i } | S _ { 1 } , . . . , S _ { t - 1 } )$ . ",
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+    {
+        "type": "text",
+        "text": "3.1 SCORING FUNCTION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We consider two choices for the scoring functions $f$ in our experiments. The first one is a single hidden layer feed-forward net that takes $s , h$ as inputs and outputs a score ",
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+        "img_path": "images/31f20574697fb32cde69a667b7bb17a5a9f36d91e1891b244f28f5bdf2e0b32e.jpg",
+        "text": "$$\nf ( s , h ) = W ^ { \\prime } { \\operatorname { t a n h } } ( W [ s ; h ] + b ) + b ^ { \\prime }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $W , b , W ^ { \\prime } , b ^ { \\prime }$ are learnable parameters. This scoring function takes a discriminative approach in classifying the next sentence. Note that the structure of this scoring function is similar to the window network in Li and Hovy (2014). While they used a local window of sentences to capture context, this scoring function exploits the RNN hidden state to score sentence candidates. ",
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+        "type": "text",
+        "text": "We also consider a bilinear scoring function ",
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+    },
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+        "type": "equation",
+        "img_path": "images/03b89f3e1c3ed05b4b4a21b4819b24bc90c4cf53113011465f13e1f79d4c633c.jpg",
+        "text": "$$\nf ( s , h ) = s ^ { T } ( W h + b )\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "Compared to the previous scoring function, this takes a generative approach of trying to regress the next sentence given the current hidden state $\\left( W h + b \\right)$ and enforcing that it be most similar to the correct next sentence. We observed that this scoring function led to learning better sentence representations (section 4.4). ",
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+    {
+        "type": "text",
+        "text": "3.2 TRAINING OBJECTIVE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The model is trained with the maximum likelihood objective: ",
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+        "img_path": "images/f48e4b6d9b2d8cd8962aa3d642ecbd7f209d38403b27aec684b0382335730beb.jpg",
+        "text": "$$\n\\operatorname* { m a x } \\sum _ { x \\in D } \\sum _ { t = 1 } ^ { | x | } \\log p ( x ^ { t } | x ^ { 1 } , . . . , x ^ { t - 1 } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $D$ denotes the training set and each training instance is given by an ordered document of sentences $x = ( x ^ { 1 } , . . . , x ^ { | x | } )$ . We also considered an alternative structured margin loss which imposes less penalty for assigning high scores to sentence candidates that are close to the correct sentence in the source document instead of uniformly penalizing all incorrect sentence candidates. However, the softmax output with cross entropy loss consistently performed better. ",
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+    {
+        "type": "text",
+        "text": "3.3 COHERENCE MODELING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We define the coherence score of an arbitrary partial/complete assignment $( s _ { p _ { 1 } } , . . . , s _ { p _ { k } } )$ to the first $k$ sentence positions as ",
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+    {
+        "type": "equation",
+        "img_path": "images/9a34b25126559b31078d4b3904649c110963b88cd8fe37f34abb84d3260101f2.jpg",
+        "text": "$$\n\\sum _ { i = 1 } ^ { k } \\log p ( S _ { i } = s _ { p _ { i } } | S _ { 1 } = s _ { p _ { 1 } } , . . . , S _ { i - 1 } = s _ { p _ { i - 1 } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $S _ { 1 } , . . , S _ { k }$ are random variables representing the sentence assignment to positions 1 through $k$ . The conditional probabilities are derived from the network. This is our measure of comparing the coherence of different renderings of a document. It is also used as a heuristic during decoding. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/06e80308b7d623d2193a4f770fdf59ec24ec74f022ead999301366ef6de1eeec.jpg",
+        "table_caption": [
+            "Table 1: Statistics of data used in our experiments. For the first two datasets, the test set size\\* is the number of permutation pairs used for order discrimination experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">Length Statistics</td><td colspan=\"3\">Data Split</td><td rowspan=\"2\">Types</td></tr><tr><td>Min</td><td>Mode</td><td>Mean</td><td>Max</td><td>Train</td><td>Val</td><td>Test</td></tr><tr><td>Accidents</td><td>6</td><td>11</td><td>11.6</td><td>19</td><td>100</td><td>-</td><td>1986*</td><td>5,140</td></tr><tr><td>Earthquakes</td><td>3</td><td>7</td><td>10.4</td><td>31</td><td>100</td><td>1</td><td>1956*</td><td>3,775</td></tr><tr><td>NIPS abstracts</td><td>2</td><td>7</td><td>6</td><td>15</td><td>2448</td><td>409</td><td>402</td><td>18,696</td></tr><tr><td>AAN abstracts</td><td>1</td><td>4</td><td>5</td><td>20</td><td>8569</td><td>962</td><td>2626</td><td>40,288</td></tr><tr><td>NSF abstracts</td><td>2</td><td>7</td><td>8.9</td><td>40</td><td>96070</td><td>10185</td><td>21580</td><td>373,909</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTAL RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 MODEL TRAINING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "For all tasks discussed in this section we train the model with the same objective (equation 11) on the training data relevant to the task. We used the single hidden layer MLP scoring function for the order discrimination and sentence ordering tasks. Models are trained end-to-end. ",
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+    {
+        "type": "text",
+        "text": "Model parameters. We use pre-trained 300 dimensional GloVe word embeddings (Pennington et al., 2014). All LSTMs use a hidden layer size of 1000 and the MLP in section 9 has a hidden layer size of 500. The number of read cycles in the encoder is set to 10. The same model architecture is used across all experiments. ",
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+    },
+    {
+        "type": "text",
+        "text": "Preprocessing. The nltk sentence tokenizer was used for word tokenization. The GloVe vocabulary was used as the reference vocabulary. Any word not in the vocabulary is checked for a case insensitive match. If a token is hyphenated, we check if the constituent words are in the vocabulary. In the AAN abstracts data (section 4.3.1), some words tend to have a hyphen in the middle because of word hyphenation across lines in the original document. Hence we also check if stripping hyphens produces a vocabulary word. If all checks fail, and a token appears in the training set above a certain frequency, it is added to the vocabulary. ",
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+    {
+        "type": "text",
+        "text": "Learning . We used a batch size of 10 and the Adam optimizer (Kingma and Ba, 2014) with a base learning rate of 5e-4 for all experiments. Early stopping is used for regularization. ",
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+    {
+        "type": "text",
+        "text": "4.2 ORDER DISCRIMINATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Finding the optimal ordering is a difficult problem when a large number of sentences are required to be rearranged or when there is inherent ambiguity in the ordering of the sentences. For this reason, the ordering problem is commonly formulated as the following binary classification task. Given a reference paragraph and a permuted version of it, the more coherently organized one needs to be identified (Barzilay and Lapata, 2008). ",
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+    {
+        "type": "text",
+        "text": "4.2.1 DATA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We consider data from two different domains that have been widely used for this task in previous work since Barzilay and Lee (2004); Barzilay and Lapata (2008). The ACCIDENTS data (aka AIRPLANE data) is a set of aviation accident reports from the National Transportation Safety Board’s database. The EARTHQUAKES data comprises newspaper articles from the North American News Text Corpus. In each of the above datasets the training and test sets include 100 articles as well as approximately 20 permutations of each article. Further statistics about the data are shown in table 1. ",
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+    {
+        "type": "text",
+        "text": "4.2.2 RESULTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Table 2 compares the performance of our model against prior approaches. We compare results against traditional approaches in the literature as well as some recent data-driven approaches (See section 2 for more details). The entity grid model provides a strong baseline on the ACCIDENTS dataset, only outperformed by our model and Li and Jurafsky (2016) . On the EARTHQUAKE data the window approach of Li and Hovy (2014) and Li and Jurafsky (2016) perform strongly. Our approach outperforms prior models on both datasets, achieving near perfect performance on the Earthquakes dataset. ",
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+    {
+        "type": "table",
+        "img_path": "images/4b589b969bd7784e25b572ffb6beb8c2818006a7e376f3f8cf3836d2fa995d49.jpg",
+        "table_caption": [
+            "Table 2: Mean Accuracy comparison on the Accidents and Earthquakes data for the order discrimination task. Reference results obtained from the respective publications. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>ACCIDENTS</td><td>EARTHQUAKES</td></tr><tr><td>Barzilay and Lapata (2008)</td><td>0.904</td><td>0.872</td></tr><tr><td>Louis and Nenkova (2012)</td><td>0.842</td><td>0.957</td></tr><tr><td>Guinaudeau and Strube (2013)</td><td>0.846</td><td>0.635</td></tr><tr><td>Liand Hovy (2014) -Recurrent</td><td>0.840</td><td>0.951</td></tr><tr><td>Li and Hovy (2014) - Recursive</td><td>0.864</td><td>0.976</td></tr><tr><td>Li and Jurafsky (2016)</td><td>0.930</td><td>0.992</td></tr><tr><td>Ours</td><td>0.944</td><td>0.997</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "While these datasets have been widely used in the literature, they are quite formulaic in nature and are no longer challenging. We hence turn to the more challenging task of ordering a given collection of sentences to make a coherent document. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 SENTENCE ORDERING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this task we directly address the ordering problem. We do not assume the availability of a set of candidate orderings to choose from and instead attempt to find a good ordering from all possible permutations of the sentences. ",
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+    {
+        "type": "text",
+        "text": "The difficulty of the ordering problem depends on the nature of the text as well as the length of paragraphs considered. Evaluation on text from arbitrary text sources makes it difficult to interpret the results, since it may not be clear whether to attribute the observed performance to a deficient model or ambiguity in next sentence choices due to many plausible orderings. ",
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+    {
+        "type": "text",
+        "text": "Text summaries are a suitable source of data for this task. They often exhibit a clear flow of ideas and have minimal redundancy. We specifically look at abstracts of conference papers and NSF research proposals. This data has several favorable properties. Abstracts usually have a particular high level format - They start out with a brief introduction, a description of the problem addressed and proposed approach and conclude with performance remarks. This would allow us to identify if the model is capable of capturing high level logical structure. Second, abstracts have an average length of about 10, making the ordering task more accessible. Furthermore, this also gives us a significant amount of data to train and test our models. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.3.1 DATA ",
+        "text_level": 1,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "NIPS Abstracts. We consider abstracts from NIPS papers in the past 10 years. We parsed 3280 abstracts from paper pdfs and obtained 3259 abstracts after omitting erroneous extracts. The dataset was split into years 2005-2013 for training and years 2014, 2015 respectively for validation and testing2. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "ACL Abstracts. A second source of abstracts we consider are papers from the ACL Anthology Network (AAN) corpus (Radev et al., 2009) of ACL papers. At the time of retrieval, the corpus had publications up to year 2013. We extracted abstracts from the text parses using simple keyword matching for the strings ‘Abstract’ and ‘Introduction’. Our extraction is successful for 12,157 articles. Most of the failures occur for older papers due to improper formatting and OCR issues. We use all extracts of papers published up to year 2010 for training, year 2011 for validation and years 2012-2013 for testing. We additionally merge words hyphenated at the edges of paragraph boundaries. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "NSF Abstracts. We also evaluate our model on the NSF Research Award Abstracts dataset (Lichman, 2013). This dataset comprises abstracts from a diverse set of scientific areas in contrast to the previous two sources of data and the abstracts are also lengthier, making this dataset more challenging. Years 1990-1999 were used for training, 2000 for validation and 2001-2003 for testing. We capped the parses of the abstracts to a maximum length of 40 sentences. Unsuccessful parses and parses of excessive length were discarded. Further details about the datasets are provided in table 1. ",
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+    {
+        "type": "table",
+        "img_path": "images/7beb037f8eff130011c5eaedec1ce434bbd9db9486e07b95168e3344bcf7a51b.jpg",
+        "table_caption": [
+            "Table 3: Comparison against prior methods on the abstracts data. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">NIPS Abstracts</td><td colspan=\"2\">AAN Abstracts</td><td colspan=\"2\">NSF Abstracts</td></tr><tr><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td></tr><tr><td>Random</td><td>15.59</td><td>0</td><td>19.36</td><td>0</td><td>9.46</td><td>0</td></tr><tr><td>Entity Grid (Barzilay and Lapata, 2008)</td><td>20.10</td><td>0.09</td><td>21.82</td><td>0.10</td><td>1</td><td>-</td></tr><tr><td>Seq2seq (Uni) (Li and Jurafsky,2016)</td><td>27.18</td><td>0.27</td><td>36.62</td><td>0.40</td><td>13.68</td><td>0.10</td></tr><tr><td>Window network (Li and Hovy,2014)</td><td>41.76</td><td>0.59</td><td>50.87</td><td>0.65</td><td>18.67</td><td>0.28</td></tr><tr><td>RNN Decoder</td><td>48.22</td><td>0.67</td><td>52.06</td><td>0.66</td><td>25.79</td><td>0.48</td></tr><tr><td>Proposed model</td><td>51.55</td><td>0.72</td><td>58.06</td><td>0.73</td><td>28.33</td><td>0.51</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.3.2 METRICS ",
+        "text_level": 1,
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+        "text": "We use the following metrics to evaluate performance on this task. Accuracy measures how often the absolute position of a sentence was correctly predicted. Being a too stringent measure, it penalizes correctly predicted subsequences that are shifted. Another metric widely used in the literature is Kendall’s tau $\\left( \\tau \\right)$ , computed as $1 - 2 \\times$ (number of inversions)/ $\\binom { n } { 2 }$ , where the number of inversions is the number of pairs in the predicted sequence with incorrect relative order and $n$ is the length of the sequence. Lapata (2006) discusses that this metric reliably correlates with human judgements. ",
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+    {
+        "type": "text",
+        "text": "4.3.3 BASELINES",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Entity Grid. Our first baseline is the Entity Grid model of Barzilay and Lapata (2008). We use the Stanford parser (Klein and Manning, 2003) to get constituency trees for all sentences in our datasets. We derive entity grid representations for the parsed sentences using the Brown Coherence Toolkit.3 A ranking SVM is trained to score correct orderings higher than incorrect orderings as in the original work. We used 20 permutations per document as training data. Since the entity grid representation only provides a means of feature extraction we evaluate the model in the ordering setting as follows. We choose 1000 random permutations for each document, one of them being the correct order, and pick the order with maximum coherence. We experimented with transitions of length at most 3 in the entity-grid. ",
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+        "type": "text",
+        "text": "Sequence to sequence. The second baseline we consider is a sequence to sequence model which is trained to predict the next sentence given the current sentence. Li and Jurafsky (2016) consider similar methods and our model is same as the uni-directional model in their work. These methods were shown to yield sentence embeddings that have competitive performance in several semantic tasks in Kiros et al. (2015). ",
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+        "type": "text",
+        "text": "Window Network. We consider the window approach of Li and Hovy (2014) and Li and Jurafsky (2016) which demonstrated strong performance in the order discrimination task as our third baseline. We adopt the same coherence score interpretation considered by the authors in the above work. In both the above models we consider a special embedding vector which is padded at the beginning of a paragraph and learned during training. This vector allows us to identify the initial few sentences during greedy decoding. ",
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+        "type": "text",
+        "text": "RNN Decoder. Another baseline we consider is our proposed model without the encoder. The decoder hidden state is initialized with zeros. We observed that using a special start symbol as for the other baselines helped obtain better performance with this model. However, a start symbol did not help when the model is equipped with an encoder as the hidden state initialization alone was good enough. ",
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+        "type": "text",
+        "text": "We do not place emphasis on the particular search algorithm in this work and thus use beam search using the coherence score heuristic for all models. A beam size of 100 was used. During decoding, sentence candidates that have been already chosen are pruned from the beam. All RNNs use a hidden layer size of 1000. For the window network we used a window size of 3 and a hidden layer size of 2000. We initialize all models with pre-trained GloVe word embeddings. ",
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+        "img_path": "images/e53d4ba67148ca85ebcb090221c5785b3890a9ea64b01607ca07a2f3792adf2a.jpg",
+        "image_caption": [
+            "Figure 2: t-SNE embeddings of representations learned by the model for sentences from the test set. The embeddings are color coded by the position of the sentence in the document it appears. "
+        ],
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+    {
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+        "text": "4.3.4 RESULTS ",
+        "text_level": 1,
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+        "text": "We assess the performance of our model against baseline methods in table 3. The window network performs strongly compared to the other baselines. Our model does better by a significant margin by exploiting global context, demonstrating that global context is important to be successful in this task. ",
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+        "text": "While the Entity-Grid model has been fairly successful for the order discrimination task in the past we observe that it fails to discriminate between a large number of candidates. One reason could be that the feature representation is fairly less sensitive to local changes in sentence order (such as swapping adjacent sentences). We did not use coreference resolution for computing the entity-grids due to the computational overhead. This could potentially improve results by a few percentage points. The computational expense of obtaining parse trees and constructing grids on a large amount of data prohibited us from experimenting with this model on the NSF abstracts data. ",
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+    {
+        "type": "text",
+        "text": "The sequence to sequence model falls short of the window network in performance. Interestingly, Li and Jurafsky (2016) observe that the seq2seq model outperforms the window network in an order discrimination task on wikipedia data. However, the wikipedia data considered in their work has an order of magnitude more data that the datasets considered here, and that could have potentially helped the generative model. These models are also expensive during inference since they involve computing and sampling from word distributions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Figure 3 we attempt to visualize the sentence representations learned by the sentence encoder in our model. The figure shows 2-dimensional t-SNE embeddings of test set sentences from each of the datasets color coded by their positions in the source abstract. This shows that the model learns high-level structure in the documents, generalizing well to unseen documents. The structure is less apparent in the NSF data which we presume is because of the data diversity and longer documents. While approaches based on the content model of Barzilay and Lee (2004) attempt to explicitly capture topics by discovering clusters in sentences, we observe that the neural approach implicitly discovers such structure. ",
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+    {
+        "type": "text",
+        "text": "4.4 LEARNED SENTENCE REPRESENTATIONS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "One of the original motivations for this work is the question whether we can learn high quality sentence representations by learning to model text coherence. To address this question we trained our model on a large dataset of paragraphs. We chose the BookCorpus dataset (Kiros et al., 2015) for this purpose. We trained the model with two key changes from the models trained on the abstracts data - 1) In addition to the sentences in the paragraph being considered, we added more contrastive sentences from other paragraphs as well. 2) We use the bilinear scoring function. These techniques helped obtain better representations when training on large amounts of data. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To evaluate the quality of the sentence embeddings derived from the model, we use the evaluation pipeline of Kiros et al. (2015) for tasks that involve understanding sentence semantics. These evaluations are performed by training a classifier on top of the embeddings derived from the model so that the performance is indicative of the quality of sentence representations. We consider the semantic relatedness and paraphrase detection tasks. Our results are presented in tables 4a, 4b. Results for only uni-directional versions of different models are discussed here for a reasonable comparison. ",
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+        "type": "table",
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+        "table_caption": [
+            "Table 4: Performance comparison for the semantic similarity (SICK dataset) and paraphrase detection (MSR paraphrase corpus) tasks. In each table the first section shows some best performing supervised methods in the literature. The second section shows models relevant to the skip-thought model. The third section shows our models. ",
+            "(a) Sentence similarity "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>r</td><td>p</td><td>MSE</td></tr><tr><td colspan=\"4\">Purely supervised methods</td></tr><tr><td>DT-RNN (Tai et al., 2015)</td><td>0.792</td><td>0.732</td><td>0.382</td></tr><tr><td>LSTM (Tai et al.,2015)</td><td>0.853</td><td>0.791</td><td>0.283</td></tr><tr><td>DT-LSTM (Tai et al.,2015)</td><td>0.868</td><td>0.808</td><td>0.253</td></tr><tr><td colspan=\"4\">Classifier trained on sentence embeddings</td></tr><tr><td>skip-bow (Kiros et al.,2015)</td><td>0.782</td><td>0.724</td><td>0.398</td></tr><tr><td>uni-skip (Kiros et al., 2015)</td><td>0.848</td><td>0.778</td><td>0.287</td></tr><tr><td>Ordering model</td><td>0.807</td><td>0.742</td><td>0.356</td></tr><tr><td>+BoW</td><td>0.842</td><td>0.775</td><td>0.299</td></tr><tr><td>+ uni-skip</td><td>0.860</td><td>0.795</td><td>0.270</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/94118c30df713d691fd964138b57d939e547f517eea568303a77ee8f1d44d9de.jpg",
+        "table_caption": [
+            "(b) Paraphrase detection "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Acc F1</td></tr><tr><td>Purely supervised methods</td><td>83.6</td></tr><tr><td>Socher et al. (2011) Madnani et al. (2012) Ji and Eisenstein (2013)</td><td>76.8 77.4 84.1 80.4</td></tr><tr><td> Classifier trained on sentence embeddings</td><td>86.0</td></tr><tr><td>skip-bow (Kiros et al., 2015) uni-skip (Kiros et al., 2015)</td><td>67.8 80.3 73.0 81.9</td></tr><tr><td>Ordering model</td><td>72.3</td></tr><tr><td>+BoW + uni-skip</td><td>81.0 74.0 81.9 74.9 82.5</td></tr></table>",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Skip-thought vectors are learned by predicting both the previous and next sentences given the current sentence. Following suit, we train two models - one predicting the correct order in the forward direction and another in the backward direction. Note that the sentence level RNN is still unidirectional in both cases. The numbers shown for the ordering model were obtained by concatenating the representations obtained from the two models. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Concatenating the above representation with the bag of words representation (using the fine-tuned word embeddings) of the sentence further improves performance4. We believe the reason to be that the ordering model can choose to pay less attention to specific lexical information and instead focus on the high level document structure. Hence the two representations can be seen as capturing complementary semantics. Adding the skip-thought embedding features as well improves performance further. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Our model has several key advantages over the skip-thought model. The skip-thought model has a word-level reconstruction objective and requires training with large softmax output layers. This limits the size of the vocabulary and makes training very time consuming (they use a vocabulary size of $2 0 \\mathrm { k }$ and report 2 weeks of training). Our model achieves comparable performance and does not have such a word reconstruction component. We are able to train with a large vocabulary of $4 0 0 \\mathrm { k }$ words and the above results were obtained with a training time of 2 days. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A conceptual issue surrounding word-level reconstruction is that it forces the model to predict both the meaning and syntax of the target sentence. This makes learning difficult since there are numerous ways of expressing the same idea in syntax. In our model we instead let the model discover features from a sentence which are both predictive (of the next sentence) and predictable (from the previous sentences) and interpret these set of features as a meaning representation. We believe this is an important distinction and hope to study these models further in the context of learning syntax independent semantic representations of sentences. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this work we considered the challenging problem of coherently organizing a given set of sentences. Our RNN based model performs strongly compared to baseline methods as well as prior work on sentence ordering and order discrimination tasks. We further demonstrated that the model captures high level document structure and learns useful sentence representations when trained on large amounts of data. Our approach to the ordering problem deviates from most prior work that use handcrafted features. However, exploiting linguistic features for next sentence classification can potentially further improve performance on the task. Entity distribution patterns can provide useful features about named entities that are treated as out of vocabulary words. The ordering problem can be further studied at higher level discourse units such as paragraphs, sections and chapters. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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+        "text": "J. Li and D. Jurafsky. Neural net models for open-domain discourse coherence. arXiv preprint arXiv:1606.01545, 2016.   \nJ. Li, X. Chen, E. Hovy, and D. Jurafsky. Visualizing and understanding neural models in nlp. arXiv preprint arXiv:1506.01066, 2015a.   \nJ. Li, M.-T. Luong, and D. Jurafsky. A hierarchical neural autoencoder for paragraphs and documents. arXiv preprint arXiv:1506.01057, 2015b.   \nM. Lichman. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ ml.   \nR. Lin, S. Liu, M. Yang, M. Li, M. Zhou, and S. Li. Hierarchical recurrent neural network for document modeling. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 899–907, 2015.   \nA. Louis and A. Nenkova. A coherence model based on syntactic patterns. In Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pages 1157–1168. Association for Computational Linguistics, 2012.   \nN. Madnani, J. Tetreault, and M. Chodorow. Re-examining machine translation metrics for paraphrase identification. In Proceedings of the 2012 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 182–190. Association for Computational Linguistics, 2012.   \nE. Miltsakaki and K. Kukich. Evaluation of text coherence for electronic essay scoring systems. Natural Language Engineering, 10(01):25–55, 2004.   \nJ. Pennington, R. Socher, and C. D. Manning. Glove: Global vectors for word representation. In EMNLP, volume 14, pages 1532–43, 2014.   \nD. R. Radev, M. T. Joseph, B. Gibson, and P. Muthukrishnan. A Bibliometric and Network Analysis of the field of Computational Linguistics. Journal of the American Society for Information Science and Technology, 2009.   \nR. Socher, E. H. Huang, J. Pennin, C. D. Manning, and A. Y. Ng. Dynamic pooling and unfolding recursive autoencoders for paraphrase detection. In Advances in Neural Information Processing Systems, pages 801–809, 2011.   \nR. Soricut and D. Marcu. Discourse generation using utility-trained coherence models. In Proceedings of the COLING/ACL on Main conference poster sessions, pages 803–810. Association for Computational Linguistics, 2006.   \nI. Sutskever, O. Vinyals, and Q. V. Le. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pages 3104–3112, 2014.   \nK. S. Tai, R. Socher, and C. D. Manning. Improved semantic representations from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.   \nO. Vinyals, S. Bengio, and M. Kudlur. Order matters: Sequence to sequence for sets. arXiv preprint arXiv:1511.06391, 2015a.   \nO. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In Advances in Neural Information Processing Systems, pages 2674–2682, 2015b. ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/bcfc620c12f004b9bfeeb2d3abda8d7ffdb80fda26f1ed4823fb19d5c8c6a41e.jpg",
+        "table_caption": [
+            "Table 5: Visualizing salient words. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>In this paper,we propose a new method for semantic class induction . First ,we introduce a generative model of sentences ,based on dependency trees and which takes into account homonymy Our model can thus be seen as a generalization of Brown clustering . Second , we describe an efficient algorithm to perform inference and learning in this model . Third ,we apply our proposed method on two large datasets （108 tokens ,105 words types ）,and demonstrate that classes induced by our algorithm improve performance over Brown clustering on the task of semisupervised supersense tagging and named entity recognition .</td></tr><tr><td>Representation learning is a promising technique for discovering features that allow supervised classifiers to generalize from a source domain dataset to arbitrary new domains We present a novel, formal statement of the representation learning task . We argue that because the task is computationally intractable in general,it is important for arepresentation learner to be able to incorporate expert knowledge during its search for helpful features . Leveraging the Posterior Regularization framework ,we develop an architecture for incorporating biases into</td></tr><tr><td>learners identify significantly better sets offeatures than unbiased learners,resulting inarelative reduction in error of more than 16% forboth tasks ,with respect to existing state-of-the-art representation learning techniques. We present an approach for detecting salient (important）dates in texts in order to automatically build event timelines from a search query（e.g . the name of an event or person,etc .）. This work was carried out on a corpus of newswire texts in English provided by the Agence France Presse</td></tr><tr><td>(AFP). In order to extract salient dates that warrant inclusion in an event timeline ,we first recognize and normalize temporal expressons in texts and then use a machine-learning approach to extract salient dates that relate to a particular topic . We focused only on extracting the dates and not the events to which they are related . The paper aims to come up with a system that examines the degree of semantic equivalence between two</td></tr><tr><td>sentences. At the core of the paper is the attempt to grade the similarity of two sentences by finding the maximal weighted bipartite match between the tokens of the two sentences . The tokens include single words,or multiwords in case of Named Entitites ，adjectivally and numerically modified words. Two token similarity measures are used for the task -WordNet based similarity,and a statistical word similarity</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "A WORD INFLUENCE ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We attempt to understand what text level clues the model captures to perform the ordering task. Some techniques for visualizing neural network models in the context of text applications are discussed in Li et al. (2015a). Drawing inspiration from this work, we use gradients of prediction decisions with respect to the words of the correct sentence as a proxy for the salience of each word. ",
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+    {
+        "type": "text",
+        "text": "For each time step during decoding we do the following. Assume the sentence assignments for all previous time steps have been correct. let $h$ be the current hidden state in this setting and $s = ( w _ { 1 } , . . . , w _ { n } )$ be the correct next sentence candidate, the $w _ { i }$ being its words. The score for this sentence is defined as $e = f ( s , h )$ (See equation 7). The importance of word $w _ { i }$ in predicting $s$ as the correct next sentence is interpreted as $\\big | \\big | \\frac { \\partial e } { \\partial w _ { i } } \\big | \\big |$ . We assume $h$ to be fixed and only backpropagate gradients through the sentence encoder. ",
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+    {
+        "type": "text",
+        "text": "Table 5 shows visualizations of a few selected abstracts. Words expressed in darker shades correspond to higher gradient norms. In the first example the model seems to be using the word clues ‘first’, ‘second’ and ‘third’. A similar observation was made by Chen et al. (2016) in their experiments. In the second example we observe that the model has paid attention to phrases such as ‘We present’, ‘We argue’ which are typical of abstract texts. The model has also focused on the word ‘representation’ ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/adad558c7205bc48c9fabf9b69b0c9378dffcd77969ecbe41c7f2faafcc2571f.jpg",
+        "image_caption": [
+            "(b) Accuracy of predicting the correct sentence at a given position. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/e81e192d491a4ec3d3ee35f9f997b4da73575cf61465110ee3b4df1540c5e875.jpg",
+        "image_caption": [
+            "Figure 3: Performance with respect to paragraph length and sentence position - NIPS abstracts test data. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(a) $\\tau$ scores of order predictions on paragraphs of a given length. ",
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+    {
+        "type": "text",
+        "text": "appearing in the first two sentences. Similarly in the third example, the words ‘salient’ and ‘dates’ have been attended to. In the last example, the words ‘token’, ‘tokens’, ‘tokenization’ have received attention. We believe that these observations link to ideas from centering theory which state that entity distributions in coherent discourses adhere to certain patterns. The model has implicitly learned learned these patterns with no syntax annotations or handcrafted features. ",
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+    {
+        "type": "text",
+        "text": "B PERFORMANCE ANALYSIS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Figure 3a shows the average $\\tau$ for the models on the NIPS abstracts test set for a given paragraph length. The performance of local approaches dies down fairly quickly as we can expect and face difficulties handling lengthy paragraphs. Our model attempts to maintain consistent performance with increasing paragraph size with a more gradual decline in performance. ",
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+        "type": "text",
+        "text": "Figure 3b compares the average prediction accuracy for a given sentence position in the test set. It is interesting to observe that all models fair well in predicting the first sentence. The greedy decoding procedure also contributes to the decline in performance as we move right. Our model remains more robust compared to the other two methods. ",
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+    {
+        "type": "text",
+        "text": "Another trend to be observed is that as the context size increases (2 for next sentence generation, 3 for window network, complete sentential history for our model) the performance decline is more gradual. ",
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+    {
+        "type": "table",
+        "img_path": "images/1871ec5585707d89670db84a1894baa8aef2a3b01c4c777a3756da3894eb8534.jpg",
+        "table_caption": [
+            "(a) Classify 1 of 2 - Accuracy "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>NIPS</td><td>AAN</td><td>NSF</td></tr><tr><td>Entity Grid</td><td>0.712</td><td>0.660</td><td>=</td></tr><tr><td>Seq2seq (Uni)</td><td>0.890</td><td>0.888</td><td></td></tr><tr><td>Window network</td><td>0.944</td><td>0.942</td><td>0.936</td></tr><tr><td>RNNDecoder</td><td>0.964</td><td>0.952</td><td>0.972</td></tr><tr><td>Proposed model</td><td>0.970</td><td>0.955</td><td>0.982</td></tr></table>",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/bd781d72c2c5de547896b0033dda67eedb528a1577a0907d8161393b5c0a9c02.jpg",
+        "table_caption": [
+            "(b) Classify 1 of 100 - Accuracy "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>NIPS</td><td>AAN</td><td>NSF</td></tr><tr><td>Entity Grid</td><td>0.070</td><td>0.102</td><td>=</td></tr><tr><td>Seq2seq (Uni)</td><td>0.171</td><td>0.290</td><td>=</td></tr><tr><td>Window network</td><td>0.385</td><td>0.470</td><td>0.300</td></tr><tr><td>RNN Decoder</td><td>0.516</td><td>0.541</td><td>0.647</td></tr><tr><td>Proposed model</td><td>0.566</td><td>0.581</td><td>0.710</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/de030d16c61363ae1e30e8153432773f25ed0758a9ec9d62a39a76e0562ec1b5.jpg",
+        "table_caption": [
+            "Table 7: Accuracy (of predicting sentence position) and $\\tau$ metrics for the 1 of 100 classification task. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">NIPS Abstracts</td><td colspan=\"2\">AAN Abstracts</td><td colspan=\"2\">NSF Abstracts</td></tr><tr><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td><td>Accuracy</td><td>T</td></tr><tr><td>Entity Grid</td><td>21.30</td><td>0.12</td><td>23.22</td><td>0.11</td><td></td><td></td></tr><tr><td>Seq2seq (Uni)</td><td>38.36</td><td>0.40</td><td>48.47</td><td>0.50</td><td>=</td><td>=</td></tr><tr><td>Window network</td><td>59.20</td><td>0.67</td><td>64.02</td><td>0.71</td><td>44.65</td><td>0.46</td></tr><tr><td>RNN Decoder</td><td>67.05</td><td>0.73</td><td>68.54</td><td>0.74</td><td>79.01</td><td>0.76</td></tr><tr><td>Proposed model</td><td>72.25</td><td>0.79</td><td>72.25</td><td>0.77</td><td>83.85</td><td>0.81</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "C ADDITIONAL EXPERIMENTAL RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "C.1 CLASSIFICATION EXPERIMENTS FOR ABSTRACTS DATA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Classify 1 of 2 (Pairwise ranking). We create a random permutation for each document (different from the correct order) and compute the pairwise classification accuracy. The mean result over 100 such experiments is reported in table 6a. ",
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+    {
+        "type": "text",
+        "text": "Classify 1 of N. In this experiment we consider a pool of $\\Nu = 1 0 0$ permutations where one of them is the correct order and the rest are random permutations. We compute coherence scores of all orderings in the pool and pick the best one. Table 6b reports how accurately each model identified the correct order. Table 7 computes the same metrics in table 3 for the orders that were chosen by the model. ",
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+        "type": "text",
+        "text": "The performance gaps are not significant for the first experiment. However, they are more pronounced in the second experiment. The reason is because in the binary classification setting, a majority of the permutations will be very different from the correct order, and the models can discriminate well for these cases. However, when choosing from a large set of permutations the models need to be sensitive to permutations which deviate from the correct ordering by a small amount (Eg: only two sentences out of place from correct order). Models incapable of discriminating at this finer level perform tend to perform poorly. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Note that the second experiment is closer to the practical task of finding an appropriate presentation ordering for a given collection of sentences, while taking the decoding algorithm out of the picture. ",
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+    },
+    {
+        "type": "text",
+        "text": "C.2 ORDER DISCRIMINATION - PENN TREEBANK DATASET ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We perform order discrimination experiments on the Penn Treebank dataset. The experimental protocol is identical to that of Ji et al. (2015). The standard train, dev, test split was used. The vocabulary comprises the most 10,000 frequent words and an additional special symbol representing low frequency words. A bootstrapping procedure is used for evaluation - 1000 test sets are generated by randomly sampling with replacement 155 documents from the test set and constructing a random permutation different from the correct order for each sampled document. We used the same model hyperparameters described in section 4.1. We did not use pre-trained word embeddings for fair comparison with the reference method. Performance statistics are computed over the 1000 bootstrapped test sets. Table 8 shows a performance comparison. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A key difference of this dataset compared to the other datasets is that the documents are more open domain and they are significantly longer. Our model performs strongly despite these differences. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/576da8469aaf6a6ee86cf258830f4647d3e771a3a3664354d6baa23e43b98145.jpg",
+        "table_caption": [
+            "Table 8: Order discrimination on PTB dataset. Reference results re-printed from Ji et al. (2015). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">Accuracy</td></tr><tr><td>Mean (%)</td><td>Standard deviation (%)</td></tr><tr><td>Hierarchical RNNLM (Lin et al., 2015)</td><td>75.32</td><td>4.42</td></tr><tr><td>DCLM (Ji et al., 2015)</td><td>83.26</td><td>3.77</td></tr><tr><td>Proposed model</td><td>90.25</td><td>2.38</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/0c03ba50a6bbe4a473ded31bc2f9c92480e89d9464640fb3307328e90f4ebcf5.jpg",
+        "table_caption": [
+            "Table 9: Impact of using contrastive sentences and the bilinear scoring function for learning sentence representations. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Contrastive Sentences</td><td rowspan=\"2\">Scoring Function</td><td colspan=\"3\">Semantic Relatedness</td><td colspan=\"2\">Paraphrase detection</td></tr><tr><td>r</td><td>p</td><td>MSE</td><td>Acc</td><td>F1</td></tr><tr><td>No</td><td>MLP</td><td>0.631</td><td>0.568</td><td>0.613</td><td>0.687</td><td>0.791</td></tr><tr><td>No</td><td>Bilinear</td><td>0.650</td><td>0.609</td><td>0.588</td><td>0.681</td><td>0.785</td></tr><tr><td>Yes</td><td>MLP</td><td>0.718</td><td>0.648</td><td>0.494</td><td>0.689</td><td>0.785</td></tr><tr><td>Yes</td><td>Bilinear</td><td>0.787</td><td>0.727</td><td>0.387</td><td>0.712</td><td>0.804</td></tr></table>",
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "C.3 SENTENCE REPRESENTATION LEARNING TASK ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We briefly discussed two techniques in section 4.4 that helped obtain better sentence representations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• Adding contrastive sentence candidates for the decoder • The bilinear scoring function ",
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+    },
+    {
+        "type": "text",
+        "text": "Table 9 shows results of ablative experiments which demonstrate the effect of these ideas. Each experimental setting indicates whether or not contrastive sentences were used and the type of scoring function employed. Note that these models were trained to predict the correct order of sentences only in the forward direction (as opposed to the results reported in table 4 where two models were trained to predict the order in the forward and backward directions and the representations were concatenated). Models were chosen using the validation set of the relevant task. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We observe the trend that adding contrastive sentences or switching from the MLP to the bilinear scoring function produces a sharp improvement in the result for the semantic relatedness task. Although the performance differences are less significant in the paraphrase detection task when the individual factors are changed, we observe an overall performance gain by using contrastive sentences and the bilinear scoring function. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This confirms our intuition that adding contrastive sentences makes the task more challenging and leads to better representations being learned. Similarly, the bilinear scoring function takes a generative approach of trying to regress the next sentence as opposed to the MLP scoring function which treats the prediction task as purely discriminative, and hence encourages the learning of better representations. ",
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+    {
+        "type": "text",
+        "text": "D MODEL DETAILS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The LSTM update in equation 1 of the paper ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/f36f59b976337e8e4f7b35596292c2bcc6169176b7a5387c6eb93f76d3966ba9.jpg",
+        "text": "$$\nh _ { t } , c _ { t } = L S T M ( h _ { t - 1 } , c _ { t - 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "is as follows. ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/6f5111d597e69079ac85902a2b0182b54a75d3b5fc0a0ded873715db79d87bf9.jpg",
+        "text": "$$\n\\begin{array} { r l } & { i _ { t } = \\sigma \\big ( W _ { i } h _ { t - 1 } + b _ { i } \\big ) } \\\\ & { f _ { t } = \\sigma \\big ( W _ { f } h _ { t - 1 } + b _ { f } \\big ) } \\\\ & { o _ { t } = \\sigma \\big ( W _ { o } h _ { t - 1 } + b _ { o } \\big ) } \\\\ & { \\hat { c } _ { t } = \\mathrm { t a n h } \\big ( W _ { c } h _ { t - 1 } + b _ { c } \\big ) } \\\\ & { c _ { t } = f _ { t } \\odot c _ { t - 1 } + i _ { t } \\odot \\hat { c } _ { t } } \\\\ & { h _ { t } = o _ { t } \\odot \\mathrm { t a n h } \\big ( c _ { t } \\big ) } \\end{array}\n$$",
+        "text_format": "latex",
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+        "text": "where $W _ { \\{ i , f , o , c \\} } , b _ { \\{ i , f , o , c \\} }$ are learnable parameters. ",
+        "bbox": [
+            173,
+            103,
+            514,
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+    },
+    {
+        "type": "text",
+        "text": "The LSTM update in equation 6 ",
+        "bbox": [
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+            138,
+            387,
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+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "is given by the following. ",
+        "bbox": [
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+            184,
+            341,
+            199
+        ],
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/0b22f3d6b6fdd05c611cfd9481a1a2f93b77dde594153096a506282e8b91f941.jpg",
+        "text": "$$\nh _ { t } , c _ { t } = L S T M ( h _ { t - 1 } , c _ { t - 1 } , x _ { t - 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "img_path": "images/1320dbefecef86265983cce83275270a285792e6c400dae83de8d1be56ebbe21.jpg",
+        "text": "$$\n\\begin{array} { r l } & { i _ { t } = \\sigma \\big ( W _ { h i } h _ { t - 1 } + W _ { x i } x _ { t - 1 } + b _ { i } \\big ) } \\\\ & { f _ { t } = \\sigma \\big ( W _ { h f } h _ { t - 1 } + W _ { x f } x _ { t - 1 } + b _ { f } \\big ) } \\\\ & { o _ { t } = \\sigma \\big ( W _ { h o } h _ { t - 1 } + W _ { x o } x _ { t - 1 } + b _ { o } \\big ) } \\\\ & { \\hat { c } _ { t } = \\mathrm { t a n h } \\big ( W _ { h c } h _ { t - 1 } + W _ { x c } x _ { t - 1 } + b _ { c } \\big ) } \\\\ & { c _ { t } = f _ { t } \\odot c _ { t - 1 } + i _ { t } \\odot \\hat { c } _ { t } } \\\\ & { h _ { t } = o _ { t } \\odot \\mathrm { t a n h } \\big ( c _ { t } \\big ) } \\end{array}\n$$",
+        "text_format": "latex",
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+        "page_idx": 16
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+    {
+        "type": "text",
+        "text": "where $W _ { \\{ h i , h f , h o , h c \\} } , W _ { \\{ x i , x f , x o , x c \\} } , b _ { \\{ i , f , o , c \\} }$ are learnable parameters. ",
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+]

parse/train/WWRBHhH158K/WWRBHhH158K.md

@@ -0,0 +1,263 @@
+# Deep Learning Through the Lens of Example Difficulty
+
+Robert J. N. Baldock∗ Google Research, Brain Team rjnbaldock@gmail.com
+
+Hartmut Maennel Google Research, Brain Team hartmutm@google.com
+
+Behnam Neyshabur Google Research, Blueshift Team neyshabur@google.com
+
+# Abstract
+
+Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of the computational difficulty of making a prediction for a given input: the (effective) prediction depth. Our extensive investigation reveals surprising yet simple relationships between the prediction depth of a given input and the model’s uncertainty, confidence, accuracy and speed of learning for that data point. We further categorize difficult examples into three interpretable groups, demonstrate how these groups are processed differently inside deep models and showcase how this understanding allows us to improve prediction accuracy. Insights from our study lead to a coherent view of a number of separately reported phenomena in the literature: early layers generalize while later layers memorize; early layers converge faster and networks learn easy data and simple functions first.
+
+# 1 Introduction
+
+Much of the existing work on understanding deep learning “integrates out” the data, viewing the inductive bias of the model, or the properties of the optimizer as central to the success of the approach. Examples of such work include studies of eigenvalues of the Hessian and the geometry of the loss landscape (Ghorbani et al., 2019; Yao et al., 2020; Sagun et al., 2016; Li et al., 2018; Pennington and Bahri, 2017; Sagun et al., 2018), studies of margin and effective generalization measures (Long and Sedghi, 2019; Unterthiner et al., 2020; Jiang et al., 2020, 2018; Kawaguchi et al., 2017) and mean-field studies of stochastic optimization (Smith et al., 2021; Stephan et al., 2017; Smith and Le, 2018). However, in practice, we are rarely concerned with only the average behavior of a model.
+
+One pathway to understanding the principles that govern how deep models process data is to study the properties of deep models for data points with different “amounts” or “types” of example difficulty. There are a number of definitions of example difficulty in the literature (E.g. see Carlini et al. (2019); Hooker et al. (2019); Lalor et al. (2018); Agarwal and Hooker (2020)). Two are particularly relevant to this work. Firstly, the probability of predicting the ground truth label for an example, when that example is omitted from the training set (Jiang et al., 2021), which represents a statistical view of example difficulty. Secondly, the difficulty of learning an example, parameterized by the earliest training iteration after which the model predicts the ground truth class for that example in all subsequent iterations (Toneva et al., 2019). This measure represents a learning view of example difficulty 2.
+
+These notions suffer from two fundamental limitations. While early-exit strategies in computer vision (Teerapittayanon et al., 2016; Huang et al., 2018) and NLP (Dehghani et al., 2018; Liu et al., 2020b; Schwartz et al., 2020; Xin et al., 2020) suggest predictions for easier examples require less computation, the above example difficulty notions do not encapsulate the processing of data inside a given converged model. Moreover, existing notions of example difficulty (E.g. Carlini et al. (2019)) provide a one-dimensional view of difficulty which can not distinguish between examples that are difficult for different reasons.
+
+In this paper, we take a significant step towards resolving the above shortcomings. To take the processing of the data into account we propose a new measure of example difficulty, the prediction depth, which is determined from the hidden embeddings. To escape the one-dimensional view of difficulty, we introduce three distinct difficulty types by relating the hidden embeddings for an input to high-level concepts about example difficulty: “Does this example look mislabeled?”; “Is classifying this example only easy if the label is given?”; “Is this example ambiguous both with and without its label?”. Furthermore, we show how this enhanced notion of example difficulty can unify our understanding of several seemingly unrelated phenomena in deep learning. We hope that the results presented in this work will aid the development of models that capture heteroscedastic uncertainty, our understanding of how deep networks respond to distributional shift, and the advancement of curriculum learning approaches and machine learning fairness. These connections are discussed in Section 5.
+
+Contributions Our main contributions are as follows:
+
+• We introduce a measure of computational example difficulty: the prediction depth (PD). The prediction depth, illustrated in Figure 1, represents the number of hidden layers after which the network’s final prediction is already (effectively) determined (Section 2).   
+We show that the prediction depth is larger for examples that visually appear to be more difficult, and that prediction depth is consistent between architectures and random seeds (Section 2.2).   
+• Our empirical investigation reveals that prediction depth appears to establish a linear lower bound on the consistency of a prediction. We further show that predictions are on average more accurate for validation points with small prediction depths (Section 3.1).   
+We demonstrate that final predictions for data points that converge earlier during training are typically determined in earlier layers which establishes a correspondence between the training history of the network and the processing of data in the hidden layers (Section 3.2).   
+• We show that both the adversarial input margin and the output margin are larger for examples with smaller prediction depths. We further design an intervention to reduce the output margin of a network and show that this leads to predictions being made only in the latest hidden layers (Section 3.3).   
+We identify three extreme forms of example difficulty by considering the prediction depth in the training and validation splits independently and demonstrate how a simple algorithm that uses the hidden embeddings in one middle layer to make predictions can lead to dramatic improvements in accuracy for inputs that strongly exhibit a specific form of example difficulty (Section 4).   
+We use our results to present a coherent picture of deep learning that unifies four seemingly unrelated deep learning phenomena: early layers generalize while later layers memorize; networks converge from input layer towards output layer; easy examples are learned first and networks present simpler functions earlier in training (Section 5).
+
+Experimental Setup: To ensure that our results are robust to the choice of architectures and datasets, we report empirical findings for ResNet18 (He et al., 2016), VGG16 (Simonyan and Zisserman, 2015) and MLP architectures trained on CIFAR10, CIFAR100 (Krizhevsky et al., 2009), Fashion MNIST (FMNIST) (Xiao et al., 2017) and SVHN (Netzer et al., 2011) datasets. All models were trained using SGD with momentum. Our MLP comprises 7 hidden layers of width 2048 with ReLU activations. Details of the datasets, architectures, and hyperparameters used can be found in Appendix A.
+
+Related Work: Our work uses hidden layer probes to determine example difficulty. We have discussed how our study relates to prior work on example difficulty. Hidden layer probes have also been used to study deep learning. Deep k-NN methods (Papernot and McDaniel, 2018) determine their predictions and estimate their own uncertainties by comparing the hidden embeddings of an input to those of the training set. Cohen et al. (2018) showed that SVM, $\mathbf { k }$ -Nearest Neighbors $\mathbf { k }$ -NN)
+
+and logistic regression probes achieve similar accuracies. However, they did not study the processing of individual data points nor did they relate the $\mathbf { k }$ -NN accuracy to notions of example difficulty. Alain and Bengio (2017) used linear classifier probes in the hidden layers to interrogate deep models and demonstrated that linear separability of the embeddings increases monotonically with depth. We provide a more detailed discussion of related work in Appendix B.
+
+# 2 Prediction Depth: a Computational View of Example Difficulty
+
+We discussed the statistical and learning views of example difficulty in Section 1. In this section, we introduce a computational view of example difficulty parametrized by the prediction depth as defined in Section 2.1. This computational view asserts that, for “easy” examples, a deep model’s final prediction is effectively made after only a few layers, while more layers are used for “difficult” examples.
+
+# 2.1 Definition
+
+Asserting that the final prediction is effectively determined in earlier layers of a model, before the output, we estimate the depth at which a prediction is made for a given input as follows 3:
+
+1. We construct k-NN classifier probes from the embeddings of the training set after particular layers of the network, including the input and the final softmax. The placement of $\mathbf { k }$ -NN probes is described in Appendix A.5. We use $k = 3 0$ in the $\mathbf { k }$ -NN probes. Appendix A.4 establishes that the k-NN accuracies we report are insensitive to $k$ over a wide range. 2. A prediction is defined to be made at a depth $L = l$ if the $\mathbf { k }$ -NN classification after layer $L = l - 1$ is different from the network’s final classification, but the classifications of k-NN probes after every layer $L \geq l$ are all equal to the final classification of the network. Data points consistently classified by all $\mathbf { k }$ -NN probes are determined to be (effectively) predicted in layer 0 (the input) 4.
+
+It is worth noting that the prediction depth can be calculated for all data points: both in the training and validation splits. This leads to two notions of computational difficulty:
+
+• The difficulty of predicting the (given) class for an input (in the training split) • The difficulty of making a prediction for an input, unseen in advance (from the validation split)
+
+We examine both notions of computational difficulty in this paper and use the distinction between them to describe different forms of example difficulty in Section 4.
+
+# 2.2 Prediction depth is a meaningful and robust notion of example difficulty
+
+In this section we show that prediction depth agrees with intuitive notions of example difficulty and that it is consistent between different training runs and similar architectures.
+
+Prediction depth is higher for examples and datasets that seem more difficult If prediction depth is a sensible measure of example difficulty then we would expect the following sanity checks to be observed:
+
+1. Individual data points that are visually confusing or mislabeled should have larger prediction depths as compared to images that are clear examples of their class.   
+2. Data points from tasks that are intuitively simpler should have lower prediction depths on average.
+
+Figure 1 shows that the prediction depth passes both of these sanity checks. Appendix C.1 presents additional images, providing further evidence for this claim.
+
+Prediction depth is consistent across random seeds and similar architectures Figure 2 shows that the prediction depth is highly consistent between different architectures and random seeds for all datasets. Perfect agreement is not expected as different deep learning algorithms have different inductive biases which affects the perceived difficulty of examples. We observe stronger correlation between prediction depth for ResNet18 and VGG16, than between VGG16 and MLP. This may be explained by the fact that ResNet18 and VGG16 are both convolutional networks and we expect their inductive biases to be more similar to one another than to MLP.
+
+![](images/41ae6d0999f3d52ac3d9fed1621b96ae037b526605cd4d18c4e702c118a942c4.jpg)  
+Figure 1: Deep models use fewer layers to (effectively) determine the prediction for easy examples and more layers for hard examples. Left: A cartoon illustrating the definition of prediction depth (given in Section 2.1). Also shown are training examples from CIFAR100 (“Clock”) and SVHN (“Digit 8”). The examples shown are predicted at the input (first layer) or softmax (last layer) of ResNet18. The examples predicted in the input are visually typical (“easy”), while those predicted in the softmax are mislabeled and/or visually confusing (“hard” examples). To find the prediction depth, we build $\mathbf { k }$ -NN classifiers from the embeddings of the training set in different layers of the model. The prediction depth corresponds to the earliest layer at which the predictions of all subsequent k-NN classifiers converge to a fixed label. Right: Probability of prediction depth in ResNet18 models for four datasets (training split). We see that the four distributions have different characteristic prediction depths. Ranking the mean prediction depths of these datasets in ascending order, we observe: Fashion MNIST (smallest), SVHN (second), CIFAR10 (third), and CIFAR100 (largest). This order aligns with how one might intuitively rank the difficulties of these classification tasks.
+
+![](images/23c98a880da3f394cd13a1b9baa89a6f129ff8653082737c21aec2cb3c228e0f.jpg)  
+Figure 2: Consistency of prediction depth between architectures and random seeds. Left: The panel shows the correlation coefficient between prediction depths in different architectures, for both train and validation splits in four datasets. Diagonal comparisons between an architecture and itself show the correlation for the same architecture trained with different random seeds. Right: Histograms comparing the mean value of prediction depth obtained for each data point in the training set of CIFAR10 from an ensemble of 250 trained models. In this plot, for visual simplicity, we rescale prediction depth to the interval $[ 0 , 1 ]$ for each network. Similar results for all other datasets are presented in Appendix C.2.
+
+# 3 Deep Learning Phenomena Through the Lens of Prediction Depth
+
+In this section, we explore how the prediction depth can be used to better understand three important aspects of Deep Learning: accuracy and consistency of a prediction; the order in which data is learned and the simplicity of the learned function (as measured by the margin) in the vicinity of a data point.
+
+# 3.1 Depth of a prediction gives a linear lower bound on its consistency
+
+Adopting a statistical view of example difficulty, Jiang et al. (2021) identified example difficulty with the expected accuracy of the learning algorithm for a given input, averaged over models trained on different random subsets of the training set with different random seeds. In this section, we clarify the relationship between the prediction depth and the expected accuracy by disentangling the accuracy from the sensitivity of predictions to the particular training split and random seed. Following Jiang et al. (2021), we measure the expected accuracy using the consistency score.
+
+Consistency score $\hat { C }$ : The frequency of classifying an example correctly when it is omitted from the training set. An empirical estimator of the consistency score for a validation point $( x , y )$
+
+![](images/67ee1b181de37aba816ac42fe368a058ecc0e63537f5c06a4103f90e7f6c3a63.jpg)  
+Figure 3: Consistency score vs. prediction depth in the validation split (left) can be understood as the superposition of two simple functions (middle and right). We trained 250 ResNet18 models on CIFAR10, with $9 0 { : } 1 0 \%$ random train:validation splits as described in Appendix A. These histograms compare the frequency of correct predictions to the average prediction depth for a data point when it occurs in the validation split. The density of data points is indicated by the color bar, which follows a log scale. The average prediction depth forms two, surprisingly simple, linear bounds on the consistency score (see Section 3.1 for a full description.) This Figure is reproduced for all datasets and architectures in Appendix C.3, illustrating the consistency of this result.
+
+is given by (Jiang et al., 2021):
+
+$$
+\hat { C } _ { A , S } ( x , y ) = \hat { \mathbb { E } } _ { \tilde { S } \sim { \cal S } \setminus \{ ( x , y ) \} } ^ { r } \left[ \delta _ { y _ { A } , y } \right]
+$$
+
+where $A$ is a deep learning algorithm (architecture, loss and optimizer), $y$ is the ground truth class for $x$ , $\tilde { \cal S }$ is a random subset of $n$ points sampled from a training dataset $s$ excluding $( x , y )$ , $y _ { A }$ is the predicted class of $x$ for $A$ trained with data $\tilde { \cal S }$ , $\delta$ is the Kronecker delta and $\hat { \mathbb { E } } ^ { r }$ denotes empirical averaging with $r$ i.i.d. samples of such subsets $\tilde { \cal S }$ .
+
+Figure 3 (left panel) shows the relationship between consistency score and prediction depth. This plot indicates a surprising piecewise linear boundary which is symmetric around consistency score $\frac { 1 } { 2 }$ This suggests the existence of a missing concept that could simplify the picture. We next show that the missing concept is the notion of a consensus class which is defined below.
+
+Consensus class ${ \hat { y } } _ { A }$ : The consensus class of $x$ is defined as the predicted class for input $x$ by a majority voting ensemble of $r$ models each of which is trained on a randomly chosen subset ${ \tilde { \cal S } } \stackrel { n } { \sim } { \cal S } \backslash \{ ( x , y ) \} \stackrel { 5 } { \sim }$ .
+
+Figure 3 (middle and right) shows how conditioning on whether consensus class matches the ground truth can change the relationship between consistency score and the prediction depth. For points where the consensus class matches the ground truth (middle) we see that the prediction depth forms a, surprisingly simple, linear lower bound on the consistency score. For points where the consensus class differs from the ground truth (right) at low prediction depth the consistency score is bounded from above by a line that reflects the bound from the middle plot in $\begin{array} { r } { \hat { C } = \frac { 1 } { 2 } } \end{array}$ , suggesting that such points are repeatedly mislabeled with a wrong class label. At high prediction depth, the consistency score is low, which suggests highly inconsistent predictions and low accuracy. This result suggests a simple hypothesis: that predictions with low prediction depth are consistent with the consensus class, whether that matches the ground truth class or not, while predictions made in later layers depend strongly on the specific training split and random seed used for training and initialization. We measure consistency with the consensus class using the consensus-consistency score.
+
+Consensus-consistency score $C ^ { * }$ : The fraction of models in an ensemble that predict the ensemble’s consensus class ${ \hat { y } } _ { A } \left( x \right)$ for an unseen input $x$ .
+
+$$
+C _ { A , S } ^ { * } ( x ) = \hat { \mathbb { E } } _ { \tilde { S } \sim \tilde { S } \backslash \{ ( x , y ) \} } ^ { r } \left[ \delta _ { y _ { A } , \hat { y } _ { A } ( x ) } \right]
+$$
+
+where the notation is the same as in (1) 6.
+
+Figure 4 (left) establishes that our simple hypothesis is indeed correct: the prediction depth forms a linear lower bound on the consensus-consistency score for all data points, irrespective of whether the consensus class matches or differs from the ground truth. Interestingly, Figure 4 (middle and right) shows how the prediction depth in a single model, can be used to estimate both of these quantities. That is, predictions of data points with lower prediction depth are both more likely to be consistent and more likely to be correct.
+
+![](images/8a5ae0a88a3e513d4097c5f1dcee15b7f3d5e2e68ceae4e1b0a5b33e9d9f4a7a.jpg)  
+Figure 4: Left: Prediction depth provides us with a linear lower bound on consensus-consistency. Results for CIFAR100 with ResNet18. We train 250 models $( 9 0 { : } 1 0 \%$ random train:validation splits) and compare the average prediction depth when a point occurs in the validation set, to the consensus-consistency of the corresponding predictions. Predictions made for points with low mean prediction depths are highly consistent. Conversely, predictions for points with high mean prediction depths are typically more sensitive to the particular training split and random seed used during training. This left plot shows the result for CIFAR100 with ResNet18. The density of data points is indicated by the color bar, which follows a log scale. Middle: Prediction depth in one model predicts the consensus-consistency of an ensemble that does not include that model. For each dataset we train 25 ResNet18 models with the full training set (see Appendix A). The consensus-consistency of each test point is obtained from 24 of the models, while the prediction depth is obtained from the remaining 1 model. We see that prediction depth in one model predicts the consensus-consistency of a separate ensemble: a measure of the uncertainty of the prediction. The size of each marker in the middle and right plots shows the fraction of the dataset with each prediction depth. Reaffirming the second sanity check in Section 2.2, and in agreement with Figure 1 (right), intuitively simpler datasets (Fashion MNIST and SVHN) have low average prediction depths, while CIFAR100 (intuitively the hardest dataset) has the largest average prediction depth. Right: Prediction depth predicts accuracy. For each dataset we train 250 ResNet18 models $9 0 { : } 1 0 \%$ random train:validation splits). Each time a point appears in the validation split we record the prediction depth and whether the prediction was correct. Predictions made in earlier layers are more likely to be correct. Consistency of these plots is demonstrated for all datasets and architectures in Appendix C.3 where we also describe the relationship between the prediction depth and the entropy of the predictions for an ensemble.
+
+# 3.2 The prediction depth of an input is correlated with its learning difficulty
+
+In Section 3.1, we describe the relationship between the prediction depth, which represents a computational view of example difficulty and the consistency and consensus-consistency scores, which represent a statistical view. In this section we compare prediction depth to a learning view of example difficulty. We measure the difficulty of learning an example by the speed at which the model’s prediction converges for that input during training. The following definition is adapted from Toneva et al. (2019):
+
+Iteration learned A data point is said to be learned by a classifier at training iteration $t = \tau$ if the predicted class at iteration $t = \tau - 1$ is different from the final prediction of the converged network and the predictions at all iterations $t \geq \tau$ are equal to the final prediction of the converged network. Data points consistently classified after all training steps and at the moment of initialization, are said to be learned in step $t = 0$ 7 .
+
+Figure 5 (left plot) shows the positive correlation between the prediction depth and the iteration learned, for all four datasets in VGG16. Consistent results are presented for all architectures and datasets, in both the validation and training splits in Appendix C.4. As a result of the reported correlation, we anticipate that many of the data points correctly classified by the k-NN probe in a particular layer should also be correctly classified by the network at a corresponding interval of training steps. If this is correct then we would expect there to be a visual correspondence between the training learning curve (which shows how the accuracy of the network changes during training) and the accuracy of the $\mathbf { k }$ -NN probes as data passes from input, through the network, towards the output layer. We call the series of $\mathbf { k }$ -NN probe accuracies the inference learning curve.
+
+![](images/a02ab6322e5cd8cebfe9ac42455d2b4efbdada80864f46deb3a0b8efc92674dd.jpg)  
+Figure 5: Left: Data points with small prediction depths are on average learned before data points with higher prediction depths. We train 250 VGG16 models for each dataset, using a $9 0 { : } 1 0 \%$ random train:validation split as described in Appendix A. Each time an input appears in the validation split we record the prediction depth and the iteration learned in that model. This plot shows the average iteration learned for data points at each prediction depth. Marker size shows the fraction of the dataset with each prediction depth. The Pearson correlation coefficients for the four data sets are as follows. CIFAR100: 0.83. CIFAR10: 0.7. Fashion MNIST: 0.79. SVHN: 0.77. Middle and right: The training learning curve (middle) shares several important features with the inference learning curve (right). Blue, yellow and green curves represent different components of the CIFAR10 training split, in which we have randomized (and fixed) $40 \%$ of the labels, and red curves show the test split. The middle and right plots show results from 5 random seeds. The inference learning curve (right) is the sequence of k-NN probe accuracy values for each split. All three plots show results for VGG16. The hyperparameters used are given in Appendix A.
+
+![](images/cd8a095f06b0d86716987a5edc4dae02cc92e33acd326dbeae942c6b16d73e2a.jpg)  
+Figure 6: Left and Middle: Test examples with smaller prediction depths, on average, have larger output and input margins. We train 25 VGG16 models with different random seeds on CIFAR10 (see Appendix A for details) and compare the mean prediction depth of each test point in these 25 runs to its mean output and input margins (log scales). Correlation coefficients are $- 0 . 7 0$ (output margin) and $- 0 . 6 9$ (input margin). The density of data points is indicated by the color bar, which follows a log scale. Although the prediction depth could be at most 14, no data point has an average prediction depth greater than 12. Right: An intervention that does not encourage large output margin ( $^ { * } O$ -Hinge”) results, as predicted, in models where the predictions are effectively determined in higher layers in the network compared to the standard training $( \ ^ { \ast } C E ^ { \prime \prime } )$ .
+
+To test this hypothesis we train a model on a training split where a subset of labels are corrupted and compare the training and inference learning curves on four splits of the data: unchanged training data; mislabeled training data; the original labels of the mislabeled training data and the test split. In Figure 5 (middle and right plots) we see that many of the important features of the training learning curve are indeed present in the inference learning curve. During training (middle), mislabeled data are initially processed as though they are a member of their original class (before they were mislabeled) (Liu et al., 2020a). After an initial period of learning, the network begins to learn the new (random) labels that have been assigned to those data points, so the orange curve moves upwards, and the green curve downwards. At this point, a maximum is observed in the training accuracy (Arpit et al., 2017). In the right plot we see that these same phenomena occur in the inference learning curve.
+
+# 3.3 Deep models exhibit larger margins for inputs with lower prediction depth
+
+It is reported in the literature that deep networks learn functions of increasing complexity during training (Hu et al., 2020; Kalimeris et al., 2019). We frame this observation differently: the learned function is “locally simpler” in the vicinity of data points with smaller prediction depths, and these points are typically learned earlier in training (Section 3.2).
+
+Two known measures of the simplicity of a learned function are the output margin (the difference between the largest and second-largest logits) and the adversarial input margin (the smallest norm required for an adversarial perturbation in the input to change the model’s class prediction). We estimate the adversarial input margin, $\gamma$ , with a linear approximation (Jiang et al., 2018): for an input x with predicted class i, γ ' minj6=i |zi−zj ||∇x(zi−zj )| where $z _ { j }$ is the logit returned by the network for class $j$ . Figure 6 (left and middle plots) show that data points with smaller prediction depths have both larger input and output margins on average and that variances of the input and output margins decrease as the prediction depth increases.
+
+![](images/6adf476b71571c6b4cc9499c21b8fe2583b9b43fa207152bd6831ec0fc9ca860.jpg)  
+Figure 7: The prediction depth can be the same, or very different for the same input when it occurs in the train and validation splits. Corners of this plot correspond to different forms of example difficulty. (See Section 4 for discussion.) We train 250 ResNet18 models on CIFAR10 with random $9 0 { : } 1 0 \%$ train:validation splits as described in Appendix A. These histograms compare average prediction depth for each data point when it occurs in the validation split vs the training split. This behavior is consistently reproduced for all datasets and architectures in Appendix C.6. Below we show extreme (not hand-chosen) images of “Birds” that appear closest to the corners of this plot. The consensus class is given above each image (tiebreaks favor the class “Bird”.)
+
+To illustrate the strength of the relationship between the prediction depth and output margin, we demonstrate that reducing the output margin of the learned function results in a model that clusters the data only in the latest layers: such a solution has a very high average prediction depth. We do not minimize the output margin directly but rather use a loss and an optimizer that do not encourage high output margin. Naturally there are many unknowns that may contribute to this effect. We simply report the intervention and the outcome.
+
+The intervention is performed as follows: we construct a loss function that does not promote confidence: a zero-margin hinge loss ( $^ { 6 6 } 0$ -Hinge”), and optimize the network using full-batch gradient descent with momentum and very small learning rate. For an input $x$ with label $i$ the 0-Hinge loss is given by $\begin{array} { r } { l ( x ) = \sum _ { j \neq i } \operatorname* { m a x } ( \dot { 0 } , z _ { i } - z _ { j } ) } \end{array}$ where $z _ { j }$ represents the logit for class $j$ . The form of this intervention is justified in Appendix A.7. As a control, we additionally train a model in the standard fashion using the cross-entropy loss and SGD with momentum and large initial learning rate. Since full-batch gradients are computationally expensive, we train on a subset of CIFAR10 (see Appendix A.7, where we also give the hyperparameters and learning curves.). The output margin obtained with the intervention is 5 orders of magnitude smaller than in the control experiment: $2 . 0 \times 1 0 ^ { - 4 } \pm 2 . 0 \times 1 0 ^ { - 4 }$ for the 0-Hinge loss and $1 . { \overline { { 6 } } } \times 1 0 ^ { 1 } \pm 0 . 5 0 \times 1 0 ^ { 1 }$ for cross-entropy loss. Figure 6 (right) compares the accuracies of the $\mathbf { k }$ -NN probes resulting from these training approaches. The 0-Hinge loss training achieves only a marginal improvement in accuracy (red) over an untrained network (purple), and the training split is accurately clustered only in the latest layers. This confirms the predicted behavior: the intervention leads to a model that exhibits both very small average output margins and very late clustering of the data. Very late clustering of the data implies high prediction depths since the $\mathbf { k }$ -NN probe classifications change in the latest layers for many data points.
+
+# 4 Beyond a One-Dimensional Picture of Example Difficulty
+
+In this section we transcend the one-dimensional picture of example difficulty by identifying different underlying reasons behind the difficulty of an example, in a way that is general to different architectures and datasets.
+
+Figure 7 shows that the prediction depth can be different when an input occurs in the training split vs. the validation split. Thus, there are two axes of example difficulty:
+
+1. Difficulty of making a prediction when an input is in the validation set 2. Difficulty of finding commonalities during training with other examples of the same ground truth class
+
+Both axes have a range from “clear” to “ambiguous”. In Section 3.1 we show that predictions made for validation points with later prediction depths are often inconsistent, with low consensusconsistency. Conversely, a low prediction depth typically indicates an input with high consensusconsistency. For Axis 1 we will identify validation points with low prediction depths as “clear” and those with high prediction depths as “ambiguous”. We will additionally identify a low or high prediction depth in the training split with examples that are respectively “clear” and “ambiguous” on Axis 2. By making combinations of low/high values of $( \mathrm { P D } _ { \mathrm { V a l . } }$ , $\mathrm { P D } _ { \mathrm { T r a i n } _ { . } }$ ) we obtain four extremes of example difficulty:
+
+![](images/14930e4f6df689d31626c023acd5f7f776fdcf3f0a5998ae876b3c3fa70cabe4.jpg)  
+Figure 8: Average k-NN probe confidence (solid lines) and accuracy (dotted lines) for the ground truth class (left) and consensus class (right), in the validation split for examples exhibiting extreme forms of difficulty. Mean values for 100 examples with each form of difficulty, identified as the 100 examples closest to the corners in Figure 7 (left). This result is for CIFAR10 with ResNet18: similar plots for all datasets and architectures are shown in Appendix C.7. See Section 4 for the discussion of the result and how it can be used to improve prediction accuracy.
+
+Easy examples: (Low $\mathrm { P D } _ { \mathrm { V a l . } }$ , Low $\mathrm { P D } _ { \mathrm { T r a i n } }$ ). Such examples are often visually typical members of their class and the predicted label nearly always matches the ground truth.   
+Looks like a different class: (Low $\mathrm { P D } _ { \mathrm { V a l . } }$ , High $\mathrm { P D } _ { \mathrm { T r a i n } }$ ). In the validation set, there is a clear (and nearly always incorrect) classification for such an input, but it is difficult to connect such inputs to other examples of their ground truth class during training. Mislabeled examples are of this kind, as are visually confusing images which at first appear to show something else.   
+Ambiguous unless the label is given: (High $\mathrm { P D } _ { \mathrm { V a l . } }$ , Low $\mathrm { P D } _ { \mathrm { T r a i n } }$ ). These examples are difficult to connect to their predicted class in the validation split but easy to connect to their ground truth class during training. These points may, for example, visually resemble both their own class and another class. They are likely to be misclassified.   
+Ambiguous: (High $\mathrm { P D } _ { \mathrm { V a l . } }$ , High $\mathrm { P D } _ { \mathrm { T r a i n } }$ ). These examples may be corrupted or show an example of a rare sub-class. Predictions for these inputs can depend strongly on the random seed used for training and initialization.
+
+In Figure 7 we visualize CIFAR10 “Bird” images with the extreme forms of example difficulty for ResNet18, as identified using the prediction depth in the training and validation splits. In the full dataset (left panel) we see that the prediction depth can be very different in the training and validation splits: the two prediction depths are typically similar for points where the consensus class is equal to the ground truth (right panel), but can be very different when the consensus class is different from the ground truth (middle panel). This behavior is consistently reproduced for all datasets and architectures in Appendix C.6.
+
+Looking at these examples of the class “Bird” with different difficulty types, we observe that ResNet18 finds small garden birds easiest, while birds in flight against a blue background “look like airplanes”, ostriches are “ambiguous without their label” and the “ambiguous” examples are either unclear photographs or examples of rare sub-groups that don’t appear frequently in the data. We found the consensus-consistency of inputs that are “Ambiguous” or “Ambiguous without its label” to be significantly lower than those of examples that are “Easy” or “Look like a different class”.
+
+In order to better understand how networks process examples with different, extreme forms of example difficulty, Fig. 8 examines how the k-NN confidence (fraction of votes) and accuracy of the ground truth class and of the consensus class progress, as validation points pass through the network. “Easy” examples are classified as their consensus class (which is equal to their ground truth class) in all k-NN probes and the confidence in the consensus class steadily increases as data points proceed through the hidden layers. Examples that “look like a different class” are also processed as members of their consensus class, similarly to “easy” examples. However, unlike “easy” examples, their consensus classes do not match their ground truth classes. Examples that are “ambiguous without their labels” are initially processed as members of their ground truth classes with intermediate confidence, but in later layers become mistaken for their consensus class. “Ambiguous” examples are processed with low confidence and accuracy in the early layers, for both ground truth and consensus classes. In later layers “ambiguous” examples are recognized, with intermediate confidence and accuracy, as members of the consensus class, which matches the ground truth class for a sizeable fraction of “ambiguous” examples.
+
+Improving the prediction accuracy Can the prediction accuracy be improved using our understanding of how each class of difficult examples are processed by deep models? Figure 8 suggest that $\mathbf { k }$ -NN probes in intermediate layers may be more accurate than the full deep model for examples that are “ambiguous without their label” (data points closest to the lower right corner of Figure 7). In order to test this hypothesis, we compare the accuracy of the $\mathbf { k }$ -NN probe in layer 4 to the full model’s prediction for the 100 examples closest to the lower right corner of Figure 8. We obtain a striking improvement in accuracy from $2 5 \%$ to $98 \%$ for these examples. This showcases how insights from this study can be directly used to improve prediction accuracy.
+
+# 5 Discussion
+
+Summary We have introduced a notion of example difficulty called the prediction depth, which uses the processing of data inside the network to score the difficulty of an example. We have shown how the prediction depth is related to the accuracy and uncertainty of a prediction, the adversarial input margin and the output margin of the learned solution, and that data points that are easier according to the prediction depth are also typically learned earlier in training. We have also shown that the difficulty of an example can be both similar, or very different depending on whether an input appears in the validation split or the training split, and described four extremes of example difficulty. For data points that are “ambiguous without their label”, we have demonstrated how returning the $\mathbf { k }$ -NN prediction in a middle layer can lead to impressive increases in model accuracy: for CIFAR10 in ResNet18 we obtained an increase in accuracy from $2 5 \%$ to $98 \%$ for the inputs that are most “ambiguous without their label”.
+
+Connecting known phenomena In the literature, the following phenomena are separately reported from different experimental paradigms:
+
+1. Early layers generalize while later layers memorize (Stephenson et al., 2021).   
+2. Model layers converge from input layer towards output layer (Raghu et al., 2017; Morcos et al., 2018).   
+3. Deep models learn easy data (Jiang et al., 2021; Toneva et al., 2019) and simple functions first (Hu et al., 2020; Kalimeris et al., 2019).
+
+Following this paper, a coherent and closely related picture emerges:
+
+1. Predictions made in early layers are more likely to be consistent than those made in later layers. Consistent predictions are likely to be correct and the expected accuracy of inconsistent predictions is naturally low (Section 3.1).   
+2. Data points learned early in training typically have smaller prediction depths than those learned later during training (Section 3.2).   
+3. On average, deep neural networks exhibit wider input and output margins (common measures of “local simplicity”) in the vicinity of data with smaller prediction depths (Section 3.3).
+
+Pertinence of example difficulty to topics in machine learning Curriculum Learning attempts to treat hard examples differently from easy examples during training. Robustness to distribution shifts that change the relative frequencies of common and rare subgroups in the test set (which we have shown can have different forms of example difficulty) is important for ML Fairness. Methods developed to address heteroscedastic uncertainty typically address example difficulty as a onedimensional quantity. We expand upon the relevance of our work to these three topics in Appendix D.
+
+Limitations We believe that the results we report stem from a deep model’s representation, which is hierarchical by construction. We expect that the same results will therefore apply in larger models, larger datasets, and tasks other than image classification, but testing this remains as further work. Although we demonstrate that returning the results of a hidden k-NN can yield dramatic increases in accuracy for examples that are “ambiguous without their label”, we otherwise do not explore ways to practically apply the insights we present. In particular, we expressly do not claim that all that is required for good accuracy is to reduce the prediction depth: freezing later layers of the network would not be expected to result in good generalization.
+
+# Funding Transparency Statement
+
+This research was funded by, and undertaken at, Google. All calculations were performed using Google’s computer infrastructure.
+
+# Acknowledgment
+
+We would like to thank Hanie Sedghi, Ilya Tolstikhin, Ibrahim Alabdulmohsin, Daniel Keysers and Julian Eisenschlos for valuable discussions on the topic and Arthur Baldock for proofreading the manuscript.
+
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parse/train/WWRBHhH158K/WWRBHhH158K_content_list.json

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+    {
+        "type": "text",
+        "text": "Deep Learning Through the Lens of Example Difficulty ",
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+    {
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+        "text": "Robert J. N. Baldock∗ Google Research, Brain Team rjnbaldock@gmail.com ",
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+    {
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+        "text": "Hartmut Maennel Google Research, Brain Team hartmutm@google.com ",
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+    {
+        "type": "text",
+        "text": "Behnam Neyshabur Google Research, Blueshift Team neyshabur@google.com ",
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+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+    },
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+        "text": "Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of the computational difficulty of making a prediction for a given input: the (effective) prediction depth. Our extensive investigation reveals surprising yet simple relationships between the prediction depth of a given input and the model’s uncertainty, confidence, accuracy and speed of learning for that data point. We further categorize difficult examples into three interpretable groups, demonstrate how these groups are processed differently inside deep models and showcase how this understanding allows us to improve prediction accuracy. Insights from our study lead to a coherent view of a number of separately reported phenomena in the literature: early layers generalize while later layers memorize; early layers converge faster and networks learn easy data and simple functions first. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+    },
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+        "text": "Much of the existing work on understanding deep learning “integrates out” the data, viewing the inductive bias of the model, or the properties of the optimizer as central to the success of the approach. Examples of such work include studies of eigenvalues of the Hessian and the geometry of the loss landscape (Ghorbani et al., 2019; Yao et al., 2020; Sagun et al., 2016; Li et al., 2018; Pennington and Bahri, 2017; Sagun et al., 2018), studies of margin and effective generalization measures (Long and Sedghi, 2019; Unterthiner et al., 2020; Jiang et al., 2020, 2018; Kawaguchi et al., 2017) and mean-field studies of stochastic optimization (Smith et al., 2021; Stephan et al., 2017; Smith and Le, 2018). However, in practice, we are rarely concerned with only the average behavior of a model. ",
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+        "text": "One pathway to understanding the principles that govern how deep models process data is to study the properties of deep models for data points with different “amounts” or “types” of example difficulty. There are a number of definitions of example difficulty in the literature (E.g. see Carlini et al. (2019); Hooker et al. (2019); Lalor et al. (2018); Agarwal and Hooker (2020)). Two are particularly relevant to this work. Firstly, the probability of predicting the ground truth label for an example, when that example is omitted from the training set (Jiang et al., 2021), which represents a statistical view of example difficulty. Secondly, the difficulty of learning an example, parameterized by the earliest training iteration after which the model predicts the ground truth class for that example in all subsequent iterations (Toneva et al., 2019). This measure represents a learning view of example difficulty 2. ",
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+        "text": "These notions suffer from two fundamental limitations. While early-exit strategies in computer vision (Teerapittayanon et al., 2016; Huang et al., 2018) and NLP (Dehghani et al., 2018; Liu et al., 2020b; Schwartz et al., 2020; Xin et al., 2020) suggest predictions for easier examples require less computation, the above example difficulty notions do not encapsulate the processing of data inside a given converged model. Moreover, existing notions of example difficulty (E.g. Carlini et al. (2019)) provide a one-dimensional view of difficulty which can not distinguish between examples that are difficult for different reasons. ",
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+        "text": "In this paper, we take a significant step towards resolving the above shortcomings. To take the processing of the data into account we propose a new measure of example difficulty, the prediction depth, which is determined from the hidden embeddings. To escape the one-dimensional view of difficulty, we introduce three distinct difficulty types by relating the hidden embeddings for an input to high-level concepts about example difficulty: “Does this example look mislabeled?”; “Is classifying this example only easy if the label is given?”; “Is this example ambiguous both with and without its label?”. Furthermore, we show how this enhanced notion of example difficulty can unify our understanding of several seemingly unrelated phenomena in deep learning. We hope that the results presented in this work will aid the development of models that capture heteroscedastic uncertainty, our understanding of how deep networks respond to distributional shift, and the advancement of curriculum learning approaches and machine learning fairness. These connections are discussed in Section 5. ",
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+        "type": "text",
+        "text": "Contributions Our main contributions are as follows: ",
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+        "text": "• We introduce a measure of computational example difficulty: the prediction depth (PD). The prediction depth, illustrated in Figure 1, represents the number of hidden layers after which the network’s final prediction is already (effectively) determined (Section 2).   \nWe show that the prediction depth is larger for examples that visually appear to be more difficult, and that prediction depth is consistent between architectures and random seeds (Section 2.2).   \n• Our empirical investigation reveals that prediction depth appears to establish a linear lower bound on the consistency of a prediction. We further show that predictions are on average more accurate for validation points with small prediction depths (Section 3.1).   \nWe demonstrate that final predictions for data points that converge earlier during training are typically determined in earlier layers which establishes a correspondence between the training history of the network and the processing of data in the hidden layers (Section 3.2).   \n• We show that both the adversarial input margin and the output margin are larger for examples with smaller prediction depths. We further design an intervention to reduce the output margin of a network and show that this leads to predictions being made only in the latest hidden layers (Section 3.3).   \nWe identify three extreme forms of example difficulty by considering the prediction depth in the training and validation splits independently and demonstrate how a simple algorithm that uses the hidden embeddings in one middle layer to make predictions can lead to dramatic improvements in accuracy for inputs that strongly exhibit a specific form of example difficulty (Section 4).   \nWe use our results to present a coherent picture of deep learning that unifies four seemingly unrelated deep learning phenomena: early layers generalize while later layers memorize; networks converge from input layer towards output layer; easy examples are learned first and networks present simpler functions earlier in training (Section 5). ",
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+    {
+        "type": "text",
+        "text": "Experimental Setup: To ensure that our results are robust to the choice of architectures and datasets, we report empirical findings for ResNet18 (He et al., 2016), VGG16 (Simonyan and Zisserman, 2015) and MLP architectures trained on CIFAR10, CIFAR100 (Krizhevsky et al., 2009), Fashion MNIST (FMNIST) (Xiao et al., 2017) and SVHN (Netzer et al., 2011) datasets. All models were trained using SGD with momentum. Our MLP comprises 7 hidden layers of width 2048 with ReLU activations. Details of the datasets, architectures, and hyperparameters used can be found in Appendix A. ",
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+    {
+        "type": "text",
+        "text": "Related Work: Our work uses hidden layer probes to determine example difficulty. We have discussed how our study relates to prior work on example difficulty. Hidden layer probes have also been used to study deep learning. Deep k-NN methods (Papernot and McDaniel, 2018) determine their predictions and estimate their own uncertainties by comparing the hidden embeddings of an input to those of the training set. Cohen et al. (2018) showed that SVM, $\\mathbf { k }$ -Nearest Neighbors $\\mathbf { k }$ -NN) ",
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+    {
+        "type": "text",
+        "text": "and logistic regression probes achieve similar accuracies. However, they did not study the processing of individual data points nor did they relate the $\\mathbf { k }$ -NN accuracy to notions of example difficulty. Alain and Bengio (2017) used linear classifier probes in the hidden layers to interrogate deep models and demonstrated that linear separability of the embeddings increases monotonically with depth. We provide a more detailed discussion of related work in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "2 Prediction Depth: a Computational View of Example Difficulty ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We discussed the statistical and learning views of example difficulty in Section 1. In this section, we introduce a computational view of example difficulty parametrized by the prediction depth as defined in Section 2.1. This computational view asserts that, for “easy” examples, a deep model’s final prediction is effectively made after only a few layers, while more layers are used for “difficult” examples. ",
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+    {
+        "type": "text",
+        "text": "2.1 Definition ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Asserting that the final prediction is effectively determined in earlier layers of a model, before the output, we estimate the depth at which a prediction is made for a given input as follows 3: ",
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+        "type": "text",
+        "text": "1. We construct k-NN classifier probes from the embeddings of the training set after particular layers of the network, including the input and the final softmax. The placement of $\\mathbf { k }$ -NN probes is described in Appendix A.5. We use $k = 3 0$ in the $\\mathbf { k }$ -NN probes. Appendix A.4 establishes that the k-NN accuracies we report are insensitive to $k$ over a wide range. 2. A prediction is defined to be made at a depth $L = l$ if the $\\mathbf { k }$ -NN classification after layer $L = l - 1$ is different from the network’s final classification, but the classifications of k-NN probes after every layer $L \\geq l$ are all equal to the final classification of the network. Data points consistently classified by all $\\mathbf { k }$ -NN probes are determined to be (effectively) predicted in layer 0 (the input) 4. ",
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+    {
+        "type": "text",
+        "text": "It is worth noting that the prediction depth can be calculated for all data points: both in the training and validation splits. This leads to two notions of computational difficulty: ",
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+        "type": "text",
+        "text": "• The difficulty of predicting the (given) class for an input (in the training split) • The difficulty of making a prediction for an input, unseen in advance (from the validation split) ",
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+        "type": "text",
+        "text": "We examine both notions of computational difficulty in this paper and use the distinction between them to describe different forms of example difficulty in Section 4. ",
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+        "type": "text",
+        "text": "2.2 Prediction depth is a meaningful and robust notion of example difficulty ",
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+        "type": "text",
+        "text": "In this section we show that prediction depth agrees with intuitive notions of example difficulty and that it is consistent between different training runs and similar architectures. ",
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+        "type": "text",
+        "text": "Prediction depth is higher for examples and datasets that seem more difficult If prediction depth is a sensible measure of example difficulty then we would expect the following sanity checks to be observed: ",
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+    {
+        "type": "text",
+        "text": "1. Individual data points that are visually confusing or mislabeled should have larger prediction depths as compared to images that are clear examples of their class.   \n2. Data points from tasks that are intuitively simpler should have lower prediction depths on average. ",
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+    {
+        "type": "text",
+        "text": "Figure 1 shows that the prediction depth passes both of these sanity checks. Appendix C.1 presents additional images, providing further evidence for this claim. ",
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+        "text": "Prediction depth is consistent across random seeds and similar architectures Figure 2 shows that the prediction depth is highly consistent between different architectures and random seeds for all datasets. Perfect agreement is not expected as different deep learning algorithms have different inductive biases which affects the perceived difficulty of examples. We observe stronger correlation between prediction depth for ResNet18 and VGG16, than between VGG16 and MLP. This may be explained by the fact that ResNet18 and VGG16 are both convolutional networks and we expect their inductive biases to be more similar to one another than to MLP. ",
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+        "img_path": "images/41ae6d0999f3d52ac3d9fed1621b96ae037b526605cd4d18c4e702c118a942c4.jpg",
+        "image_caption": [
+            "Figure 1: Deep models use fewer layers to (effectively) determine the prediction for easy examples and more layers for hard examples. Left: A cartoon illustrating the definition of prediction depth (given in Section 2.1). Also shown are training examples from CIFAR100 (“Clock”) and SVHN (“Digit 8”). The examples shown are predicted at the input (first layer) or softmax (last layer) of ResNet18. The examples predicted in the input are visually typical (“easy”), while those predicted in the softmax are mislabeled and/or visually confusing (“hard” examples). To find the prediction depth, we build $\\mathbf { k }$ -NN classifiers from the embeddings of the training set in different layers of the model. The prediction depth corresponds to the earliest layer at which the predictions of all subsequent k-NN classifiers converge to a fixed label. Right: Probability of prediction depth in ResNet18 models for four datasets (training split). We see that the four distributions have different characteristic prediction depths. Ranking the mean prediction depths of these datasets in ascending order, we observe: Fashion MNIST (smallest), SVHN (second), CIFAR10 (third), and CIFAR100 (largest). This order aligns with how one might intuitively rank the difficulties of these classification tasks. "
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+        "image_caption": [
+            "Figure 2: Consistency of prediction depth between architectures and random seeds. Left: The panel shows the correlation coefficient between prediction depths in different architectures, for both train and validation splits in four datasets. Diagonal comparisons between an architecture and itself show the correlation for the same architecture trained with different random seeds. Right: Histograms comparing the mean value of prediction depth obtained for each data point in the training set of CIFAR10 from an ensemble of 250 trained models. In this plot, for visual simplicity, we rescale prediction depth to the interval $[ 0 , 1 ]$ for each network. Similar results for all other datasets are presented in Appendix C.2. "
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+    {
+        "type": "text",
+        "text": "3 Deep Learning Phenomena Through the Lens of Prediction Depth ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we explore how the prediction depth can be used to better understand three important aspects of Deep Learning: accuracy and consistency of a prediction; the order in which data is learned and the simplicity of the learned function (as measured by the margin) in the vicinity of a data point. ",
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+    {
+        "type": "text",
+        "text": "3.1 Depth of a prediction gives a linear lower bound on its consistency ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Adopting a statistical view of example difficulty, Jiang et al. (2021) identified example difficulty with the expected accuracy of the learning algorithm for a given input, averaged over models trained on different random subsets of the training set with different random seeds. In this section, we clarify the relationship between the prediction depth and the expected accuracy by disentangling the accuracy from the sensitivity of predictions to the particular training split and random seed. Following Jiang et al. (2021), we measure the expected accuracy using the consistency score. ",
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+    {
+        "type": "text",
+        "text": "Consistency score $\\hat { C }$ : The frequency of classifying an example correctly when it is omitted from the training set. An empirical estimator of the consistency score for a validation point $( x , y )$ ",
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+        "image_caption": [
+            "Figure 3: Consistency score vs. prediction depth in the validation split (left) can be understood as the superposition of two simple functions (middle and right). We trained 250 ResNet18 models on CIFAR10, with $9 0 { : } 1 0 \\%$ random train:validation splits as described in Appendix A. These histograms compare the frequency of correct predictions to the average prediction depth for a data point when it occurs in the validation split. The density of data points is indicated by the color bar, which follows a log scale. The average prediction depth forms two, surprisingly simple, linear bounds on the consistency score (see Section 3.1 for a full description.) This Figure is reproduced for all datasets and architectures in Appendix C.3, illustrating the consistency of this result. "
+        ],
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+    {
+        "type": "text",
+        "text": "is given by (Jiang et al., 2021): ",
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+    {
+        "type": "equation",
+        "img_path": "images/5730aeecf83fec515bfe03f509fd7fa6e15a2f6c15a6a194a6df8b4a4d27036c.jpg",
+        "text": "$$\n\\hat { C } _ { A , S } ( x , y ) = \\hat { \\mathbb { E } } _ { \\tilde { S } \\sim { \\cal S } \\setminus \\{ ( x , y ) \\} } ^ { r } \\left[ \\delta _ { y _ { A } , y } \\right]\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $A$ is a deep learning algorithm (architecture, loss and optimizer), $y$ is the ground truth class for $x$ , $\\tilde { \\cal S }$ is a random subset of $n$ points sampled from a training dataset $s$ excluding $( x , y )$ , $y _ { A }$ is the predicted class of $x$ for $A$ trained with data $\\tilde { \\cal S }$ , $\\delta$ is the Kronecker delta and $\\hat { \\mathbb { E } } ^ { r }$ denotes empirical averaging with $r$ i.i.d. samples of such subsets $\\tilde { \\cal S }$ . ",
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+    {
+        "type": "text",
+        "text": "Figure 3 (left panel) shows the relationship between consistency score and prediction depth. This plot indicates a surprising piecewise linear boundary which is symmetric around consistency score $\\frac { 1 } { 2 }$ This suggests the existence of a missing concept that could simplify the picture. We next show that the missing concept is the notion of a consensus class which is defined below. ",
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+        "type": "text",
+        "text": "Consensus class ${ \\hat { y } } _ { A }$ : The consensus class of $x$ is defined as the predicted class for input $x$ by a majority voting ensemble of $r$ models each of which is trained on a randomly chosen subset ${ \\tilde { \\cal S } } \\stackrel { n } { \\sim } { \\cal S } \\backslash \\{ ( x , y ) \\} \\stackrel { 5 } { \\sim }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 3 (middle and right) shows how conditioning on whether consensus class matches the ground truth can change the relationship between consistency score and the prediction depth. For points where the consensus class matches the ground truth (middle) we see that the prediction depth forms a, surprisingly simple, linear lower bound on the consistency score. For points where the consensus class differs from the ground truth (right) at low prediction depth the consistency score is bounded from above by a line that reflects the bound from the middle plot in $\\begin{array} { r } { \\hat { C } = \\frac { 1 } { 2 } } \\end{array}$ , suggesting that such points are repeatedly mislabeled with a wrong class label. At high prediction depth, the consistency score is low, which suggests highly inconsistent predictions and low accuracy. This result suggests a simple hypothesis: that predictions with low prediction depth are consistent with the consensus class, whether that matches the ground truth class or not, while predictions made in later layers depend strongly on the specific training split and random seed used for training and initialization. We measure consistency with the consensus class using the consensus-consistency score. ",
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+    {
+        "type": "text",
+        "text": "Consensus-consistency score $C ^ { * }$ : The fraction of models in an ensemble that predict the ensemble’s consensus class ${ \\hat { y } } _ { A } \\left( x \\right)$ for an unseen input $x$ . ",
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+        "type": "equation",
+        "img_path": "images/6a1a098c8a6a2978c52b97c9e07e0fa9551c7045cde12caea458017c72e5794f.jpg",
+        "text": "$$\nC _ { A , S } ^ { * } ( x ) = \\hat { \\mathbb { E } } _ { \\tilde { S } \\sim \\tilde { S } \\backslash \\{ ( x , y ) \\} } ^ { r } \\left[ \\delta _ { y _ { A } , \\hat { y } _ { A } ( x ) } \\right]\n$$",
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+    {
+        "type": "text",
+        "text": "where the notation is the same as in (1) 6. ",
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+    {
+        "type": "text",
+        "text": "Figure 4 (left) establishes that our simple hypothesis is indeed correct: the prediction depth forms a linear lower bound on the consensus-consistency score for all data points, irrespective of whether the consensus class matches or differs from the ground truth. Interestingly, Figure 4 (middle and right) shows how the prediction depth in a single model, can be used to estimate both of these quantities. That is, predictions of data points with lower prediction depth are both more likely to be consistent and more likely to be correct. ",
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+        "image_caption": [
+            "Figure 4: Left: Prediction depth provides us with a linear lower bound on consensus-consistency. Results for CIFAR100 with ResNet18. We train 250 models $( 9 0 { : } 1 0 \\%$ random train:validation splits) and compare the average prediction depth when a point occurs in the validation set, to the consensus-consistency of the corresponding predictions. Predictions made for points with low mean prediction depths are highly consistent. Conversely, predictions for points with high mean prediction depths are typically more sensitive to the particular training split and random seed used during training. This left plot shows the result for CIFAR100 with ResNet18. The density of data points is indicated by the color bar, which follows a log scale. Middle: Prediction depth in one model predicts the consensus-consistency of an ensemble that does not include that model. For each dataset we train 25 ResNet18 models with the full training set (see Appendix A). The consensus-consistency of each test point is obtained from 24 of the models, while the prediction depth is obtained from the remaining 1 model. We see that prediction depth in one model predicts the consensus-consistency of a separate ensemble: a measure of the uncertainty of the prediction. The size of each marker in the middle and right plots shows the fraction of the dataset with each prediction depth. Reaffirming the second sanity check in Section 2.2, and in agreement with Figure 1 (right), intuitively simpler datasets (Fashion MNIST and SVHN) have low average prediction depths, while CIFAR100 (intuitively the hardest dataset) has the largest average prediction depth. Right: Prediction depth predicts accuracy. For each dataset we train 250 ResNet18 models $9 0 { : } 1 0 \\%$ random train:validation splits). Each time a point appears in the validation split we record the prediction depth and whether the prediction was correct. Predictions made in earlier layers are more likely to be correct. Consistency of these plots is demonstrated for all datasets and architectures in Appendix C.3 where we also describe the relationship between the prediction depth and the entropy of the predictions for an ensemble. "
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+    {
+        "type": "text",
+        "text": "3.2 The prediction depth of an input is correlated with its learning difficulty ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In Section 3.1, we describe the relationship between the prediction depth, which represents a computational view of example difficulty and the consistency and consensus-consistency scores, which represent a statistical view. In this section we compare prediction depth to a learning view of example difficulty. We measure the difficulty of learning an example by the speed at which the model’s prediction converges for that input during training. The following definition is adapted from Toneva et al. (2019): ",
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+        "type": "text",
+        "text": "Iteration learned A data point is said to be learned by a classifier at training iteration $t = \\tau$ if the predicted class at iteration $t = \\tau - 1$ is different from the final prediction of the converged network and the predictions at all iterations $t \\geq \\tau$ are equal to the final prediction of the converged network. Data points consistently classified after all training steps and at the moment of initialization, are said to be learned in step $t = 0$ 7 . ",
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+        "type": "text",
+        "text": "Figure 5 (left plot) shows the positive correlation between the prediction depth and the iteration learned, for all four datasets in VGG16. Consistent results are presented for all architectures and datasets, in both the validation and training splits in Appendix C.4. As a result of the reported correlation, we anticipate that many of the data points correctly classified by the k-NN probe in a particular layer should also be correctly classified by the network at a corresponding interval of training steps. If this is correct then we would expect there to be a visual correspondence between the training learning curve (which shows how the accuracy of the network changes during training) and the accuracy of the $\\mathbf { k }$ -NN probes as data passes from input, through the network, towards the output layer. We call the series of $\\mathbf { k }$ -NN probe accuracies the inference learning curve. ",
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+            "Figure 5: Left: Data points with small prediction depths are on average learned before data points with higher prediction depths. We train 250 VGG16 models for each dataset, using a $9 0 { : } 1 0 \\%$ random train:validation split as described in Appendix A. Each time an input appears in the validation split we record the prediction depth and the iteration learned in that model. This plot shows the average iteration learned for data points at each prediction depth. Marker size shows the fraction of the dataset with each prediction depth. The Pearson correlation coefficients for the four data sets are as follows. CIFAR100: 0.83. CIFAR10: 0.7. Fashion MNIST: 0.79. SVHN: 0.77. Middle and right: The training learning curve (middle) shares several important features with the inference learning curve (right). Blue, yellow and green curves represent different components of the CIFAR10 training split, in which we have randomized (and fixed) $40 \\%$ of the labels, and red curves show the test split. The middle and right plots show results from 5 random seeds. The inference learning curve (right) is the sequence of k-NN probe accuracy values for each split. All three plots show results for VGG16. The hyperparameters used are given in Appendix A. "
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+            "Figure 6: Left and Middle: Test examples with smaller prediction depths, on average, have larger output and input margins. We train 25 VGG16 models with different random seeds on CIFAR10 (see Appendix A for details) and compare the mean prediction depth of each test point in these 25 runs to its mean output and input margins (log scales). Correlation coefficients are $- 0 . 7 0$ (output margin) and $- 0 . 6 9$ (input margin). The density of data points is indicated by the color bar, which follows a log scale. Although the prediction depth could be at most 14, no data point has an average prediction depth greater than 12. Right: An intervention that does not encourage large output margin ( $^ { * } O$ -Hinge”) results, as predicted, in models where the predictions are effectively determined in higher layers in the network compared to the standard training $( \\ ^ { \\ast } C E ^ { \\prime \\prime } )$ . "
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+        "text": "To test this hypothesis we train a model on a training split where a subset of labels are corrupted and compare the training and inference learning curves on four splits of the data: unchanged training data; mislabeled training data; the original labels of the mislabeled training data and the test split. In Figure 5 (middle and right plots) we see that many of the important features of the training learning curve are indeed present in the inference learning curve. During training (middle), mislabeled data are initially processed as though they are a member of their original class (before they were mislabeled) (Liu et al., 2020a). After an initial period of learning, the network begins to learn the new (random) labels that have been assigned to those data points, so the orange curve moves upwards, and the green curve downwards. At this point, a maximum is observed in the training accuracy (Arpit et al., 2017). In the right plot we see that these same phenomena occur in the inference learning curve. ",
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+        "text": "3.3 Deep models exhibit larger margins for inputs with lower prediction depth ",
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+        "text": "It is reported in the literature that deep networks learn functions of increasing complexity during training (Hu et al., 2020; Kalimeris et al., 2019). We frame this observation differently: the learned function is “locally simpler” in the vicinity of data points with smaller prediction depths, and these points are typically learned earlier in training (Section 3.2). ",
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+        "text": "Two known measures of the simplicity of a learned function are the output margin (the difference between the largest and second-largest logits) and the adversarial input margin (the smallest norm required for an adversarial perturbation in the input to change the model’s class prediction). We estimate the adversarial input margin, $\\gamma$ , with a linear approximation (Jiang et al., 2018): for an input x with predicted class i, γ ' minj6=i |zi−zj ||∇x(zi−zj )| where $z _ { j }$ is the logit returned by the network for class $j$ . Figure 6 (left and middle plots) show that data points with smaller prediction depths have both larger input and output margins on average and that variances of the input and output margins decrease as the prediction depth increases. ",
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+            "Figure 7: The prediction depth can be the same, or very different for the same input when it occurs in the train and validation splits. Corners of this plot correspond to different forms of example difficulty. (See Section 4 for discussion.) We train 250 ResNet18 models on CIFAR10 with random $9 0 { : } 1 0 \\%$ train:validation splits as described in Appendix A. These histograms compare average prediction depth for each data point when it occurs in the validation split vs the training split. This behavior is consistently reproduced for all datasets and architectures in Appendix C.6. Below we show extreme (not hand-chosen) images of “Birds” that appear closest to the corners of this plot. The consensus class is given above each image (tiebreaks favor the class “Bird”.) "
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+        "text": "To illustrate the strength of the relationship between the prediction depth and output margin, we demonstrate that reducing the output margin of the learned function results in a model that clusters the data only in the latest layers: such a solution has a very high average prediction depth. We do not minimize the output margin directly but rather use a loss and an optimizer that do not encourage high output margin. Naturally there are many unknowns that may contribute to this effect. We simply report the intervention and the outcome. ",
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+        "text": "The intervention is performed as follows: we construct a loss function that does not promote confidence: a zero-margin hinge loss ( $^ { 6 6 } 0$ -Hinge”), and optimize the network using full-batch gradient descent with momentum and very small learning rate. For an input $x$ with label $i$ the 0-Hinge loss is given by $\\begin{array} { r } { l ( x ) = \\sum _ { j \\neq i } \\operatorname* { m a x } ( \\dot { 0 } , z _ { i } - z _ { j } ) } \\end{array}$ where $z _ { j }$ represents the logit for class $j$ . The form of this intervention is justified in Appendix A.7. As a control, we additionally train a model in the standard fashion using the cross-entropy loss and SGD with momentum and large initial learning rate. Since full-batch gradients are computationally expensive, we train on a subset of CIFAR10 (see Appendix A.7, where we also give the hyperparameters and learning curves.). The output margin obtained with the intervention is 5 orders of magnitude smaller than in the control experiment: $2 . 0 \\times 1 0 ^ { - 4 } \\pm 2 . 0 \\times 1 0 ^ { - 4 }$ for the 0-Hinge loss and $1 . { \\overline { { 6 } } } \\times 1 0 ^ { 1 } \\pm 0 . 5 0 \\times 1 0 ^ { 1 }$ for cross-entropy loss. Figure 6 (right) compares the accuracies of the $\\mathbf { k }$ -NN probes resulting from these training approaches. The 0-Hinge loss training achieves only a marginal improvement in accuracy (red) over an untrained network (purple), and the training split is accurately clustered only in the latest layers. This confirms the predicted behavior: the intervention leads to a model that exhibits both very small average output margins and very late clustering of the data. Very late clustering of the data implies high prediction depths since the $\\mathbf { k }$ -NN probe classifications change in the latest layers for many data points. ",
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+        "text": "4 Beyond a One-Dimensional Picture of Example Difficulty ",
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+        "type": "text",
+        "text": "In this section we transcend the one-dimensional picture of example difficulty by identifying different underlying reasons behind the difficulty of an example, in a way that is general to different architectures and datasets. ",
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+        "type": "text",
+        "text": "Figure 7 shows that the prediction depth can be different when an input occurs in the training split vs. the validation split. Thus, there are two axes of example difficulty: ",
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+        "text": "1. Difficulty of making a prediction when an input is in the validation set 2. Difficulty of finding commonalities during training with other examples of the same ground truth class ",
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+        "text": "Both axes have a range from “clear” to “ambiguous”. In Section 3.1 we show that predictions made for validation points with later prediction depths are often inconsistent, with low consensusconsistency. Conversely, a low prediction depth typically indicates an input with high consensusconsistency. For Axis 1 we will identify validation points with low prediction depths as “clear” and those with high prediction depths as “ambiguous”. We will additionally identify a low or high prediction depth in the training split with examples that are respectively “clear” and “ambiguous” on Axis 2. By making combinations of low/high values of $( \\mathrm { P D } _ { \\mathrm { V a l . } }$ , $\\mathrm { P D } _ { \\mathrm { T r a i n } _ { . } }$ ) we obtain four extremes of example difficulty: ",
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+            "Figure 8: Average k-NN probe confidence (solid lines) and accuracy (dotted lines) for the ground truth class (left) and consensus class (right), in the validation split for examples exhibiting extreme forms of difficulty. Mean values for 100 examples with each form of difficulty, identified as the 100 examples closest to the corners in Figure 7 (left). This result is for CIFAR10 with ResNet18: similar plots for all datasets and architectures are shown in Appendix C.7. See Section 4 for the discussion of the result and how it can be used to improve prediction accuracy. "
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+        "text": "Easy examples: (Low $\\mathrm { P D } _ { \\mathrm { V a l . } }$ , Low $\\mathrm { P D } _ { \\mathrm { T r a i n } }$ ). Such examples are often visually typical members of their class and the predicted label nearly always matches the ground truth.   \nLooks like a different class: (Low $\\mathrm { P D } _ { \\mathrm { V a l . } }$ , High $\\mathrm { P D } _ { \\mathrm { T r a i n } }$ ). In the validation set, there is a clear (and nearly always incorrect) classification for such an input, but it is difficult to connect such inputs to other examples of their ground truth class during training. Mislabeled examples are of this kind, as are visually confusing images which at first appear to show something else.   \nAmbiguous unless the label is given: (High $\\mathrm { P D } _ { \\mathrm { V a l . } }$ , Low $\\mathrm { P D } _ { \\mathrm { T r a i n } }$ ). These examples are difficult to connect to their predicted class in the validation split but easy to connect to their ground truth class during training. These points may, for example, visually resemble both their own class and another class. They are likely to be misclassified.   \nAmbiguous: (High $\\mathrm { P D } _ { \\mathrm { V a l . } }$ , High $\\mathrm { P D } _ { \\mathrm { T r a i n } }$ ). These examples may be corrupted or show an example of a rare sub-class. Predictions for these inputs can depend strongly on the random seed used for training and initialization. ",
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+        "type": "text",
+        "text": "In Figure 7 we visualize CIFAR10 “Bird” images with the extreme forms of example difficulty for ResNet18, as identified using the prediction depth in the training and validation splits. In the full dataset (left panel) we see that the prediction depth can be very different in the training and validation splits: the two prediction depths are typically similar for points where the consensus class is equal to the ground truth (right panel), but can be very different when the consensus class is different from the ground truth (middle panel). This behavior is consistently reproduced for all datasets and architectures in Appendix C.6. ",
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+        "type": "text",
+        "text": "Looking at these examples of the class “Bird” with different difficulty types, we observe that ResNet18 finds small garden birds easiest, while birds in flight against a blue background “look like airplanes”, ostriches are “ambiguous without their label” and the “ambiguous” examples are either unclear photographs or examples of rare sub-groups that don’t appear frequently in the data. We found the consensus-consistency of inputs that are “Ambiguous” or “Ambiguous without its label” to be significantly lower than those of examples that are “Easy” or “Look like a different class”. ",
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+        "type": "text",
+        "text": "In order to better understand how networks process examples with different, extreme forms of example difficulty, Fig. 8 examines how the k-NN confidence (fraction of votes) and accuracy of the ground truth class and of the consensus class progress, as validation points pass through the network. “Easy” examples are classified as their consensus class (which is equal to their ground truth class) in all k-NN probes and the confidence in the consensus class steadily increases as data points proceed through the hidden layers. Examples that “look like a different class” are also processed as members of their consensus class, similarly to “easy” examples. However, unlike “easy” examples, their consensus classes do not match their ground truth classes. Examples that are “ambiguous without their labels” are initially processed as members of their ground truth classes with intermediate confidence, but in later layers become mistaken for their consensus class. “Ambiguous” examples are processed with low confidence and accuracy in the early layers, for both ground truth and consensus classes. In later layers “ambiguous” examples are recognized, with intermediate confidence and accuracy, as members of the consensus class, which matches the ground truth class for a sizeable fraction of “ambiguous” examples. ",
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+        "text": "Improving the prediction accuracy Can the prediction accuracy be improved using our understanding of how each class of difficult examples are processed by deep models? Figure 8 suggest that $\\mathbf { k }$ -NN probes in intermediate layers may be more accurate than the full deep model for examples that are “ambiguous without their label” (data points closest to the lower right corner of Figure 7). In order to test this hypothesis, we compare the accuracy of the $\\mathbf { k }$ -NN probe in layer 4 to the full model’s prediction for the 100 examples closest to the lower right corner of Figure 8. We obtain a striking improvement in accuracy from $2 5 \\%$ to $98 \\%$ for these examples. This showcases how insights from this study can be directly used to improve prediction accuracy. ",
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+    {
+        "type": "text",
+        "text": "5 Discussion ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Summary We have introduced a notion of example difficulty called the prediction depth, which uses the processing of data inside the network to score the difficulty of an example. We have shown how the prediction depth is related to the accuracy and uncertainty of a prediction, the adversarial input margin and the output margin of the learned solution, and that data points that are easier according to the prediction depth are also typically learned earlier in training. We have also shown that the difficulty of an example can be both similar, or very different depending on whether an input appears in the validation split or the training split, and described four extremes of example difficulty. For data points that are “ambiguous without their label”, we have demonstrated how returning the $\\mathbf { k }$ -NN prediction in a middle layer can lead to impressive increases in model accuracy: for CIFAR10 in ResNet18 we obtained an increase in accuracy from $2 5 \\%$ to $98 \\%$ for the inputs that are most “ambiguous without their label”. ",
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+    {
+        "type": "text",
+        "text": "Connecting known phenomena In the literature, the following phenomena are separately reported from different experimental paradigms: ",
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+        "type": "text",
+        "text": "1. Early layers generalize while later layers memorize (Stephenson et al., 2021).   \n2. Model layers converge from input layer towards output layer (Raghu et al., 2017; Morcos et al., 2018).   \n3. Deep models learn easy data (Jiang et al., 2021; Toneva et al., 2019) and simple functions first (Hu et al., 2020; Kalimeris et al., 2019). ",
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+    {
+        "type": "text",
+        "text": "Following this paper, a coherent and closely related picture emerges: ",
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+    {
+        "type": "text",
+        "text": "1. Predictions made in early layers are more likely to be consistent than those made in later layers. Consistent predictions are likely to be correct and the expected accuracy of inconsistent predictions is naturally low (Section 3.1).   \n2. Data points learned early in training typically have smaller prediction depths than those learned later during training (Section 3.2).   \n3. On average, deep neural networks exhibit wider input and output margins (common measures of “local simplicity”) in the vicinity of data with smaller prediction depths (Section 3.3). ",
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+    {
+        "type": "text",
+        "text": "Pertinence of example difficulty to topics in machine learning Curriculum Learning attempts to treat hard examples differently from easy examples during training. Robustness to distribution shifts that change the relative frequencies of common and rare subgroups in the test set (which we have shown can have different forms of example difficulty) is important for ML Fairness. Methods developed to address heteroscedastic uncertainty typically address example difficulty as a onedimensional quantity. We expand upon the relevance of our work to these three topics in Appendix D. ",
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+    {
+        "type": "text",
+        "text": "Limitations We believe that the results we report stem from a deep model’s representation, which is hierarchical by construction. We expect that the same results will therefore apply in larger models, larger datasets, and tasks other than image classification, but testing this remains as further work. Although we demonstrate that returning the results of a hidden k-NN can yield dramatic increases in accuracy for examples that are “ambiguous without their label”, we otherwise do not explore ways to practically apply the insights we present. In particular, we expressly do not claim that all that is required for good accuracy is to reduce the prediction depth: freezing later layers of the network would not be expected to result in good generalization. ",
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+    {
+        "type": "text",
+        "text": "Funding Transparency Statement ",
+        "text_level": 1,
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+        "page_idx": 10
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+    {
+        "type": "text",
+        "text": "This research was funded by, and undertaken at, Google. All calculations were performed using Google’s computer infrastructure. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgment ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Hanie Sedghi, Ilya Tolstikhin, Ibrahim Alabdulmohsin, Daniel Keysers and Julian Eisenschlos for valuable discussions on the topic and Arthur Baldock for proofreading the manuscript. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            237,
+            266,
+            253
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
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parse/train/xWq1MVj7YrE/xWq1MVj7YrE.md

@@ -0,0 +1,257 @@
+# Novel Visual Category Discovery with Dual Ranking Statistics and Mutual Knowledge Distillation
+
+Bingchen Zhao1 Kai Han2,3,4∗
+
+1Tongji University 2The University of Hong Kong 3Google Research 4University of Bristol zhaobc.gm@gmail.com kaihanx@hku.hk
+
+# Abstract
+
+In this paper, we tackle the problem of novel visual category discovery, i.e., grouping unlabelled images from new classes into different semantic partitions by leveraging a labelled dataset that contains images from other different but relevant categories. This is a more realistic and challenging setting than conventional semi-supervised learning. We propose a two-branch learning framework for this problem, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. To transfer knowledge from labelled data to unlabelled data, we propose using dual ranking statistics on both branches to generate pseudo labels for training on the unlabelled data. We further introduce a mutual knowledge distillation method to allow information exchange and encourage agreement between the two branches for discovering new categories, allowing our model to enjoy the benefits of global and local features. We comprehensively evaluate our method on public benchmarks for generic object classification, as well as the more challenging benchmarks for fine-grained visual recognition, achieving state-of-the-art performance.
+
+# 1 Introduction
+
+Superior performance on many problems has been achieved by recent machine learning models, especially the ones based on deep learning. While the success comes at the cost of large-scale human annotation, which is prohibitively expensive in practice. For example, modern convolutional neural networks (CNNs) can surpass human-level recognition performance on ImageNet after training with over one million labelled images [22]. On the one hand, it is not possible to annotate all possible classes in the real world, as there are way more classes than the 1, 000 classes in ImageNet and new classes keep growing over time. On the other hand, annotating specific data, such as the medical data, may require specific expertise, which renders the large-scale annotation extremely difficult, if not impossible. Therefore, it is desired to enable the machine learning systems to deal with unlabelled data automatically.
+
+Recently, the problem of novel category discovery was formalized in [20, 18], which aims at discovering new visual categories on unlabelled data by transferring knowledge from labelled data. The labelled data is assumed to contain similar but different categories to those in the unlabelled data. This problem is similar to semi-supervised learning in the sense that both labelled and unlabelled data are used to learn the model. While novel category discovery is much harder because semi-supervised learning assumes that every class contains labelled instances, while for novel category discovery there are no labels available for the new classes in the unlabelled data. This setting is also relevant to unsupervised clustering. But differently, novel category discovery makes use of the labelled data to extract a specific class prior (i.e., the properties that delineate a class) for partitioning the unlabelled data, while the unsupervised clustering may produce multiple different but equally valid clustering results by adopting different properties (e.g., color, shape, pose, lighting, etc). In this paper, we introduce a simple and effective two-branch framework for novel category discovery, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. Our contributions are as follows.
+
+First, we propose to apply dual ranking statistics for transferring knowledge from the known classes in the labelled data to the unlabelled data, resulting in more robust pseudo label generation for learning on the unlabelled data. We maintain a dynamic object part dictionary and apply part-level ranking statistics on the similarity distribution of each instance over the dictionary to obtain pseudo labels, which are complementary to the pseudo labels obtained by simply examining the ranking statistics of global descriptors.
+
+Second, we introduce a mutual knowledge distillation method to allow information exchange and encourage agreement between the local and global branches. The dual ranking statistics provide global and part-level information for learning in two branches separately. The mutual knowledge distillation further allows information exchange between the two branches and makes them benefit from each other. Unlike conventional methods that distill between teacher and student models with known labels, our method distills between two branches of the same model without any manual annotations.
+
+Third, we comprehensively evaluate our method on public benchmarks for generic object classification, including CIFAR10, CIFAR100, and ImageNet, obtaining state-of-the-art results. Furthermore, we also validate our approach on the more challenging fine-grained datasets CUB-200, Stanford-Cars, and FGVC-Aircraft, in which the local details are more important to distinguish different classes. Our method outperforms existing methods by a substantial margin, thanks to the ability of our model to subtly exploit both local and global information. Our code can be found at https://github.com/DTennant/dual-rank-ncd.
+
+# 2 Related work
+
+Our work is relevant to novel category discovery, knowledge distillation, and part-level feature learning. We briefly review the most relevant work below.
+
+Novel category discovery is a relatively new problem setting recently formalized by [20, 18] with the task being automatically discovering new object categories in the unlabelled data by making use of a labeled dataset containing different but relevant object classes. The purpose of using the extra labelled data is to learn a category prior to reduce the ambiguity of class definition. This task is closely related to unsupervised clustering and semi-supervised learning, but also significantly different from them. Unsupervised clustering has been studied for decades with many classical approaches [35, 3, 9] and deep learning based solutions [50, 16, 40] being proposed. Due to the lack of a proper class prior, multiple equally valid clustering results can be achieved by different criteria. Therefore, it can not be directly applied to discovery new classes as we expect the model to follow a unique class definition. In semi-supervised learning [43, 39, 6, 38, 46], unlabelled data are used together with labelled data to train a more robust model, with the assumption that all classes in the unlabelled data have labelled instances. However, this is unlikely to be true for real applications where unlabelled data may come from new classes. Thus, novel category discovery is a more realistic setting. The DTC method introduced in [20] approaches this problem in two steps. The model is firstly trained with supervised learning on the labelled data to capture high-level semantic class information and then trained on the unlabelled data with a clustering loss to discover new categories. In [18, 19], Han et al. proposed to use self-supervision to bootstrap feature learning and introduced ranking statistics on the feature embedding to provide pseudo labels for training on unlabelled data. The KCL [25] and MCL [26] methods were designed for general transfer learning across domains and tasks, which can also be applied for novel category discovery. These two methods maintain two models for training and testing, a pretrained binary classifier for pseudo label generation and a clustering model. The binary classifier pretrained on the labelled data is used to provide pseudo labels to train the clustering model on unlabelled data. Concurrent to our work, several methods [28, 58, 57, 14] are proposed to improve the performance of novel category discovery from different perspectives, showing promising results.
+
+The existing methods only consider the global feature descriptors while ignoring the local object parts which are essential to distinguish classes that look similar. In our approach, we jointly consider both and allow information exchange between them for more reliable new category discovery.
+
+Knowledge distillation is often employed to learn a compact student model using the knowledge distilled from a larger teacher model by enforcing the agreement of outputs or representations between the two models (e.g., [24, 41, 54, 52, 27, 29, 1, 48]). Apart from distilling a larger teacher model to a smaller student model, self-distillation methods show that distilling between two identical models can also improve the performance [53, 15, 4]. Mutual learning [56] is a similar technique that trains two models of the same architecture simultaneously but with different initialization and encourages them to learn collaboratively from each other. It has been shown that different initialization leads the model to focus on different regions of the input and thus the trained model can better capture the holistic structure of the data, resulting in better performance. Though effective, the above methods require the labels for training. Thus they can not be applied for novel category discovery. Recently, [13] introduced a self-supervised distillation method called SEED to improve the representation learning on a small model (student) by distilling from a pretrained large model (teacher). The student model is trained to predict the same similarity score distribution inferred by the frozen teacher model over a queue of instances. We draw inspiration from [13] to design the mutual knowledge distillation module in our method for novel category discovery between the local and global branches.
+
+Part-level features have been shown to be effective for tasks involving image verification such as few-shot learning [10, 55, 12] and image retrieval [7, 34, 5, 2, 37, 42, 45]. In [10], the part-level visual concepts are generated by clustering feature vectors from the feature maps obtained using a trained neural network. These visual concepts are used as matching primitives at test time for few-shot learning. Zhang et al. [55] used the Earth-Mover’s Distance (EMD) between local part features to measure the distance between two images for matching. Doersch et al. [12] proposed CrossTransformers to model the cross-attention between each local part of a query image and a set of support images for few-shot learning. Part-level features have been more widely used in the domain of image retrieval with both classical [34, 5] and deep learning based [2, 37, 42, 45, 7] methods. Intuitively, the part-level features provide better precision for the retrieved results because the local matching is more restricted, and global features yield better recall [7]. In our work, we leverage both local and global features to enjoy the benefits of both through the dual ranking statistics and the mutual knowledge distillation, for more robust novel category discovery.
+
+# 3 Method
+
+The goal of novel category discovery is to automatically partition unlabelled instances $x _ { i } ^ { u } \in \mathcal { D } ^ { u }$ into $C ^ { u }$ semantic clusters by transferring the knowledge from the labelled instances $( x _ { i } ^ { l } , y _ { i } ^ { l } ) \in \mathcal { D } ^ { l }$ , where $y _ { i } ^ { l } \in \{ 1 , \ldots , C ^ { l } \}$ . The key assumption is that the classes in $\mathcal { D } ^ { l }$ and $\mathcal { D } ^ { u }$ are relevant though different, so that the properties that constitute a class learned from $\mathcal { D } ^ { l }$ can be transferred to $\mathcal { D } ^ { u }$ . Following [18], we assume $C ^ { u }$ is known a priori. When it is unknown, we can employ off-the-shelf methods such as [20] to get an estimate.
+
+To tackle this challenge, we introduce a framework with mutual knowledge distillation between a global branch and a local branch (see fig. 1). The global branch is designed to capture the overall feature, while the local branch is designed to focus on each individual spatial local part. They have a shared feature extractor $f _ { \theta }$ . Each branch has a feature projection layer and two linear heads. We denote the feature projection layer as $\psi$ and the two linear heads as $\eta ^ { l }$ and $\eta ^ { u }$ respectively. We also denote $\psi$ followed by the average pooling operation as $\bar { \psi }$ . Unless stated otherwise, we use subscripts $g$ and $p$ to differentiate feature projection layers and linear heads of global and local branches respectively in the rest of the paper. The two linear heads are responsible for classifying $C ^ { l }$ labelled categories and clustering $C ^ { u }$ unlabelled categories respectively. To transfer knowledge from the labelled data to the unlabelled data, we adopt global image level and local object part-level ranking statistics on the feature representations. In this way, the model will have reliable pseudo labels for training on the unlabelled data. Moreover, we also incorporate mutual knowledge distillation between the two branches to enforce global and local agreement, leading to more reliable novel category discovery. Next, we will introduce each component of our framework in more detail. In section 3.1, we first introduce the our knowledge transfer method using dual ranking statistics. In section 3.2, we describe our mutual knowledge distillation method for novel category discovery. Lastly, we summarize the overall training loss in section 3.3.
+
+![](images/2dd763a851145b2b50eaa5dc81b0f5491e1b84c655a2ef8f98c275b9f126162c.jpg)  
+Figure 1: Overview of our proposed method. An input image $x _ { i }$ is firstly processed by the feature extractor ranking s $f _ { \theta }$ . The resulting feature is sent to the glistics on the global feature embedding al and local branches. The globato generate pseudo labels to the ch usesloss for $z _ { i }$ $\mathcal { L } _ { \mathrm { B C E } } ^ { g }$ new class discovery, while the local branch uses ranking statistics on the similarity score vector $o _ { i }$ between each of the local parts and a dynamic part dictionary to generate pseudo-labels. The two branches mutually distill knowledge from each other to allow information exchange and encourage agreement through two auxiliary memory banks with $\mathcal { L } _ { \mathrm { s K L D } }$ loss. We omit the supervised linear head, cross-entropy loss $\mathcal { L } _ { \mathrm { C E } }$ and consistency loss $\mathcal { L } _ { \mathrm { M S E } }$ in the plot for the sake of clarity.
+
+# 3.1 Dual ranking statistics for knowledge transfer
+
+It is proven that ranking statistics is robust to noise, especially in high-dimensional space [51]. Han et al. [18] proposed to use ranking statistics for novel category discovery. The idea is to generate pair-wise pseudo labels by comparing the top- $k$ ranks of two feature vectors via examining the feature magnitude. Specifically, the binary pseudo label $s _ { i j }$ is determined by
+
+$$
+s _ { i j } = \mathbb { 1 } \left\{ \mathrm { t o p } _ { k } ( z _ { i } ) = \mathrm { t o p } _ { k } ( z _ { j } ) \right\} ,
+$$
+
+where $z _ { i }$ and $z _ { j }$ are feature vectors of two unlabelled images. With the binary pseudo labels, the model can then be trained using the binary cross-entropy loss on the unlabelled data.
+
+Unlike [18] which only considers global image feature descriptors, we also explore each individual object part for novel category discovery. Verification based on part-level features has been shown to be effective to match two images (e.g. [55, 12]). The pair-wise verification using global features focuses on the holistic structure of the object and thus may introduce more false positives with high recall (but low precision). While pair-wise verification using local part features focuses on local details, which is more strict, and thus may introduce more false negatives with high precision (but low recall) [7]. Hence, local part features and global features are complementary to each other for verification and should be considered jointly for more robust category discovery, as ideally we expect to have both high precision and recall. Therefore, to achieve this goal, we propose to have one branch using global features and another branch using part-level features. Ranking statistics is applied on each branch to generate pseudo labels. For the global one, we simply apply a soft extension of the hard ranking statistics [18]. In particular, instead of forcing $s _ { i j }$ in eq. (1) to be either 0 or 1, it can be replaced by a continuous value $\begin{array} { r } { s _ { i j } = \frac { c } { k } \in [ 0 , 1 ] } \end{array}$ where $c$ is the number of shared elements in $\mathrm { t o p } _ { k } ( z _ { i } )$ and $\mathrm { t o p } _ { k } ( z _ { j } )$ . Hence, the BCE loss for the global branch can be written as
+
+$$
+\mathcal { L } _ { \mathrm { B C E } } ^ { g } = - \frac { 1 } { M ^ { 2 } } \sum _ { i = 1 } ^ { M } \sum _ { j = 1 } ^ { M } [ s _ { i j } ^ { g } \log \eta _ { g } ^ { u } ( z _ { i } ^ { u } ) ^ { \top } \eta _ { g } ^ { u } ( z _ { j } ^ { u } ) + ( 1 - s _ { i j } ^ { g } ) \log ( 1 - \eta _ { g } ^ { u } ( z _ { i } ^ { u } ) ^ { \top } \eta _ { g } ^ { u } ( z _ { j } ^ { u } ) ) ] ,
+$$
+
+where $M$ is the number of unlabelled images, $z _ { i } ^ { u } = \bar { \psi } _ { g } ( f _ { \theta } ( x _ { i } ^ { u } ) ) \in \mathbb { R } ^ { d }$ is a global feature vector of the image $x _ { i } ^ { u }$ , and $s _ { i j } ^ { g }$ is the soft ranking statistics score between $x _ { i } ^ { u }$ and $x _ { j } ^ { u }$ .
+
+For the local one, we propose to maintain a memory bank to act as a dynamic object part dictionary and obtain the ranking statistics by comparing each object part with the collection of part descriptors in the memory bank. Concretely, the memory bank is a First-In-First-Out (FIFO) queue $\mathcal { V } = [ v _ { 1 } , \dotsc , v _ { e } ]$ storing the part-level features, where $e$ is the number of part-level features in the queue. Each part feature in $v$ is the $d$ -dimensional feature vector from a randomly selected spatial location in the feature map $\psi _ { p } ( f _ { \theta } ( x _ { i } ) ) \in \mathbb { R } ^ { d \times h \times w }$ of an randomly sampled image $x _ { i } \in \mathcal { D } ^ { l } \dot { \cup } \mathcal { D } ^ { u }$ . We select one part feature vector from each image in current mini-batch. Other part sampling methods like using all parts or selecting based on activation maps can also be applied (as will be seen in section 4.3), while we found that the simple random sampling is on par with other more complicated methods. Following MoCo [21], when the current mini-batch of part features is enqueued into $\nu$ , the oldest mini-batch in $\nu$ is dequeued. For the feature vector $q _ { j } ^ { u }$ drawn at every spatial location of the feature map $\psi _ { p } ( f _ { \theta } ( x _ { i } ^ { u } ) )$ in current mini-batch, we can then obtain a $e$ -dimensional vector representing the similarity between $q _ { j }$ and all part features in the dictionary $\nu$ . All $q _ { j }$ for $x _ { i } ^ { u }$ across $h \times w$ locations are then fused together by average-pooling. Let us denote by $o _ { i } ^ { u } \in \mathbb { R } ^ { e }$ the fused similarity vector (see fig. 2). For any pair of unlabelled images $x _ { i } ^ { u }$ and $x _ { j } ^ { u }$ in current mini-batch, their soft ranking statistics score $s _ { i j } ^ { p }$ can then be obtained by comparing $o _ { i } ^ { u }$ and $o _ { j } ^ { u }$ as described above for the global feature descriptors. Similar to eq. (2), we can define the BCE loss $\mathcal { L } _ { \mathrm { B C E } } ^ { p }$ to train the local branch. The BCE loss for both branches can then be written as
+
+![](images/cb7a4df580fce62457decb56c6de81a066ec16a461e9267e44526bb300df2b49.jpg)  
+Figure 2: Design of the local comparison process. Each part of an image is compared against all parts in the memory bank $\nu$ , forming one similarity vector for each part. All resulting similarity vectors are then fused to a single vector by average pooling, which is used to generate pair-wise pseudo labels.
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { B C E } } = \mathcal { L } _ { \mathrm { B C E } } ^ { g } + \mathcal { L } _ { \mathrm { B C E } } ^ { p } . } \end{array}
+$$
+
+# 3.2 Mutual knowledge distillation for novel category discovery
+
+So far, our model considers local and global information in two branches independently. To make the two branches directly benefit from each other, we propose a mutual knowledge distillation method for novel category discovery to allow information exchange and encourage agreement between the local and global branches.
+
+Existing mutual knowledge distillation methods are normally designed for two models (i.e., teacher model and student model or two peer models) [24, 56], while we distill between two branches of the same model with each branch having a different focus. More importantly, unlike the conventional mutual learning and knowledge distillation methods that have the same class assignment for the same input due to the availability of labels, in our setting, the cluster assignments of the unlabelled linear heads $\eta _ { g } ^ { u }$ and $\eta _ { p } ^ { u }$ for the same unlabelled data point may be completely different for the two branches. Therefore, these knowledge distillation methods can not be applied for novel category discovery. Recently, [13] introduced the knowledge distillation between the teacher and student models by comparing the similarity score distribution between each instance and a queue of features from the larger teacher model. Inspired by [13], we develop a mutual knowledge distillation method between the local and global branches for novel category discovery without using labels.
+
+Instead of using the softmax output of $\eta _ { g } ^ { u }$ and $\eta _ { p } ^ { u }$ for mutual learning, which is invalid in our case, we mutually distill the two branches via the similarity score distribution over a memory bank per branch. Specifically, we maintain two FIFO feature banks to store the features extracted by $\bar { \psi } _ { p }$ and $\bar { \psi } _ { g }$ , denoted as $B _ { p } = [ b _ { 1 } ^ { p } , \ldots , b _ { T } ^ { p } ]$ and $B _ { g } = [ b _ { 1 } ^ { g } , \dotsc , b _ { T } ^ { g } ]$ . Both $B _ { p }$ and $B _ { g }$ contain features of $x _ { i } \in \mathcal { D } ^ { l } \cup \mathcal { D } ^ { u }$ . Again, similar to MoCo [21], when the current mini-batch is enqueued, the oldest mini-batch is dequeued in both memory banks. For each unlabelled image $x _ { i } ^ { u }$ , we first obtain the feature representations using $z _ { i } ^ { u } = \bar { \psi } _ { g } ( \dot { f } _ { \theta } ( x _ { i } ^ { u } ) )$ and $z _ { i } ^ { \prime u } = \bar { \psi } _ { p } ( f _ { \theta } ( x _ { i } ^ { u } ) )$ . The similarity score distribution $p ^ { g } ( x _ { i } ^ { u } , B _ { g } )$ and $p ^ { p } ( x _ { i } ^ { u } , B _ { p } )$ can be defined as
+
+$$
+p ^ { g } ( x _ { i } ^ { u } , \mathcal { B } _ { g } ) = [ p _ { 1 } ^ { g } , \dotsc , p _ { T } ^ { g } ] , \quad p _ { j } ^ { g } = \frac { e x p ( z _ { i } ^ { u } \cdot b _ { j } ^ { g } / \tau ) } { \sum _ { b _ { k } ^ { g } \sim \mathcal { B } _ { g } } e x p ( z _ { i } ^ { u } \cdot b _ { k } ^ { g } / \tau ) }
+$$
+
+and
+
+$$
+p ^ { p } ( x _ { i } ^ { u } , \mathcal { B } _ { p } ) = [ p _ { 1 } ^ { p } , \ldots , p _ { T } ^ { p } ] , \quad p _ { j } ^ { p } = \frac { e x p ( z _ { i } ^ { \prime u } \cdot b _ { j } ^ { p } / \tau ) } { \sum _ { b _ { k } ^ { p } \sim \mathcal { B } _ { p } } e x p ( z _ { i } ^ { \prime u } \cdot b _ { k } ^ { p } / \tau ) }
+$$
+
+where $\tau$ is a scalar temperature to control the sharpness of the similarity score distribution.
+
+To encourage agreement between the similarity score distributions of an unlabelled image from two branches, we apply mutual learning on the score distribution using the symmetric Kullback-Leibler Divergence (sKLD) loss
+
+$$
+\mathcal { L } _ { \mathrm { s K L D } } = \frac { 1 } { 2 } ( D _ { K L } ( p ^ { p } \| p ^ { g } ) + D _ { K L } ( p ^ { g } \| p ^ { p } ) )
+$$
+
+where $D _ { K L }$ is the Kullback–Leibler (KL) divergence with $\begin{array} { r } { D _ { K L } ( p _ { 1 } \| p _ { 2 } ) = p _ { 1 } \log \frac { p _ { 1 } } { p _ { 2 } } } \end{array}$ . In this way, the global and local branches of the model can learn from each other, while maintaining their own merits. Our mutual knowledge distillation method differs from SEED [13] in several aspects. First, SEED aims at improving high level visual representation, while we aim at enforcing the agreement between local and global features for novel category discovery; second, SEED distills between two different models while we distill between two branches of the same model; third, SEED maintains a queue derived from the global features of the teacher model, while we maintain two queues as dictionaries for global and local features; last, in SEED the larger teacher model is frozen during distillation and the student model is trained with cross-entropy loss, whereas in our method both branches are jointly trained with the sKLD loss.
+
+# 3.3 Overall training loss
+
+Apart from the BCE and sKLD losses introduced above, we also apply the standard cross-entropy loss on both branches, which is written as
+
+$$
+\mathcal { L } _ { \mathrm { C E } } = - \frac { 1 } { N } \sum _ { i = 1 } ^ { N } y _ { i } \log \eta _ { g } ^ { l } ( z _ { i } ^ { l } ) + y _ { i } \log \eta _ { p } ^ { l } ( z _ { i } ^ { \prime l } )
+$$
+
+where $N$ is the number of labeled images, $z _ { i } ^ { l } = \bar { \psi } _ { g } ( f _ { \theta } ( x _ { i } ^ { l } ) )$ , and $z _ { i } ^ { \prime l } = \bar { \psi } _ { p } ( f _ { \theta } ( x _ { i } ^ { l } ) )$ . Similar to [18], the feature extractor $f _ { \theta }$ is pretrained with self-supervised learning and is frozen during the training for novel category discovery.
+
+Following [18, 20], we also include the consistency regularization loss to enforce the predictions of the same data point under different transformations to be the same. Specifically, let ${ \hat { x } } _ { i }$ be a randomly transformed counterpart of the input image $x _ { i }$ . The consistency loss is then defined as
+
+$$
+\begin{array} { r l r } & { } & { \mathcal { L } _ { \mathrm { M S E } } = \displaystyle \frac { 1 } { N } \sum _ { i = 1 } ^ { N } [ ( \eta _ { g } ^ { l } ( z _ { i } ^ { l } ) - \eta _ { g } ^ { l } ( \hat { z } _ { i } ^ { l } ) ) ^ { 2 } + ( \eta _ { p } ^ { l } ( z _ { i } ^ { \prime l } ) - \eta _ { p } ^ { l } ( \hat { z } _ { i } ^ { \prime l } ) ) ^ { 2 } ) ] + } \\ & { } & { \displaystyle \frac { 1 } { M } \sum _ { i = 1 } ^ { M } [ ( \eta _ { g } ^ { u } ( z _ { i } ^ { u } ) - \eta _ { g } ^ { u } ( \hat { z } _ { i } ^ { u } ) ) ^ { 2 } + ( \eta _ { p } ^ { u } ( z _ { i } ^ { \prime u } ) - \eta _ { p } ^ { u } ( \hat { z } _ { i } ^ { \prime u } ) ) ^ { 2 } ] , } \end{array}
+$$
+
+where $\hat { z } _ { i }$ is the feature embedding of the transformed image ${ \hat { x } } _ { i }$ . Without enforcing the consistency, we may have different ranking statistics for $\hat { z } _ { i }$ and $z _ { i }$ , which will lead to diffferent $s _ { i j }$ for the same images under different augmentation, confusing the training.
+
+In summary, the overall loss function used to train our model is
+
+$$
+\begin{array} { r } { \mathcal { L } = \mathcal { L } _ { \mathrm { B C E } } + \mathcal { L } _ { \mathrm { s K L D } } + \mathcal { L } _ { \mathrm { C E } } + \omega ( t ) \mathcal { L } _ { \mathrm { M S E } } , } \end{array}
+$$
+
+where $\omega ( t ) = \lambda e ^ { - 5 ( 1 - \frac { t } { r } ) ^ { 2 } }$ is a ramp-up function as widely used in the literature [46, 33, 18] with $\lambda \in \mathbb { R } _ { + }$ . $t$ and $r$ are the current time step and the ramp-up length respectively.
+
+After training, as the two branches already agree with each other, we simply take the output of the global branch as the final prediction. In particular, for each unlabelled image, we take the index of the max value in the softmax output as its cluster assignment. It is also worth noting that the memory banks and ranking statistics are no longer needed at inference time.
+
+# 4 Experimental results
+
+# 4.1 Experimental setup
+
+Benchmark and evaluation metric. We follow [18] to validate our method on a variety of benchmark datasets for generic image classification including CIFAR-10 [31], CIFAR-100 [31] and ImageNet-1K [11]. For ImageNet-1K, three 30-class unlabelled splits are used in the experiments and the average performance is reported. We further experiment with ImageNet100 [47] which has less number of labelled classes but the same number of unlabelled classes as ImageNet-1K. In addition, we also validate our method on the more challenging fine-grained datasets including CUB-200 [49], Stanford-Cars [30], and FGVC aircraft [36]. One key assumption for novel category discovery is that the labelled classes are relevant to the unlabelled ones.
+
+Table 1: Data splits in the experiments.   
+
+<table><tr><td></td><td>labelled</td><td>unlabelled</td></tr><tr><td>CIFAR-10</td><td>5</td><td>5</td></tr><tr><td>CIFAR-100</td><td>80</td><td>20</td></tr><tr><td>ImageNet-1K</td><td>882</td><td>{30,30,30}</td></tr><tr><td>ImageNet-100</td><td>70</td><td>30</td></tr><tr><td>CUB-200</td><td>160</td><td>40</td></tr><tr><td>Stanford-Cars</td><td>156</td><td>40</td></tr><tr><td>FGVC-aircraft</td><td>81</td><td>21</td></tr></table>
+
+Due to the diversity of classes in generic image recognition datasets, it is not easy to tell the relevance between classes, though it is implicitly contained in the rules used to identify classes during data curation. In contrast, the relevance of the fine-grained datasets is explicitly determined by the fact that all classes in a fine-grained dataset belong to the same entry level class, e.g., birds, cars, and airplanes for the above fine-grained datasets. Besides, the fine-grained datasets pose more challenges for novel category discovery because of the high inter-class similarity. In this case, spatial local details become crucial clues to distinguish them. The labelled and unlabelled splits are summarized in table 1.
+
+We follow the standard practice in the literature to adopt clustering accuracy (ACC) on the unlabelled data as the metric for evaluation. It is defined as 1N PNti=1 $\begin{array} { r } { \frac { 1 } { N _ { t } } \dot { \sum } _ { i = 1 } ^ { N _ { t } } \mathbb { 1 } ( y _ { i } ^ { * } = h ( y _ { i } ) ) } \end{array}$ where $h$ is the optimal permutation obtained by Hungarian algorithm [32] that can match the clustering assignment $y _ { i }$ with the ground-truth label $y _ { i } ^ { * }$ , and $N _ { t }$ is the number of unlabelled images.
+
+Implementation details. We follow [18] to initialize our model with parameters pretrained by self-supervised learning. Our default model is realized based on ResNet50 [23]. Namely, the first three macro blocks of ResNet50 are the feature extractor, $f _ { \theta }$ , which is initialized with MoCov2 [8] pretrained on ImageNet via self-supervision and are frozen during training for novel category discovery. The last macro block is duplicated into two as the projection layers $\psi _ { p }$ and $\psi _ { g }$ , for local and global branches respectively. Each of them is followed by two linear heads, $\eta ^ { l }$ and $\eta ^ { u }$ , for labelled and unlabelled data respectively. For a fair comparison with prior methods, we also experiment using ResNet18 with RotNet [17] initialization. For all our experiments, we use SGD with momentum [44] as the optimizer and use a batch size of 128 for labelled data and 64 for unlabelled data. The temperature parameter $\tau$ is set to 0.07, and the size of the three memory-banks are all set to 2048 for memory efficiency and also considering the relatively limited number of images in the fine-grained datasets. For the dual ranking statistics, we set $k = 5$ for the global branch following [18], and $k = 3 0$ for the local branch to include more local parts into consideration. Our experiments are performed using GTX 1080Ti GPUs.
+
+# 4.2 Comparison to the state-of-the-art
+
+Comparison on generic image classification datasets. In table 2, we compare our method with baselines and state-of-the-art methods for novel category discovery on generic image classification datasets CIFAR-10, CIFAR-100, and ImageNet following the same protocol as RankStat [18] for fairness. Our method achieves state-of-the-art results on all datasets. It can be seen that our method significantly outperforms $k$ -means, KCL [25], MCL [26], and DTC [20]. Notably, our method outperforms the previous state-of-the-art [18] on the most challenging ImageNet-1K dataset by a significant margin of $6 . 4 \%$ . The improvements on CIFAR-10 and CIFAR-100 are smaller. We hypothesize that this is due to the spatial resolution discrepancy. The image resolution of CIFAR-10 and CIFAR-100 is only $3 2 \times 3 2$ , which leads to very small spatial local features. Thus, the local branch cannot offer much more useful information than the global branch. In contrast, the input resolution of ImageNet-1K is $2 2 4 \times 2 2 4$ . Hence, a larger spatial feature map can be obtained to take more advantages of the local branch.
+
+Table 2: Comparison of novel category discovery on generic classification datasets. For fair comparison, our method uses ResNet18 [23] backbone initialized with RotNet [17] following [18].   
+
+<table><tr><td>No</td><td>Method</td><td>CIFAR-10</td><td>CIFAR-100</td><td>ImageNet-1K</td></tr><tr><td>(1)</td><td>k-means [35]</td><td>72.5±0.0%</td><td>56.3±1.7%</td><td>71.9%</td></tr><tr><td>(2)</td><td>KCL [25]</td><td>66.5±3.9%</td><td>14.3±1.3%</td><td>73.8%</td></tr><tr><td>（3）</td><td>MCL [26]</td><td>64.2±0.1%</td><td>21.3±3.4%</td><td>74.4%</td></tr><tr><td>(4)</td><td>DTC[20]</td><td>87.5±0.3%</td><td>56.7±1.2%</td><td>78.3%</td></tr><tr><td>(5)</td><td>RankStat [18]</td><td>90.4±0.5%</td><td>73.2±2.1%</td><td>82.5%</td></tr><tr><td>(6)</td><td>Ours</td><td>91.6±0.6%</td><td>75.3±2.3%</td><td>88.9%</td></tr></table>
+
+Comparison on fine-grained image classification datasets. In table 3, we compare with other methods on fine-grained image classification datasets. In these datasets, the difference of holistic structure between classes is small, and the classes are mostly differentiated by the local details. Thus, only looking at the global feature descriptors is far from enough for the fine-grained scenario, where the local information plays a vital role. Comparing rows 2–3 with row 5, it can be observed that our proposed method substantially outperforms previous state-of-the-art models that only use global features. For example, our method shows $8 . 3 \%$ , $8 . 1 \%$ and $4 . 1 \%$ improvements respectively on CUB-200, Stanford-Cars and FGVC-Aircraft over RankStat [18]. To further verify the effectiveness of our local branch, we carry out another experiment by dropping the global branch (row 4 in table 3). Dropping the global branch will disable the mutual knowledge distillation accordingly. It can be seen that using the local branch alone already yields a notable improvement over RankStat [18] (row 3 vs row 4). Our full method establishes the new state-of-the-art.
+
+Table 3: Comparison of novel category discovery on fine-grained classification datasets. “Ours w/o global” means our proposed method without global branch and mutual distillation.   
+
+<table><tr><td>No</td><td>Method</td><td>CUB-200</td><td>Stanford-Cars</td><td>FGVC-Aircraft</td></tr><tr><td>(1)</td><td>k-means [35]</td><td>20.4 ±1.1%</td><td>31.4 ± 0.9%</td><td>44.7 ± 1.3%</td></tr><tr><td>(2)</td><td>DTC[20]</td><td>33.6 ± 0.7%</td><td>46.5 ± 2.4%</td><td>58.7 ± 1.2%</td></tr><tr><td>(3)</td><td>RankStat [18]</td><td>39.5 ± 1.7%</td><td>53.8 ± 2.0%</td><td>66.3 ± 0.7%</td></tr><tr><td>(4)</td><td>Ours w/o global</td><td>43.1 ± 2.3%</td><td>56.8 ± 2.3%</td><td>67.3 ± 1.0%</td></tr><tr><td>(5)</td><td>Ours full</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>70.4 ± 0.9%</td></tr></table>
+
+# 4.3 Ablation study
+
+Effectiveness of different components. In table 4, we ablate different components of our method. It is clear that all components in our method are effective as removing any of them will cause the performance drop. Without BCE loss, our dual ranking statistics is disabled and no pair-wise pseudo labels are transferred from the labelled data. Therefore, the parameters within $\eta ^ { u }$ remain untrained, leading to poor performance equivalent to a random baseline. The sKLD loss also has a strong impact on the final performance. Without it, the performance drops $8 . 0 { - } 1 1 . 3 \%$ absolute ACC. This performance drop shows that the information exchange between the global and the local branches are crucial. The consistency loss also plays an important role, as the performance without consistency drops $9 . 9 \mathrm { - } 1 2 . 2 \%$ absolute ACC. Similar to [18, 20] the cross-entropy loss, consistency loss and self-supervision are also important for our method. Having all these components in a unified framework, our full method obtains the best performance.
+
+Table 4: Effectiveness of different components of our method. “MSE” means MSE consistency loss; “CE” means cross-entropy loss for training on labelled data; “BCE” means binary cross-entropy loss for training both global and local branches on unlabeled data; “sKLD” means the sKLD loss for mutual distillation between the two branches; “Self-sup.” means self-supervised pre-training.   
+
+<table><tr><td></td><td>CUB-200</td><td>Stanford-Cars</td><td>FGVC-Aircraft</td><td>ImageNet-100</td></tr><tr><td>Ours w/o BCE</td><td>2.2 ± 1.3%</td><td>3.1 ± 0.4%</td><td>5.1 ± 0.4%</td><td>3.0 ± 0.3%</td></tr><tr><td>Ours w/o sKLD</td><td>39.8 ± 1.8%</td><td>50.6 ± 2.1%</td><td>60.8 ± 1.5%</td><td>58.2 ± 1.2%</td></tr><tr><td>Ours w/o CE</td><td>41.2 ± 2.4%</td><td>52.4 ± 4.3%</td><td>60.2 ± 2.7%</td><td>59.1 ± 2.7%</td></tr><tr><td>Ours w/o MSE</td><td>37.9 ± 4.5%</td><td>50.6 ± 6.2%</td><td>58.9 ± 5.7%</td><td>57.2 ± 3.6%</td></tr><tr><td> Ours w/o Self-sup.</td><td>44.3 ± 3.5%</td><td>58.2 ± 1.8%</td><td>67.4 ± 1.3%</td><td>65.3 ± 1.3%</td></tr><tr><td>Ours full</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>70.4 ± 0.9%</td><td>69.4 ± 2.1%</td></tr></table>
+
+Different configurations of the two-branch design. Our two-branch design allows mutual knowledge distillation between local and global branches. In table 5 we compare different branch configurations. Row 1 and row 2 represent the global and local single-branch baselines. As can be seen, the local branch configuration performs better than the global one which is the configuration of [18], demonstrating the local ranking statistics with the part dictionary is more effective than that with global features. By introducing another branch of the same type (row $1  \mathrm { r o w } 3$ , row $2  \mathrm { r o w } 4$ ) to incorporate mutual knowledge distillation, the performance can be consistently boosted, which further verifies the effectiveness of our mutual knowledge distillation method for novel category discovery. Mutual knowledge distillation between two local branches is more effective than the counterpart between two global branches. Row 5 presents the results of mutual distillation between global branch and local branch, showing best performance, which corroborates that mutual knowledge distillation between local and global branches enables them to complement each other.
+
+Table 5: Different configurations of the two-branch design.   
+
+<table><tr><td>No</td><td colspan="2">Configuration</td><td>CUB200</td><td>Stanford-Cars</td><td>ImageNet-100</td></tr><tr><td>(1)</td><td>global</td><td></td><td>39.5 ± 1.7%</td><td>53.8 ± 2.0%</td><td>62.5 ± 1.2%</td></tr><tr><td>(2)</td><td>local</td><td>=</td><td>43.1 ± 0.9%</td><td>56.8 ± 1.7%</td><td>64.2 ± 1.6%</td></tr><tr><td>(3)</td><td>global</td><td>global</td><td>41.2 ± 0.8%</td><td>54.6 ± 0.7%</td><td>63.2 ± 0.9%</td></tr><tr><td>(4)</td><td>local</td><td>local</td><td>44.7 ± 1.1%</td><td>57.9 ± 0.5%</td><td>65.7 ± 1.4%</td></tr><tr><td>(5)</td><td>global</td><td>local</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>69.4 ± 2.1%</td></tr></table>
+
+Effects of larger memory banks. It has been shown in [21] that increasing the size of the memory bank can improve self-supervised representation learning. In our experiments, we set the memory sizes of $B _ { p }$ , $B _ { g }$ and $\nu$ to 2048 for training efficiency. In table 6, we show the results by increasing the memory sizes. As can be seen, similar to [21], the memory size and the performance is positively correlated. With more instances or parts in the memory banks, more useful information can be used for mutual knowledge distillation $\boldsymbol { B } _ { p }$ and $B _ { g . }$ ) and local part ranking statistics measure $( \mathcal { V } )$ , thus improving the results. However, with a relatively small memory size of 2048, our method already achieves promising results. Note that due to the limited number of images in CUB-200 and Stanford-Cars, the performance boost with the increase of bank size for $B _ { p }$ and $B _ { g }$ quickly reaches a plateau. While for CIFAR-10 and ImageNet-100, more instances can be enqueued to foster the knowledge distillation. In terms of $\nu$ , the performance is consistently improved with the increase of the size of $\nu$ for all datasets. Due to the larger image resolution in CUB-200 and Stanford-Cars, more useful part features can be extracted from each image for local ranking statistics. Therefore, the performance is less affected by the smaller number of images. This further demonstrates the effectiveness of our local part-level ranking statistics.
+
+Different sampling methods for memory bank $\nu$ . The part memory bank $\nu$ stores the part-level features for the local-comparison branch, and is updated in a FIFO manner. Here we compare different ways of maintaining $\nu$ . Our default choice is to randomly sample one part-level feature from each image in a training mini-batch. However, random sampling may not select the most informative part-level features from the image, so an alternative is to select part-level features based on class-activation-map (CAM) [59]. Instead of random sampling, the part with the highest response is selected by CAM. Rather than sampling only a single part from each image, we can simply use all
+
+(a) ACC with varying size for $\boldsymbol { B } _ { p }$ and $B _ { g }$ .
+
+Table 6: Increasing the size of memory bank. “SCars” denotes Stanford-Cars dataset; “IM-100” denotes ImageNet-100 dataset.   
+
+<table><tr><td>Bank size</td><td>2048</td><td>4096</td><td>8192</td><td>16384</td><td>32768</td></tr><tr><td>CIFAR-10</td><td>91.6%</td><td>92.3%</td><td>92.4%</td><td>92.7%</td><td>93.0%</td></tr><tr><td>CUB-200</td><td>47.8%</td><td>48.3%</td><td>48.4%</td><td>48.5%</td><td>48.4%</td></tr><tr><td>SCars</td><td>61.9%</td><td>62.4%</td><td>62.8%</td><td>62.9%</td><td>62.9%</td></tr><tr><td>IM-100</td><td>69.4%</td><td>70.2%</td><td>70.8%</td><td>71.1%</td><td>71.3%</td></tr></table>
+
+(b) ACC with varying size for $\nu$   
+
+<table><tr><td>Bank size</td><td>2048</td><td>4096</td><td>8192</td><td>1638432768</td><td></td></tr><tr><td>CIFAR-10 91.6% 91.7%</td><td></td><td></td><td>91.7%</td><td>91.9%</td><td>92.0%</td></tr><tr><td>CUB-200 47.8% 48.5% 48.7% 49.2%</td><td></td><td></td><td></td><td></td><td>49.3%</td></tr><tr><td>SCars</td><td></td><td>61.9% 62.7% 63.4%</td><td></td><td>663.6%</td><td>63.7%</td></tr><tr><td>IM-100</td><td></td><td></td><td></td><td>69.4% 70.5% 71.2% 71.3% 71.4%</td><td></td></tr></table>
+
+the parts for each image. We compare these three different choices in table 7. It can be seen that using all the parts causes slight performance drop. This is reasonable because using all parts introduces redundancy in $\nu$ , making the local comparison more prone to noise. On the other hand, selecting the most activated part using CAM shows a better performance than the random selection, indicating that more informative parts in the memory bank can enable better local comparison. As the gap is not significant, we use the random sampling as our default choice for its simplicity and efficacy.
+
+Table 7: Effects of using different way to update $\nu$ . “Random” means random part selection; “All” means using all parts; “CAM” means selecting the most activated parts using CAM [59].   
+
+<table><tr><td></td><td>CIFAR-100</td><td>ImageNet-100</td><td>CUB-200</td><td>Stanford-Cars</td></tr><tr><td>Random</td><td>75.3 ± 2.3%</td><td>69.4 ± 2.1%</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td></tr><tr><td>All</td><td>76.0 ± 2.6%</td><td>68.7 ± 2.3%</td><td>46.5 ± 1.9%</td><td>61.0 ± 2.4%</td></tr><tr><td>CAM</td><td>76.5 ± 2.4%</td><td>70.3 ± 2.4%</td><td>48.5 ± 1.8%</td><td>62.4 ± 2.1%</td></tr></table>
+
+Unknown number of novel classes. In a more realistic setting, the unlabelled class number $C ^ { u }$ may not be known. In this case, we can apply existing methods to estimate category number in the unlabelled data, such as the algorithm from DTC [20], before adopting our method. In table 8 we provide the results of novel category discovery using the estimated number of classes on CUB200/ImageNet-100 by DTC [20]. We denote the estimated class number as $\hat { C } ^ { u }$ . As shown in table 8, with the estimated class number by DTC, our model also obtains a significantly better performance than RankStat [18].
+
+Table 8: Results with estimated class numbers and ground truth class numbers.   
+
+<table><tr><td></td><td colspan="2">CUB-200</td><td colspan="2">ImageNet-100</td></tr><tr><td>Class numbers</td><td>Cu = 40</td><td>Cu= 43</td><td>Cu = 30</td><td>Cu =32</td></tr><tr><td>RankStat [18]</td><td>39.5±1.7%</td><td>38.2±2.1%</td><td>66.3±0.7%</td><td>65.0±1.2%</td></tr><tr><td>Ours</td><td>47.8±2.4%</td><td>44.6±2.6%</td><td>70.4±0.9%</td><td>68.8±1.5%</td></tr></table>
+
+Please refer to the supplementary for more results and analysis. Our code can be found at https: //github.com/DTennant/dual-rank-ncd.
+
+# 5 Conclusion
+
+We have introduced a two-branch learning framework for novel category discovery, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. To transfer knowledge from labelled data to unlabelled data, we proposed to use local ranking statistics by maintaining a local part dictionary build on-the-fly for training, together with the global ranking statistics. We further introduced a mutual knowledge distillation method for information exchange and encouraging the agreement between the two branches. We thoroughly evaluated our method on generic image classification datasets as well as fine-grained recognition datasets, achieving state-of-the-art performance.
+
+# References
+
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parse/train/xWq1MVj7YrE/xWq1MVj7YrE_content_list.json

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+    {
+        "type": "text",
+        "text": "Novel Visual Category Discovery with Dual Ranking Statistics and Mutual Knowledge Distillation ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Bingchen Zhao1 Kai Han2,3,4∗ ",
+        "bbox": [
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+            256,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1Tongji University 2The University of Hong Kong 3Google Research 4University of Bristol zhaobc.gm@gmail.com kaihanx@hku.hk ",
+        "bbox": [
+            186,
+            282,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
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+            363
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we tackle the problem of novel visual category discovery, i.e., grouping unlabelled images from new classes into different semantic partitions by leveraging a labelled dataset that contains images from other different but relevant categories. This is a more realistic and challenging setting than conventional semi-supervised learning. We propose a two-branch learning framework for this problem, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. To transfer knowledge from labelled data to unlabelled data, we propose using dual ranking statistics on both branches to generate pseudo labels for training on the unlabelled data. We further introduce a mutual knowledge distillation method to allow information exchange and encourage agreement between the two branches for discovering new categories, allowing our model to enjoy the benefits of global and local features. We comprehensively evaluate our method on public benchmarks for generic object classification, as well as the more challenging benchmarks for fine-grained visual recognition, achieving state-of-the-art performance. ",
+        "bbox": [
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+            381,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            614,
+            310,
+            631
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Superior performance on many problems has been achieved by recent machine learning models, especially the ones based on deep learning. While the success comes at the cost of large-scale human annotation, which is prohibitively expensive in practice. For example, modern convolutional neural networks (CNNs) can surpass human-level recognition performance on ImageNet after training with over one million labelled images [22]. On the one hand, it is not possible to annotate all possible classes in the real world, as there are way more classes than the 1, 000 classes in ImageNet and new classes keep growing over time. On the other hand, annotating specific data, such as the medical data, may require specific expertise, which renders the large-scale annotation extremely difficult, if not impossible. Therefore, it is desired to enable the machine learning systems to deal with unlabelled data automatically. ",
+        "bbox": [
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+            647,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, the problem of novel category discovery was formalized in [20, 18], which aims at discovering new visual categories on unlabelled data by transferring knowledge from labelled data. The labelled data is assumed to contain similar but different categories to those in the unlabelled data. This problem is similar to semi-supervised learning in the sense that both labelled and unlabelled data are used to learn the model. While novel category discovery is much harder because semi-supervised learning assumes that every class contains labelled instances, while for novel category discovery there are no labels available for the new classes in the unlabelled data. This setting is also relevant to unsupervised clustering. But differently, novel category discovery makes use of the labelled data to extract a specific class prior (i.e., the properties that delineate a class) for partitioning the unlabelled data, while the unsupervised clustering may produce multiple different but equally valid clustering results by adopting different properties (e.g., color, shape, pose, lighting, etc). In this paper, we introduce a simple and effective two-branch framework for novel category discovery, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. Our contributions are as follows. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
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+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "First, we propose to apply dual ranking statistics for transferring knowledge from the known classes in the labelled data to the unlabelled data, resulting in more robust pseudo label generation for learning on the unlabelled data. We maintain a dynamic object part dictionary and apply part-level ranking statistics on the similarity distribution of each instance over the dictionary to obtain pseudo labels, which are complementary to the pseudo labels obtained by simply examining the ranking statistics of global descriptors. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Second, we introduce a mutual knowledge distillation method to allow information exchange and encourage agreement between the local and global branches. The dual ranking statistics provide global and part-level information for learning in two branches separately. The mutual knowledge distillation further allows information exchange between the two branches and makes them benefit from each other. Unlike conventional methods that distill between teacher and student models with known labels, our method distills between two branches of the same model without any manual annotations. ",
+        "bbox": [
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+            284,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Third, we comprehensively evaluate our method on public benchmarks for generic object classification, including CIFAR10, CIFAR100, and ImageNet, obtaining state-of-the-art results. Furthermore, we also validate our approach on the more challenging fine-grained datasets CUB-200, Stanford-Cars, and FGVC-Aircraft, in which the local details are more important to distinguish different classes. Our method outperforms existing methods by a substantial margin, thanks to the ability of our model to subtly exploit both local and global information. Our code can be found at https://github.com/DTennant/dual-rank-ncd. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2 Related work ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our work is relevant to novel category discovery, knowledge distillation, and part-level feature learning. We briefly review the most relevant work below. ",
+        "bbox": [
+            176,
+            545,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Novel category discovery is a relatively new problem setting recently formalized by [20, 18] with the task being automatically discovering new object categories in the unlabelled data by making use of a labeled dataset containing different but relevant object classes. The purpose of using the extra labelled data is to learn a category prior to reduce the ambiguity of class definition. This task is closely related to unsupervised clustering and semi-supervised learning, but also significantly different from them. Unsupervised clustering has been studied for decades with many classical approaches [35, 3, 9] and deep learning based solutions [50, 16, 40] being proposed. Due to the lack of a proper class prior, multiple equally valid clustering results can be achieved by different criteria. Therefore, it can not be directly applied to discovery new classes as we expect the model to follow a unique class definition. In semi-supervised learning [43, 39, 6, 38, 46], unlabelled data are used together with labelled data to train a more robust model, with the assumption that all classes in the unlabelled data have labelled instances. However, this is unlikely to be true for real applications where unlabelled data may come from new classes. Thus, novel category discovery is a more realistic setting. The DTC method introduced in [20] approaches this problem in two steps. The model is firstly trained with supervised learning on the labelled data to capture high-level semantic class information and then trained on the unlabelled data with a clustering loss to discover new categories. In [18, 19], Han et al. proposed to use self-supervision to bootstrap feature learning and introduced ranking statistics on the feature embedding to provide pseudo labels for training on unlabelled data. The KCL [25] and MCL [26] methods were designed for general transfer learning across domains and tasks, which can also be applied for novel category discovery. These two methods maintain two models for training and testing, a pretrained binary classifier for pseudo label generation and a clustering model. The binary classifier pretrained on the labelled data is used to provide pseudo labels to train the clustering model on unlabelled data. Concurrent to our work, several methods [28, 58, 57, 14] are proposed to improve the performance of novel category discovery from different perspectives, showing promising results. ",
+        "bbox": [
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+            579,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The existing methods only consider the global feature descriptors while ignoring the local object parts which are essential to distinguish classes that look similar. In our approach, we jointly consider both and allow information exchange between them for more reliable new category discovery. ",
+        "bbox": [
+            174,
+            92,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Knowledge distillation is often employed to learn a compact student model using the knowledge distilled from a larger teacher model by enforcing the agreement of outputs or representations between the two models (e.g., [24, 41, 54, 52, 27, 29, 1, 48]). Apart from distilling a larger teacher model to a smaller student model, self-distillation methods show that distilling between two identical models can also improve the performance [53, 15, 4]. Mutual learning [56] is a similar technique that trains two models of the same architecture simultaneously but with different initialization and encourages them to learn collaboratively from each other. It has been shown that different initialization leads the model to focus on different regions of the input and thus the trained model can better capture the holistic structure of the data, resulting in better performance. Though effective, the above methods require the labels for training. Thus they can not be applied for novel category discovery. Recently, [13] introduced a self-supervised distillation method called SEED to improve the representation learning on a small model (student) by distilling from a pretrained large model (teacher). The student model is trained to predict the same similarity score distribution inferred by the frozen teacher model over a queue of instances. We draw inspiration from [13] to design the mutual knowledge distillation module in our method for novel category discovery between the local and global branches. ",
+        "bbox": [
+            174,
+            140,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Part-level features have been shown to be effective for tasks involving image verification such as few-shot learning [10, 55, 12] and image retrieval [7, 34, 5, 2, 37, 42, 45]. In [10], the part-level visual concepts are generated by clustering feature vectors from the feature maps obtained using a trained neural network. These visual concepts are used as matching primitives at test time for few-shot learning. Zhang et al. [55] used the Earth-Mover’s Distance (EMD) between local part features to measure the distance between two images for matching. Doersch et al. [12] proposed CrossTransformers to model the cross-attention between each local part of a query image and a set of support images for few-shot learning. Part-level features have been more widely used in the domain of image retrieval with both classical [34, 5] and deep learning based [2, 37, 42, 45, 7] methods. Intuitively, the part-level features provide better precision for the retrieved results because the local matching is more restricted, and global features yield better recall [7]. In our work, we leverage both local and global features to enjoy the benefits of both through the dual ranking statistics and the mutual knowledge distillation, for more robust novel category discovery. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Method ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            550,
+            269,
+            568
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The goal of novel category discovery is to automatically partition unlabelled instances $x _ { i } ^ { u } \\in \\mathcal { D } ^ { u }$ into $C ^ { u }$ semantic clusters by transferring the knowledge from the labelled instances $( x _ { i } ^ { l } , y _ { i } ^ { l } ) \\in \\mathcal { D } ^ { l }$ , where $y _ { i } ^ { l } \\in \\{ 1 , \\ldots , C ^ { l } \\}$ . The key assumption is that the classes in $\\mathcal { D } ^ { l }$ and $\\mathcal { D } ^ { u }$ are relevant though different, so that the properties that constitute a class learned from $\\mathcal { D } ^ { l }$ can be transferred to $\\mathcal { D } ^ { u }$ . Following [18], we assume $C ^ { u }$ is known a priori. When it is unknown, we can employ off-the-shelf methods such as [20] to get an estimate. ",
+        "bbox": [
+            174,
+            582,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To tackle this challenge, we introduce a framework with mutual knowledge distillation between a global branch and a local branch (see fig. 1). The global branch is designed to capture the overall feature, while the local branch is designed to focus on each individual spatial local part. They have a shared feature extractor $f _ { \\theta }$ . Each branch has a feature projection layer and two linear heads. We denote the feature projection layer as $\\psi$ and the two linear heads as $\\eta ^ { l }$ and $\\eta ^ { u }$ respectively. We also denote $\\psi$ followed by the average pooling operation as $\\bar { \\psi }$ . Unless stated otherwise, we use subscripts $g$ and $p$ to differentiate feature projection layers and linear heads of global and local branches respectively in the rest of the paper. The two linear heads are responsible for classifying $C ^ { l }$ labelled categories and clustering $C ^ { u }$ unlabelled categories respectively. To transfer knowledge from the labelled data to the unlabelled data, we adopt global image level and local object part-level ranking statistics on the feature representations. In this way, the model will have reliable pseudo labels for training on the unlabelled data. Moreover, we also incorporate mutual knowledge distillation between the two branches to enforce global and local agreement, leading to more reliable novel category discovery. Next, we will introduce each component of our framework in more detail. In section 3.1, we first introduce the our knowledge transfer method using dual ranking statistics. In section 3.2, we describe our mutual knowledge distillation method for novel category discovery. Lastly, we summarize the overall training loss in section 3.3. ",
+        "bbox": [
+            174,
+            676,
+            825,
+            911
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/2dd763a851145b2b50eaa5dc81b0f5491e1b84c655a2ef8f98c275b9f126162c.jpg",
+        "image_caption": [
+            "Figure 1: Overview of our proposed method. An input image $x _ { i }$ is firstly processed by the feature extractor ranking s $f _ { \\theta }$ . The resulting feature is sent to the glistics on the global feature embedding al and local branches. The globato generate pseudo labels to the ch usesloss for $z _ { i }$ $\\mathcal { L } _ { \\mathrm { B C E } } ^ { g }$ new class discovery, while the local branch uses ranking statistics on the similarity score vector $o _ { i }$ between each of the local parts and a dynamic part dictionary to generate pseudo-labels. The two branches mutually distill knowledge from each other to allow information exchange and encourage agreement through two auxiliary memory banks with $\\mathcal { L } _ { \\mathrm { s K L D } }$ loss. We omit the supervised linear head, cross-entropy loss $\\mathcal { L } _ { \\mathrm { C E } }$ and consistency loss $\\mathcal { L } _ { \\mathrm { M S E } }$ in the plot for the sake of clarity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            238,
+            89,
+            758,
+            313
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 Dual ranking statistics for knowledge transfer ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            438,
+            532,
+            453
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "It is proven that ranking statistics is robust to noise, especially in high-dimensional space [51]. Han et al. [18] proposed to use ranking statistics for novel category discovery. The idea is to generate pair-wise pseudo labels by comparing the top- $k$ ranks of two feature vectors via examining the feature magnitude. Specifically, the binary pseudo label $s _ { i j }$ is determined by ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5a2c479ee1f578e24436be898fe014614f7307b0782058f35cd28d783aa80e6e.jpg",
+        "text": "$$\ns _ { i j } = \\mathbb { 1 } \\left\\{ \\mathrm { t o p } _ { k } ( z _ { i } ) = \\mathrm { t o p } _ { k } ( z _ { j } ) \\right\\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $z _ { i }$ and $z _ { j }$ are feature vectors of two unlabelled images. With the binary pseudo labels, the model can then be trained using the binary cross-entropy loss on the unlabelled data. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Unlike [18] which only considers global image feature descriptors, we also explore each individual object part for novel category discovery. Verification based on part-level features has been shown to be effective to match two images (e.g. [55, 12]). The pair-wise verification using global features focuses on the holistic structure of the object and thus may introduce more false positives with high recall (but low precision). While pair-wise verification using local part features focuses on local details, which is more strict, and thus may introduce more false negatives with high precision (but low recall) [7]. Hence, local part features and global features are complementary to each other for verification and should be considered jointly for more robust category discovery, as ideally we expect to have both high precision and recall. Therefore, to achieve this goal, we propose to have one branch using global features and another branch using part-level features. Ranking statistics is applied on each branch to generate pseudo labels. For the global one, we simply apply a soft extension of the hard ranking statistics [18]. In particular, instead of forcing $s _ { i j }$ in eq. (1) to be either 0 or 1, it can be replaced by a continuous value $\\begin{array} { r } { s _ { i j } = \\frac { c } { k } \\in [ 0 , 1 ] } \\end{array}$ where $c$ is the number of shared elements in $\\mathrm { t o p } _ { k } ( z _ { i } )$ and $\\mathrm { t o p } _ { k } ( z _ { j } )$ . Hence, the BCE loss for the global branch can be written as ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ba36f05637bdeb30fefdeff42ea38835e59c22d033bae20b54419d0a6f5f0cd1.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { B C E } } ^ { g } = - \\frac { 1 } { M ^ { 2 } } \\sum _ { i = 1 } ^ { M } \\sum _ { j = 1 } ^ { M } [ s _ { i j } ^ { g } \\log \\eta _ { g } ^ { u } ( z _ { i } ^ { u } ) ^ { \\top } \\eta _ { g } ^ { u } ( z _ { j } ^ { u } ) + ( 1 - s _ { i j } ^ { g } ) \\log ( 1 - \\eta _ { g } ^ { u } ( z _ { i } ^ { u } ) ^ { \\top } \\eta _ { g } ^ { u } ( z _ { j } ^ { u } ) ) ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            782,
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+            827
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $M$ is the number of unlabelled images, $z _ { i } ^ { u } = \\bar { \\psi } _ { g } ( f _ { \\theta } ( x _ { i } ^ { u } ) ) \\in \\mathbb { R } ^ { d }$ is a global feature vector of the image $x _ { i } ^ { u }$ , and $s _ { i j } ^ { g }$ is the soft ranking statistics score between $x _ { i } ^ { u }$ and $x _ { j } ^ { u }$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the local one, we propose to maintain a memory bank to act as a dynamic object part dictionary and obtain the ranking statistics by comparing each object part with the collection of part descriptors in the memory bank. Concretely, the memory bank is a First-In-First-Out (FIFO) queue $\\mathcal { V } = [ v _ { 1 } , \\dotsc , v _ { e } ]$ storing the part-level features, where $e$ is the number of part-level features in the queue. Each part feature in $v$ is the $d$ -dimensional feature vector from a randomly selected spatial location in the feature map $\\psi _ { p } ( f _ { \\theta } ( x _ { i } ) ) \\in \\mathbb { R } ^ { d \\times h \\times w }$ of an randomly sampled image $x _ { i } \\in \\mathcal { D } ^ { l } \\dot { \\cup } \\mathcal { D } ^ { u }$ . We select one part feature vector from each image in current mini-batch. Other part sampling methods like using all parts or selecting based on activation maps can also be applied (as will be seen in section 4.3), while we found that the simple random sampling is on par with other more complicated methods. Following MoCo [21], when the current mini-batch of part features is enqueued into $\\nu$ , the oldest mini-batch in $\\nu$ is dequeued. For the feature vector $q _ { j } ^ { u }$ drawn at every spatial location of the feature map $\\psi _ { p } ( f _ { \\theta } ( x _ { i } ^ { u } ) )$ in current mini-batch, we can then obtain a $e$ -dimensional vector representing the similarity between $q _ { j }$ and all part features in the dictionary $\\nu$ . All $q _ { j }$ for $x _ { i } ^ { u }$ across $h \\times w$ locations are then fused together by average-pooling. Let us denote by $o _ { i } ^ { u } \\in \\mathbb { R } ^ { e }$ the fused similarity vector (see fig. 2). For any pair of unlabelled images $x _ { i } ^ { u }$ and $x _ { j } ^ { u }$ in current mini-batch, their soft ranking statistics score $s _ { i j } ^ { p }$ can then be obtained by comparing $o _ { i } ^ { u }$ and $o _ { j } ^ { u }$ as described above for the global feature descriptors. Similar to eq. (2), we can define the BCE loss $\\mathcal { L } _ { \\mathrm { B C E } } ^ { p }$ to train the local branch. The BCE loss for both branches can then be written as ",
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+    {
+        "type": "image",
+        "img_path": "images/cb7a4df580fce62457decb56c6de81a066ec16a461e9267e44526bb300df2b49.jpg",
+        "image_caption": [
+            "Figure 2: Design of the local comparison process. Each part of an image is compared against all parts in the memory bank $\\nu$ , forming one similarity vector for each part. All resulting similarity vectors are then fused to a single vector by average pooling, which is used to generate pair-wise pseudo labels. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/16d8f47546925c5617567648a7bd985bc9600adf8fc1b71a27ee79a7864f792e.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { B C E } } = \\mathcal { L } _ { \\mathrm { B C E } } ^ { g } + \\mathcal { L } _ { \\mathrm { B C E } } ^ { p } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Mutual knowledge distillation for novel category discovery ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "So far, our model considers local and global information in two branches independently. To make the two branches directly benefit from each other, we propose a mutual knowledge distillation method for novel category discovery to allow information exchange and encourage agreement between the local and global branches. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Existing mutual knowledge distillation methods are normally designed for two models (i.e., teacher model and student model or two peer models) [24, 56], while we distill between two branches of the same model with each branch having a different focus. More importantly, unlike the conventional mutual learning and knowledge distillation methods that have the same class assignment for the same input due to the availability of labels, in our setting, the cluster assignments of the unlabelled linear heads $\\eta _ { g } ^ { u }$ and $\\eta _ { p } ^ { u }$ for the same unlabelled data point may be completely different for the two branches. Therefore, these knowledge distillation methods can not be applied for novel category discovery. Recently, [13] introduced the knowledge distillation between the teacher and student models by comparing the similarity score distribution between each instance and a queue of features from the larger teacher model. Inspired by [13], we develop a mutual knowledge distillation method between the local and global branches for novel category discovery without using labels. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Instead of using the softmax output of $\\eta _ { g } ^ { u }$ and $\\eta _ { p } ^ { u }$ for mutual learning, which is invalid in our case, we mutually distill the two branches via the similarity score distribution over a memory bank per branch. Specifically, we maintain two FIFO feature banks to store the features extracted by $\\bar { \\psi } _ { p }$ and $\\bar { \\psi } _ { g }$ , denoted as $B _ { p } = [ b _ { 1 } ^ { p } , \\ldots , b _ { T } ^ { p } ]$ and $B _ { g } = [ b _ { 1 } ^ { g } , \\dotsc , b _ { T } ^ { g } ]$ . Both $B _ { p }$ and $B _ { g }$ contain features of $x _ { i } \\in \\mathcal { D } ^ { l } \\cup \\mathcal { D } ^ { u }$ . Again, similar to MoCo [21], when the current mini-batch is enqueued, the oldest mini-batch is dequeued in both memory banks. For each unlabelled image $x _ { i } ^ { u }$ , we first obtain the feature representations using $z _ { i } ^ { u } = \\bar { \\psi } _ { g } ( \\dot { f } _ { \\theta } ( x _ { i } ^ { u } ) )$ and $z _ { i } ^ { \\prime u } = \\bar { \\psi } _ { p } ( f _ { \\theta } ( x _ { i } ^ { u } ) )$ . The similarity score distribution $p ^ { g } ( x _ { i } ^ { u } , B _ { g } )$ and $p ^ { p } ( x _ { i } ^ { u } , B _ { p } )$ can be defined as ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/e5f619a092210288e1b498fd2d006058190429b2a6095cb0e8d0fdca7edaa471.jpg",
+        "text": "$$\np ^ { g } ( x _ { i } ^ { u } , \\mathcal { B } _ { g } ) = [ p _ { 1 } ^ { g } , \\dotsc , p _ { T } ^ { g } ] , \\quad p _ { j } ^ { g } = \\frac { e x p ( z _ { i } ^ { u } \\cdot b _ { j } ^ { g } / \\tau ) } { \\sum _ { b _ { k } ^ { g } \\sim \\mathcal { B } _ { g } } e x p ( z _ { i } ^ { u } \\cdot b _ { k } ^ { g } / \\tau ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "and ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/45e7a8ed78d9e6ce99d4682956be3caf248e0b1df3885cec6f6c897ab3abbf1b.jpg",
+        "text": "$$\np ^ { p } ( x _ { i } ^ { u } , \\mathcal { B } _ { p } ) = [ p _ { 1 } ^ { p } , \\ldots , p _ { T } ^ { p } ] , \\quad p _ { j } ^ { p } = \\frac { e x p ( z _ { i } ^ { \\prime u } \\cdot b _ { j } ^ { p } / \\tau ) } { \\sum _ { b _ { k } ^ { p } \\sim \\mathcal { B } _ { p } } e x p ( z _ { i } ^ { \\prime u } \\cdot b _ { k } ^ { p } / \\tau ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            213,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\tau$ is a scalar temperature to control the sharpness of the similarity score distribution. ",
+        "bbox": [
+            176,
+            256,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To encourage agreement between the similarity score distributions of an unlabelled image from two branches, we apply mutual learning on the score distribution using the symmetric Kullback-Leibler Divergence (sKLD) loss ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0edc5ba469b7b673ed8c4ed500b5012db474c945cdb4434cb6cc16cc9072fb1c.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { s K L D } } = \\frac { 1 } { 2 } ( D _ { K L } ( p ^ { p } \\| p ^ { g } ) + D _ { K L } ( p ^ { g } \\| p ^ { p } ) )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            356,
+            325,
+            640,
+            356
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $D _ { K L }$ is the Kullback–Leibler (KL) divergence with $\\begin{array} { r } { D _ { K L } ( p _ { 1 } \\| p _ { 2 } ) = p _ { 1 } \\log \\frac { p _ { 1 } } { p _ { 2 } } } \\end{array}$ . In this way, the global and local branches of the model can learn from each other, while maintaining their own merits. Our mutual knowledge distillation method differs from SEED [13] in several aspects. First, SEED aims at improving high level visual representation, while we aim at enforcing the agreement between local and global features for novel category discovery; second, SEED distills between two different models while we distill between two branches of the same model; third, SEED maintains a queue derived from the global features of the teacher model, while we maintain two queues as dictionaries for global and local features; last, in SEED the larger teacher model is frozen during distillation and the student model is trained with cross-entropy loss, whereas in our method both branches are jointly trained with the sKLD loss. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3 Overall training loss ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Apart from the BCE and sKLD losses introduced above, we also apply the standard cross-entropy loss on both branches, which is written as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/737a2273cec0375fe0a1665e2b8e0e6eb56c0b69be5d158f431718c64e25dd40.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { C E } } = - \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } y _ { i } \\log \\eta _ { g } ^ { l } ( z _ { i } ^ { l } ) + y _ { i } \\log \\eta _ { p } ^ { l } ( z _ { i } ^ { \\prime l } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            580,
+            648,
+            625
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $N$ is the number of labeled images, $z _ { i } ^ { l } = \\bar { \\psi } _ { g } ( f _ { \\theta } ( x _ { i } ^ { l } ) )$ , and $z _ { i } ^ { \\prime l } = \\bar { \\psi } _ { p } ( f _ { \\theta } ( x _ { i } ^ { l } ) )$ . Similar to [18], the feature extractor $f _ { \\theta }$ is pretrained with self-supervised learning and is frozen during the training for novel category discovery. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Following [18, 20], we also include the consistency regularization loss to enforce the predictions of the same data point under different transformations to be the same. Specifically, let ${ \\hat { x } } _ { i }$ be a randomly transformed counterpart of the input image $x _ { i }$ . The consistency loss is then defined as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4807437b0699850e032e926492139b8086d006acd543d936203265f5329d5476.jpg",
+        "text": "$$\n\\begin{array} { r l r } & { } & { \\mathcal { L } _ { \\mathrm { M S E } } = \\displaystyle \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } [ ( \\eta _ { g } ^ { l } ( z _ { i } ^ { l } ) - \\eta _ { g } ^ { l } ( \\hat { z } _ { i } ^ { l } ) ) ^ { 2 } + ( \\eta _ { p } ^ { l } ( z _ { i } ^ { \\prime l } ) - \\eta _ { p } ^ { l } ( \\hat { z } _ { i } ^ { \\prime l } ) ) ^ { 2 } ) ] + } \\\\ & { } & { \\displaystyle \\frac { 1 } { M } \\sum _ { i = 1 } ^ { M } [ ( \\eta _ { g } ^ { u } ( z _ { i } ^ { u } ) - \\eta _ { g } ^ { u } ( \\hat { z } _ { i } ^ { u } ) ) ^ { 2 } + ( \\eta _ { p } ^ { u } ( z _ { i } ^ { \\prime u } ) - \\eta _ { p } ^ { u } ( \\hat { z } _ { i } ^ { \\prime u } ) ) ^ { 2 } ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            290,
+            731,
+            700,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { z } _ { i }$ is the feature embedding of the transformed image ${ \\hat { x } } _ { i }$ . Without enforcing the consistency, we may have different ranking statistics for $\\hat { z } _ { i }$ and $z _ { i }$ , which will lead to diffferent $s _ { i j }$ for the same images under different augmentation, confusing the training. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In summary, the overall loss function used to train our model is ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f19903b196c3c3b67ee93ba70830a5286523c5f1902e405ceeb4460e28fd2b3f.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } = \\mathcal { L } _ { \\mathrm { B C E } } + \\mathcal { L } _ { \\mathrm { s K L D } } + \\mathcal { L } _ { \\mathrm { C E } } + \\omega ( t ) \\mathcal { L } _ { \\mathrm { M S E } } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            364,
+            896,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\omega ( t ) = \\lambda e ^ { - 5 ( 1 - \\frac { t } { r } ) ^ { 2 } }$ is a ramp-up function as widely used in the literature [46, 33, 18] with $\\lambda \\in \\mathbb { R } _ { + }$ . $t$ and $r$ are the current time step and the ramp-up length respectively. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "After training, as the two branches already agree with each other, we simply take the output of the global branch as the final prediction. In particular, for each unlabelled image, we take the index of the max value in the softmax output as its cluster assignment. It is also worth noting that the memory banks and ranking statistics are no longer needed at inference time. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Experimental results ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1 Experimental setup ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Benchmark and evaluation metric. We follow [18] to validate our method on a variety of benchmark datasets for generic image classification including CIFAR-10 [31], CIFAR-100 [31] and ImageNet-1K [11]. For ImageNet-1K, three 30-class unlabelled splits are used in the experiments and the average performance is reported. We further experiment with ImageNet100 [47] which has less number of labelled classes but the same number of unlabelled classes as ImageNet-1K. In addition, we also validate our method on the more challenging fine-grained datasets including CUB-200 [49], Stanford-Cars [30], and FGVC aircraft [36]. One key assumption for novel category discovery is that the labelled classes are relevant to the unlabelled ones. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/bd52297edd59fbfaaa7576c415561103ddc8d8b32165c96b585f8e401c826e4c.jpg",
+        "table_caption": [
+            "Table 1: Data splits in the experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>labelled</td><td>unlabelled</td></tr><tr><td>CIFAR-10</td><td>5</td><td>5</td></tr><tr><td>CIFAR-100</td><td>80</td><td>20</td></tr><tr><td>ImageNet-1K</td><td>882</td><td>{30,30,30}</td></tr><tr><td>ImageNet-100</td><td>70</td><td>30</td></tr><tr><td>CUB-200</td><td>160</td><td>40</td></tr><tr><td>Stanford-Cars</td><td>156</td><td>40</td></tr><tr><td>FGVC-aircraft</td><td>81</td><td>21</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Due to the diversity of classes in generic image recognition datasets, it is not easy to tell the relevance between classes, though it is implicitly contained in the rules used to identify classes during data curation. In contrast, the relevance of the fine-grained datasets is explicitly determined by the fact that all classes in a fine-grained dataset belong to the same entry level class, e.g., birds, cars, and airplanes for the above fine-grained datasets. Besides, the fine-grained datasets pose more challenges for novel category discovery because of the high inter-class similarity. In this case, spatial local details become crucial clues to distinguish them. The labelled and unlabelled splits are summarized in table 1. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "We follow the standard practice in the literature to adopt clustering accuracy (ACC) on the unlabelled data as the metric for evaluation. It is defined as 1N PNti=1 $\\begin{array} { r } { \\frac { 1 } { N _ { t } } \\dot { \\sum } _ { i = 1 } ^ { N _ { t } } \\mathbb { 1 } ( y _ { i } ^ { * } = h ( y _ { i } ) ) } \\end{array}$ where $h$ is the optimal permutation obtained by Hungarian algorithm [32] that can match the clustering assignment $y _ { i }$ with the ground-truth label $y _ { i } ^ { * }$ , and $N _ { t }$ is the number of unlabelled images. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Implementation details. We follow [18] to initialize our model with parameters pretrained by self-supervised learning. Our default model is realized based on ResNet50 [23]. Namely, the first three macro blocks of ResNet50 are the feature extractor, $f _ { \\theta }$ , which is initialized with MoCov2 [8] pretrained on ImageNet via self-supervision and are frozen during training for novel category discovery. The last macro block is duplicated into two as the projection layers $\\psi _ { p }$ and $\\psi _ { g }$ , for local and global branches respectively. Each of them is followed by two linear heads, $\\eta ^ { l }$ and $\\eta ^ { u }$ , for labelled and unlabelled data respectively. For a fair comparison with prior methods, we also experiment using ResNet18 with RotNet [17] initialization. For all our experiments, we use SGD with momentum [44] as the optimizer and use a batch size of 128 for labelled data and 64 for unlabelled data. The temperature parameter $\\tau$ is set to 0.07, and the size of the three memory-banks are all set to 2048 for memory efficiency and also considering the relatively limited number of images in the fine-grained datasets. For the dual ranking statistics, we set $k = 5$ for the global branch following [18], and $k = 3 0$ for the local branch to include more local parts into consideration. Our experiments are performed using GTX 1080Ti GPUs. ",
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+    {
+        "type": "text",
+        "text": "4.2 Comparison to the state-of-the-art ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparison on generic image classification datasets. In table 2, we compare our method with baselines and state-of-the-art methods for novel category discovery on generic image classification datasets CIFAR-10, CIFAR-100, and ImageNet following the same protocol as RankStat [18] for fairness. Our method achieves state-of-the-art results on all datasets. It can be seen that our method significantly outperforms $k$ -means, KCL [25], MCL [26], and DTC [20]. Notably, our method outperforms the previous state-of-the-art [18] on the most challenging ImageNet-1K dataset by a significant margin of $6 . 4 \\%$ . The improvements on CIFAR-10 and CIFAR-100 are smaller. We hypothesize that this is due to the spatial resolution discrepancy. The image resolution of CIFAR-10 and CIFAR-100 is only $3 2 \\times 3 2$ , which leads to very small spatial local features. Thus, the local branch cannot offer much more useful information than the global branch. In contrast, the input resolution of ImageNet-1K is $2 2 4 \\times 2 2 4$ . Hence, a larger spatial feature map can be obtained to take more advantages of the local branch. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "table",
+        "img_path": "images/85539cc589c76a4ab1b4312bb92863971bda641195612df14532cde322506730.jpg",
+        "table_caption": [
+            "Table 2: Comparison of novel category discovery on generic classification datasets. For fair comparison, our method uses ResNet18 [23] backbone initialized with RotNet [17] following [18]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>No</td><td>Method</td><td>CIFAR-10</td><td>CIFAR-100</td><td>ImageNet-1K</td></tr><tr><td>(1)</td><td>k-means [35]</td><td>72.5±0.0%</td><td>56.3±1.7%</td><td>71.9%</td></tr><tr><td>(2)</td><td>KCL [25]</td><td>66.5±3.9%</td><td>14.3±1.3%</td><td>73.8%</td></tr><tr><td>（3）</td><td>MCL [26]</td><td>64.2±0.1%</td><td>21.3±3.4%</td><td>74.4%</td></tr><tr><td>(4)</td><td>DTC[20]</td><td>87.5±0.3%</td><td>56.7±1.2%</td><td>78.3%</td></tr><tr><td>(5)</td><td>RankStat [18]</td><td>90.4±0.5%</td><td>73.2±2.1%</td><td>82.5%</td></tr><tr><td>(6)</td><td>Ours</td><td>91.6±0.6%</td><td>75.3±2.3%</td><td>88.9%</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison on fine-grained image classification datasets. In table 3, we compare with other methods on fine-grained image classification datasets. In these datasets, the difference of holistic structure between classes is small, and the classes are mostly differentiated by the local details. Thus, only looking at the global feature descriptors is far from enough for the fine-grained scenario, where the local information plays a vital role. Comparing rows 2–3 with row 5, it can be observed that our proposed method substantially outperforms previous state-of-the-art models that only use global features. For example, our method shows $8 . 3 \\%$ , $8 . 1 \\%$ and $4 . 1 \\%$ improvements respectively on CUB-200, Stanford-Cars and FGVC-Aircraft over RankStat [18]. To further verify the effectiveness of our local branch, we carry out another experiment by dropping the global branch (row 4 in table 3). Dropping the global branch will disable the mutual knowledge distillation accordingly. It can be seen that using the local branch alone already yields a notable improvement over RankStat [18] (row 3 vs row 4). Our full method establishes the new state-of-the-art. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f45a485ceb4479670a43c65f627906a1acca721d0098bbc8ac827ec4a2993b70.jpg",
+        "table_caption": [
+            "Table 3: Comparison of novel category discovery on fine-grained classification datasets. “Ours w/o global” means our proposed method without global branch and mutual distillation. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>No</td><td>Method</td><td>CUB-200</td><td>Stanford-Cars</td><td>FGVC-Aircraft</td></tr><tr><td>(1)</td><td>k-means [35]</td><td>20.4 ±1.1%</td><td>31.4 ± 0.9%</td><td>44.7 ± 1.3%</td></tr><tr><td>(2)</td><td>DTC[20]</td><td>33.6 ± 0.7%</td><td>46.5 ± 2.4%</td><td>58.7 ± 1.2%</td></tr><tr><td>(3)</td><td>RankStat [18]</td><td>39.5 ± 1.7%</td><td>53.8 ± 2.0%</td><td>66.3 ± 0.7%</td></tr><tr><td>(4)</td><td>Ours w/o global</td><td>43.1 ± 2.3%</td><td>56.8 ± 2.3%</td><td>67.3 ± 1.0%</td></tr><tr><td>(5)</td><td>Ours full</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>70.4 ± 0.9%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.3 Ablation study ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Effectiveness of different components. In table 4, we ablate different components of our method. It is clear that all components in our method are effective as removing any of them will cause the performance drop. Without BCE loss, our dual ranking statistics is disabled and no pair-wise pseudo labels are transferred from the labelled data. Therefore, the parameters within $\\eta ^ { u }$ remain untrained, leading to poor performance equivalent to a random baseline. The sKLD loss also has a strong impact on the final performance. Without it, the performance drops $8 . 0 { - } 1 1 . 3 \\%$ absolute ACC. This performance drop shows that the information exchange between the global and the local branches are crucial. The consistency loss also plays an important role, as the performance without consistency drops $9 . 9 \\mathrm { - } 1 2 . 2 \\%$ absolute ACC. Similar to [18, 20] the cross-entropy loss, consistency loss and self-supervision are also important for our method. Having all these components in a unified framework, our full method obtains the best performance. ",
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+    {
+        "type": "table",
+        "img_path": "images/dd1ae19585a64f88035ef906388d2fe9d39cc5a48db4b15fc0e1d0f78bf2d07a.jpg",
+        "table_caption": [
+            "Table 4: Effectiveness of different components of our method. “MSE” means MSE consistency loss; “CE” means cross-entropy loss for training on labelled data; “BCE” means binary cross-entropy loss for training both global and local branches on unlabeled data; “sKLD” means the sKLD loss for mutual distillation between the two branches; “Self-sup.” means self-supervised pre-training. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CUB-200</td><td>Stanford-Cars</td><td>FGVC-Aircraft</td><td>ImageNet-100</td></tr><tr><td>Ours w/o BCE</td><td>2.2 ± 1.3%</td><td>3.1 ± 0.4%</td><td>5.1 ± 0.4%</td><td>3.0 ± 0.3%</td></tr><tr><td>Ours w/o sKLD</td><td>39.8 ± 1.8%</td><td>50.6 ± 2.1%</td><td>60.8 ± 1.5%</td><td>58.2 ± 1.2%</td></tr><tr><td>Ours w/o CE</td><td>41.2 ± 2.4%</td><td>52.4 ± 4.3%</td><td>60.2 ± 2.7%</td><td>59.1 ± 2.7%</td></tr><tr><td>Ours w/o MSE</td><td>37.9 ± 4.5%</td><td>50.6 ± 6.2%</td><td>58.9 ± 5.7%</td><td>57.2 ± 3.6%</td></tr><tr><td> Ours w/o Self-sup.</td><td>44.3 ± 3.5%</td><td>58.2 ± 1.8%</td><td>67.4 ± 1.3%</td><td>65.3 ± 1.3%</td></tr><tr><td>Ours full</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>70.4 ± 0.9%</td><td>69.4 ± 2.1%</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Different configurations of the two-branch design. Our two-branch design allows mutual knowledge distillation between local and global branches. In table 5 we compare different branch configurations. Row 1 and row 2 represent the global and local single-branch baselines. As can be seen, the local branch configuration performs better than the global one which is the configuration of [18], demonstrating the local ranking statistics with the part dictionary is more effective than that with global features. By introducing another branch of the same type (row $1  \\mathrm { r o w } 3$ , row $2  \\mathrm { r o w } 4$ ) to incorporate mutual knowledge distillation, the performance can be consistently boosted, which further verifies the effectiveness of our mutual knowledge distillation method for novel category discovery. Mutual knowledge distillation between two local branches is more effective than the counterpart between two global branches. Row 5 presents the results of mutual distillation between global branch and local branch, showing best performance, which corroborates that mutual knowledge distillation between local and global branches enables them to complement each other. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c1b755fafcc2407df4e822640710f2481b51c150a89f30d73553424411c95d60.jpg",
+        "table_caption": [
+            "Table 5: Different configurations of the two-branch design. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>No</td><td colspan=\"2\">Configuration</td><td>CUB200</td><td>Stanford-Cars</td><td>ImageNet-100</td></tr><tr><td>(1)</td><td>global</td><td></td><td>39.5 ± 1.7%</td><td>53.8 ± 2.0%</td><td>62.5 ± 1.2%</td></tr><tr><td>(2)</td><td>local</td><td>=</td><td>43.1 ± 0.9%</td><td>56.8 ± 1.7%</td><td>64.2 ± 1.6%</td></tr><tr><td>(3)</td><td>global</td><td>global</td><td>41.2 ± 0.8%</td><td>54.6 ± 0.7%</td><td>63.2 ± 0.9%</td></tr><tr><td>(4)</td><td>local</td><td>local</td><td>44.7 ± 1.1%</td><td>57.9 ± 0.5%</td><td>65.7 ± 1.4%</td></tr><tr><td>(5)</td><td>global</td><td>local</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td><td>69.4 ± 2.1%</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effects of larger memory banks. It has been shown in [21] that increasing the size of the memory bank can improve self-supervised representation learning. In our experiments, we set the memory sizes of $B _ { p }$ , $B _ { g }$ and $\\nu$ to 2048 for training efficiency. In table 6, we show the results by increasing the memory sizes. As can be seen, similar to [21], the memory size and the performance is positively correlated. With more instances or parts in the memory banks, more useful information can be used for mutual knowledge distillation $\\boldsymbol { B } _ { p }$ and $B _ { g . }$ ) and local part ranking statistics measure $( \\mathcal { V } )$ , thus improving the results. However, with a relatively small memory size of 2048, our method already achieves promising results. Note that due to the limited number of images in CUB-200 and Stanford-Cars, the performance boost with the increase of bank size for $B _ { p }$ and $B _ { g }$ quickly reaches a plateau. While for CIFAR-10 and ImageNet-100, more instances can be enqueued to foster the knowledge distillation. In terms of $\\nu$ , the performance is consistently improved with the increase of the size of $\\nu$ for all datasets. Due to the larger image resolution in CUB-200 and Stanford-Cars, more useful part features can be extracted from each image for local ranking statistics. Therefore, the performance is less affected by the smaller number of images. This further demonstrates the effectiveness of our local part-level ranking statistics. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Different sampling methods for memory bank $\\nu$ . The part memory bank $\\nu$ stores the part-level features for the local-comparison branch, and is updated in a FIFO manner. Here we compare different ways of maintaining $\\nu$ . Our default choice is to randomly sample one part-level feature from each image in a training mini-batch. However, random sampling may not select the most informative part-level features from the image, so an alternative is to select part-level features based on class-activation-map (CAM) [59]. Instead of random sampling, the part with the highest response is selected by CAM. Rather than sampling only a single part from each image, we can simply use all ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "(a) ACC with varying size for $\\boldsymbol { B } _ { p }$ and $B _ { g }$ . ",
+        "bbox": [
+            215,
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+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/fc2bafeaa300c483ebd03362d3e2039ddda0a27d655db646c07cdc13e899cbf0.jpg",
+        "table_caption": [
+            "Table 6: Increasing the size of memory bank. “SCars” denotes Stanford-Cars dataset; “IM-100” denotes ImageNet-100 dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Bank size</td><td>2048</td><td>4096</td><td>8192</td><td>16384</td><td>32768</td></tr><tr><td>CIFAR-10</td><td>91.6%</td><td>92.3%</td><td>92.4%</td><td>92.7%</td><td>93.0%</td></tr><tr><td>CUB-200</td><td>47.8%</td><td>48.3%</td><td>48.4%</td><td>48.5%</td><td>48.4%</td></tr><tr><td>SCars</td><td>61.9%</td><td>62.4%</td><td>62.8%</td><td>62.9%</td><td>62.9%</td></tr><tr><td>IM-100</td><td>69.4%</td><td>70.2%</td><td>70.8%</td><td>71.1%</td><td>71.3%</td></tr></table>",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/025db46b530927d0e3c11b150457758ca4dc93d6e3616eef1e0ee315c2fe7ed4.jpg",
+        "table_caption": [
+            "(b) ACC with varying size for $\\nu$ "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Bank size</td><td>2048</td><td>4096</td><td>8192</td><td>1638432768</td><td></td></tr><tr><td>CIFAR-10 91.6% 91.7%</td><td></td><td></td><td>91.7%</td><td>91.9%</td><td>92.0%</td></tr><tr><td>CUB-200 47.8% 48.5% 48.7% 49.2%</td><td></td><td></td><td></td><td></td><td>49.3%</td></tr><tr><td>SCars</td><td></td><td>61.9% 62.7% 63.4%</td><td></td><td>663.6%</td><td>63.7%</td></tr><tr><td>IM-100</td><td></td><td></td><td></td><td>69.4% 70.5% 71.2% 71.3% 71.4%</td><td></td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "the parts for each image. We compare these three different choices in table 7. It can be seen that using all the parts causes slight performance drop. This is reasonable because using all parts introduces redundancy in $\\nu$ , making the local comparison more prone to noise. On the other hand, selecting the most activated part using CAM shows a better performance than the random selection, indicating that more informative parts in the memory bank can enable better local comparison. As the gap is not significant, we use the random sampling as our default choice for its simplicity and efficacy. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/29d11cbaa2242712dfb7f757c488efd4ce68455692e3e87085322cd2154c07f8.jpg",
+        "table_caption": [
+            "Table 7: Effects of using different way to update $\\nu$ . “Random” means random part selection; “All” means using all parts; “CAM” means selecting the most activated parts using CAM [59]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CIFAR-100</td><td>ImageNet-100</td><td>CUB-200</td><td>Stanford-Cars</td></tr><tr><td>Random</td><td>75.3 ± 2.3%</td><td>69.4 ± 2.1%</td><td>47.8 ± 2.4%</td><td>61.9 ± 2.5%</td></tr><tr><td>All</td><td>76.0 ± 2.6%</td><td>68.7 ± 2.3%</td><td>46.5 ± 1.9%</td><td>61.0 ± 2.4%</td></tr><tr><td>CAM</td><td>76.5 ± 2.4%</td><td>70.3 ± 2.4%</td><td>48.5 ± 1.8%</td><td>62.4 ± 2.1%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Unknown number of novel classes. In a more realistic setting, the unlabelled class number $C ^ { u }$ may not be known. In this case, we can apply existing methods to estimate category number in the unlabelled data, such as the algorithm from DTC [20], before adopting our method. In table 8 we provide the results of novel category discovery using the estimated number of classes on CUB200/ImageNet-100 by DTC [20]. We denote the estimated class number as $\\hat { C } ^ { u }$ . As shown in table 8, with the estimated class number by DTC, our model also obtains a significantly better performance than RankStat [18]. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/ff9bd179749429918a4314b49197b8b6b86d1e1250b6c38e2cc98667c11956c3.jpg",
+        "table_caption": [
+            "Table 8: Results with estimated class numbers and ground truth class numbers. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">CUB-200</td><td colspan=\"2\">ImageNet-100</td></tr><tr><td>Class numbers</td><td>Cu = 40</td><td>Cu= 43</td><td>Cu = 30</td><td>Cu =32</td></tr><tr><td>RankStat [18]</td><td>39.5±1.7%</td><td>38.2±2.1%</td><td>66.3±0.7%</td><td>65.0±1.2%</td></tr><tr><td>Ours</td><td>47.8±2.4%</td><td>44.6±2.6%</td><td>70.4±0.9%</td><td>68.8±1.5%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Please refer to the supplementary for more results and analysis. Our code can be found at https: //github.com/DTennant/dual-rank-ncd. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We have introduced a two-branch learning framework for novel category discovery, with one branch focusing on local part-level information and the other branch focusing on overall characteristics. To transfer knowledge from labelled data to unlabelled data, we proposed to use local ranking statistics by maintaining a local part dictionary build on-the-fly for training, together with the global ranking statistics. We further introduced a mutual knowledge distillation method for information exchange and encouraging the agreement between the two branches. We thoroughly evaluated our method on generic image classification datasets as well as fine-grained recognition datasets, achieving state-of-the-art performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References ",
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