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+        "text": "Context Decoupling Augmentation for Weakly Supervised Semantic Segmentation",
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+        "text": "Yukun Su $^{1,2}$ , Ruizhou Sun $^{1,2}$ , Guosheng Lin $^{3\\dagger}$ , and Qingyao Wu $^{1,2\\dagger}$",
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+        "text": "$^{1}$ School of Software and Engineering, South China University of Technology",
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+        "text": "$^{2}$ Key Laboratory of Big Data and Intelligent Robot, Ministry of Education",
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+        "text": "$^{3}$ School of Computer Science and Engineering, Nanyang Technological University suyukun666@gmail.com, ruizhousun@foxmail.com, gslin@ntu.edu.sg, qyw@scut.edu.cn",
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+        "text": "Abstract",
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+        "text": "Data augmentation is vital for deep learning neural networks. By providing massive training samples, it helps to improve the generalization ability of the model. Weakly supervised semantic segmentation (WSSS) is a challenging problem that has been deeply studied in recent years, conventional data augmentation approaches for WSSS usually employ geometrical transformations, random cropping and color jittering. However, merely increasing the same contextual semantic data does not bring much gain to the networks to distinguish the objects, e.g., the correct image-level classification of \"aeroplane\" may be not only due to the recognition of the object itself, but also its cooccurrence context like \"sky\", which will cause the model to focus less on the object features. To this end, we present a Context Decoupling Augmentation (CDA) method, to change the inherent context in which the objects appear and thus drive the network to remove the dependence between object instances and contextual information. To validate the effectiveness of the proposed method, extensive experiments on PASCAL VOC 2012 and COCO datasets with several alternative network architectures demonstrate that CDA can boost various popular WSSS methods to the new state-of-the-art by a large margin. Code is available at https://github.com/suyukun666/CDA",
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Semantic segmentation is a foundation in the computer vision field, which aims to predict the pixel-wise classification of the images and it enjoys a wide range of applications. Recently, benefiting from the deep neural net",
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+        "image_caption": [
+            "Figure 1. Illustration of the difference between conventional augmentation approaches and our method. Classical data augmentation consists of generating images obtained by basic geometrical transformations or color changes of original training images. Context Decoupling Augmentation (CDA) aims to randomly paste the given object instances into the scenes, so as to decouple the inherent context position of the original objects in the image."
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+        "text": "works, modern semantic segmentation models [7, 8, 31, 33] have achieved remarkable progress with massive human-annotated labeled data. However, collecting pixel-level labels is very time-consuming and labor-intensive, which shifts much research attention to weakly supervised semantic segmentation (WSSS). There exist various types of weak supervision for semantic segmentation like using bounding boxes [10, 24], scribbles [30, 40], points [4], and image-level labels [21, 2, 1, 43, 50]. Among them, image-level class labels have been widely used since they demand the least annotation efforts and are already provided in existing large-scale image datasets.",
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+        "text": "In this paper, we focus on augmentation for WSSS with",
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+        "text": "†Corresponding authors.",
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+    {
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+        "text": "image-level labels, which is crucial for deep learning networks. As shown in Figure 1 upper part, given a training image, traditional data augmentation methods utilize some geometrical transformations, such as rotation, scaling, flipping, and even some color conversions to increase the diversity of images to avoid overfitting. However, for weakly supervised semantic segmentation, adjusting the image as a whole and maintain the same contextual semantic relation will not significantly help the networks to mine the object areas. For example, \"sofa\" always appears in the room in the datasets, therefore, the trained network may not only recognize the objects depending on the instance features but also their co-occurrence context information [29]. Specifically, when object instances often appear at the same time with some accompanying backgrounds, it will cause the networks to yield confounding bias. Namely, the networks can perform classification task well is not due to successfully distinguishing the characteristics of objects, but to being aware of the appearance of certain contextual semantic information, which is harmful to mine the object regions.",
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+        "text": "Based on this observation, we propose a Context Decoupling Augmentation (CDA) method, designing for disassembling the inherent contextual information of the original image. As shown in Figure 1 bottom half, the \"cat\" shows in the \"sky\", and the \"sofa\" falls on the \"road\". Although some of these scene collocations rarely appear in life, the models can pay more attention to the objects corresponding to the classification labels. Unlike the fully-supervised data augmentation approaches [13], we cannot access the object instance labels to extract the objects under the weakly supervised setting. Therefore, we first adopt off-the-shelf WSSS approaches to obtain the object instances that have been well-segmented. Secondly, we randomly paste the selected foreground instances into the input images to get the new enhanced images and put them into the model for training together with the original ones without augmentation. In this way, we can break the dependency between objects and contextual background, and the models will focus on the internal information of the foreground instances rather than the context information to predict the categories they belong to. Besides, we use an online training technique to conduct data augmentation, which means that the combination of the raw input images and the object instances to be pasted are different each time. This greatly increases the diversity of combinations of various scenes and object instances, and thus enhance the decoupling capability of the networks.",
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+        "text": "In the proposed context decoupling augmentation framework, we utilize different WSSS networks as our baselines. To verify the effectiveness of our proposed method, extensive experiments show that CDA can improve pseudomasks more than  $2.8\\%$  mIoU on average. We achieve new state-of-the-art performance by  $66.1\\%$  mIoU on the",
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+        "text": "val set and  $66.8\\%$  mIoU on the test set of PASCAL VOC 2012 [15], and  $33.7\\%$  mIoU on the val set of COCO [32]. The main contributions of our paper can be summarized as follows:",
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+            "- We present a generally applicable data augmentation approach for weakly supervised semantic segmentation, which, to the best of our knowledge, has not been well explored.",
+            "- The proposed context decoupling augmentation (CDA) method does not require additional data and it can remove the correlation between foreground object instances and background context information, which can drive the network focus on object regions rather than the background.",
+            "- Experiments on PASCAL VOC 2012 and COCO show the effectiveness of our proposed method and CDA can boost the performance of different WSSS methods to the new state-of-the-art by a large margin."
+        ],
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+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "2.1.WSSS",
+        "text_level": 1,
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+    {
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+        "text": "Image labels as the weak supervision for segmentation have been widely studied in the past few years. Many approaches [44, 2, 1] use CAM [51] to mine the object seed regions by predicting image labels. To solve the problem that only the discriminative regions can be highlighted, researchers designed to expand the object seed regions in various ways. For example, in [47], the target regions are expanded by fusing different discriminative regions generated by convolutional layers with different expansion rates. [44] drives the network to learn the rest parts of the objects by iteratively erasing the target areas. In addition, some previous works [21, 22] use additional data, such as videos and saliency maps, to explore the objects areas.",
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+        "type": "text",
+        "text": "Although object expansion technologies emerge endlessly, they all use CAM [51] as the cornerstone. The effect of subsequent diffusion depends on the first step of the CAM learning features. As only image-level labels are provided, when objects are closely coupled with contextual backgrounds, such as \"boat\" and \"water\", \"aeroplane\" and \"sky\", \"train\" and \"track\", CAM will mistakenly recognize the background together with foreground objects. As mentioned in [29], the training networks have no incentive to focus attention only on the foreground class as there may be bias towards other contextual factors as a distractor with high correlation. Thus, this is an issue that's worth thinking about and that needs to be solved.",
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+        "type": "text",
+        "text": "2.2. Data Augmentation",
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+        "text": "Data augmentation is a major trick to train deep neural networks, which aims to increase the diversity of the data",
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+        "image_caption": [
+            "Figure 2. Overview of the proposed augmentation scheme. Stage-I: use the off-the-shelf weakly supervised semantic segmentation methods to obtain some simple object instances with good segmentation. Stage-II: paste the object instances randomly into the raw images to form the new input images, and perform online data augmentation training in a pairwise way with the original input images."
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+        "type": "text",
+        "text": "by increasing the training samples and avoid overfitting to a certain extent. Conventional data augmentation approaches perform a series of operations on the basic data, such as rotation, flipping, adding Gaussian noise, etc. Some works have explored synthesizing training data [17, 35] for further generalizability. Generating new training samples by Stylizing ImageNet [18] can lead to better classification performances. Recently, GAN [52] has been employed to transfer the style of the images and to make the content of the images from one domain to another, which can enrich the semantic information of the images to train the deep neural networks. Furthermore, [49] introduced a method to mix two random samples and divide the classification results proportionally to enhance images. [12] conducted augmentation by randomly cutting out some areas in the sample and filled it with 0 pixel value, and keep the result of classification unchanged.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For object detection and segmentation, a popular data augmentation way is \"copy-and-paste\" [13, 14]. These works pasted real segmented objects into natural images, which is beneficial to increase the object complexity of the internal images and can help to solve the problem of small target detection. However, obtaining these segmented objects requires pixel-wise instance labels. [36] used box-supervision and the off-the-shelf faster-RCNN [37] method to segment and generate masks via cut-and-paste. [3] adopted the unsupervised cut-and-paste learning method to",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "generate new combined images, but this kind of method is only applicable to the image of single object. It is the first time that we employ copy-and-paste in the WSSS field and it does not require the help of pixel-wise labels and other auxiliary approaches. Thus, for WSSS, such a data augmentation scheme is significant and has not been well explored.",
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+    },
+    {
+        "type": "text",
+        "text": "3. Framework",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our approach mainly consists of two stages: (1) we first collect the easy examples of well-segmented objects by using off-the-shelf WSSS methods; (2) then we train the network in a pairwise manner with online augmentation. In this section, we will describe these two stages in details.",
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+    {
+        "type": "text",
+        "text": "3.1. Object Instances Collecting",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "We aim to apply data augmentation on one of the WSSS models (i.e., IRNet [1]). To some extent, the WSSS method can successfully predict good masks for some easy objects with class labels. Therefore, as shown in Figure 2, in the first stage, we train the original network and we are able to select qualified object instances through the scene complexity of the image, the scope of the object and the semantic relevance by setting some criteria.",
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+    {
+        "type": "text",
+        "text": "Specifically, for the inferring phase after training the network, we follow two main criteria for collecting object instances: (i) the current image should only have a single",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/8ff2c6873eea62cdb3dcaa0e832a23a2f00e1e07964a17f609897ce8ed0ce9e9.jpg",
+        "image_caption": [
+            "Figure 3. Different kinds of pasting methods used in experiments. (a) Raw input, (b) Random rescale pasting, (c) Random rescale + rotation pasting, (d) Random rescale + rotation + Gaussian smoothing pasting."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "class. The intuition behind this is that in the case of only a single class, the image information should be simple and without a complex semantic environment, the segmentation results of the model should be more accurate; (ii) the segmentation result of the current image should meet the condition,  $\\epsilon_1 < \\frac{m}{n} < \\epsilon_2$ , where  $\\epsilon_1$  and  $\\epsilon_2$  are two threshold factors, respectively.  $m$  is the number of pixels belonging to the foreground object,  $n$  is the number of pixels of the entire image. The reason lies that if the scale value of  $\\frac{m}{n}$  is too large, it should be that the background is incorrectly identified as the foreground. In contrast, if the scale value is too small, it should be that the model has not been able to recognize enough foreground object pixel information. Different from existing synthesis approaches [13, 14], our method is based on self-provided masks to obtain qualified object instances images.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Online Augmentation Training",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Blending. Before we take a step to train the network in the second stage, we first introduce how to blend the object instances into the natural images. As shown in Figure 3, we show different types of pasting skills in our experiments. It's worth mentioning that we only paste objects that have not appeared in the original images. The significance of this is that we can increase the diversity of objects of the images, while also reducing the dependence of the same objects in the inherent scene. By randomly rescaling the objects, we can paste them into the images appropriately to prevent them from being too large or too small. The addition of random rotation can change the inherent orientation properties of the objects. Adding Gaussian smoothing can help the added objects boundary blend more naturally.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In some cases, the blending may not be ideal, we elaborate on several possibilities for random pasting. As shown in Figure 4, we have listed several augmented images of random pasting and we call them \"perfect\", \"good\" and \"noise\" examples. As for the \"good\" example, the new object \"bird\" covers part of the \"dog\" in the original image, however, we argue that this could help to erase the discriminative regions and force the network to discover more object regions like the function in [44]. The noise example shows that the",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e94b503f8e97b5f5bfc6f5753253b75aa354fb452481be23d233e7160e7d1812.jpg",
+        "image_caption": [
+            "(a) perfect"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/532b965eb88241768233cac61775e4ebb1602af9667f24c13a17c0f9f03665a5.jpg",
+        "image_caption": [
+            "(b) good"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            90,
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+            190
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/9650832bdc63a7b09bbd44a2b3fc06ee888601bba252c29b5c7dd83227432b6f.jpg",
+        "image_caption": [
+            "(c) noise"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4bd65e7b9983c3b1a30aadd31f8a58642ea57a7d77660881fdb940eb2d5d2d78.jpg",
+        "image_caption": [
+            "Figure 4. Examples of the input augmented images with varying degrees of occlusion."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "\"sofa\" completely covers the \"aeroplane\" in the original image, which will cause confusion to network classification. However, we consider that such hard examples do not account for the majority. Most objects occupy in the middle or prominent location of the natural images. The random blending method we employ tends to paste the new objects into the off-center position of the images. Thus, this case does not affect learning. Hence, our framework is robust to the quality of augmentation. According to our experiments, this simple random blending method performs well in boosting the performance.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Online Training. The augmentation scheme is conducted online to enhance the network trained in stage-I to improve the ability to distinguish object features. Formally, in each batch, we sample  $N / 2$  images from the training dataset and the same number object instances images from the subset which is provided from stage-I. Then we randomly paste the segmented objects into the input images, which creates a  $N / 2$  batch new images. Thus, a batch of size  $N$  is generated online for each augmentation iteration. The construction process of the online augmentation learning is summarized in Algorithm 1.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that we train the online augmentation method in a pairwise manner as shown in Figure 2 stage-II left. We consider this can further help the networks to recognize the objects for the reason that some images have new blended objects, while some do not, which can help the classifier find more discriminative features. The motivation behind this is similar to \"finding the differences\" with the human visual system. When the two images have a different object but with a duplicated background, which can often leave a deep impression. For the same reason, this can make the network classifier learn better features of this kind of object.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Stage-II: Online Augmentation."
+        ],
+        "code_body": "Input: The training dataset images  $\\mathcal{I}$  and the corresponding labels  $\\mathcal{L}$ ; The object instances  $\\mathcal{O}$  and the corresponding labels  $\\mathcal{T}$ .  \n1: while not done do  \n2:  $(\\mathcal{I}_i, \\mathcal{L}_i) \\gets$  Draw one sample from training dataset;  \n3:  $(\\mathcal{O}_j, \\mathcal{T}_j) \\gets$  Draw one sample from object instances subset;  \n4: while  $\\mathcal{T}_j$  in  $\\mathcal{L}_i$  do  \n5:  $(\\mathcal{O}_j, \\mathcal{T}_j) \\gets$  Resample;  \n6: end while  \n7:  $\\mathcal{I}_i' \\gets$  Blend  $\\mathcal{O}_j$  into  $\\mathcal{I}_i$ ;  \n8:  $\\mathcal{L}_i' \\gets$  Append  $\\mathcal{T}_j$  in  $\\mathcal{L}_i$ ;  \n9: Train CAM  $\\leftarrow$  Loss( $\\mathbb{C}(\\mathcal{I}_i), \\mathcal{L}_i)$  + Loss( $\\mathbb{C}(\\mathcal{I}_i')$ ,  $\\mathcal{L}_i'$ );  \n10: end while  \n11: Expansion.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Discussion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The proposed CDA framework contributes a new data augmentation learning strategy. Unlike the previous \"copy-and-paste\" works, we do not use additional pixel-wise labels. Specifically, by using the self-provided initial segmentation masks of the models, we can obtain the object instances for the next phase augmentation training. Furthermore, since our goal is to decouple the high correlation between objects and their contextual background, we don't need to consider much about visual context [13, 9], which can greatly improve the efficiency of pasting objects into the images. Besides, we adopt online augmentation training skills. Compared with static offline data augmentation, which merely enlarges the scale of the training dataset in linear-level. Namely, once a new dataset is formed, the number of images will remain unchanged. However, our method is able to obtain exponential-level augmentation, because the combination of object instances and natural images can be ever-changing in each round of training.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the contributions of the proposed method, we conduct several ablation studies to show the effectiveness of CDA and compare different baselines models to the state-of-the-arts. We will give the details of the datasets, evaluation metric, and baseline models in the following.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Dataset",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All the networks in our framework are trained and evaluated on the PASCAL VOC 2012 [15] and COCO [32] segmentation benchmark for a fair comparison to previous",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "approaches. As for PASCAL VOC, the official dataset separation has 1464 images for training, 1449 for validation and 1456 for testing. Following the common practice, we take additional annotations to build an augmented training set with 10582 images presented in [19]. COCO is a more challenging benchmark with 81 semantic classes (one background class), 80k, and 40k images for training and validation. We use the standard mean Intersection-over-Union (mIoU) as the evaluation metric for all experiments.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            500,
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+    },
+    {
+        "type": "text",
+        "text": "To validate the applicability of CDA, we deploy it on three popular WSSS models including IRNet [1], AffinityNet [2] and SEAM [43]. The general training architecture components include a multi-label image classification step, a pseudo-mask generation step, and the final segmentation model (DeepLab-v2 [7]). We strictly follow the same settings as reported in the official codes. Specially, for SEAM [43] and AffinityNet [2] baselines, ResNet38 [20] that pre-trained on ImageNet [11] is adopted as backbone with batch size as 8 and 16, respectively. When training the networks, multi-scale and data augmentation techniques like horizontal flip, random cropping, and color jittering are deployed in both architectures. Following the poly policy  $lr_{init} = lr_{init}(1 - itr / max\\_ itr)^{\\rho}$  with  $\\rho = 0.9$  for decay, the models are trained with a fix input size as  $448 \\times 448$  using Adam optimizer [25]. Besides, online hard example mining [39] is employed on the training loss in SEAM. As for IRNet [1], ResNet50 [20] is used as the backbone network (pretrained on ImageNet). The batch size is set to 16 for the image classification model and 32 for the inter-pixel relation model. The input image is cropped into a fix size of  $512 \\times 512$  using zero padding if needed. The model is trained with the same polynomial decay strategy as in AffinityNet [2] using stochastic gradient descent (SGD) for optimization with 8,000 iterations. The fully-connected CRF [27] is used in three baselines to refine CAM, pseudo-mask, and segmentation mask with the default parameters in the public code. We set the threshold  $\\epsilon_1 = 0.1$  and  $\\epsilon_2 = 0.7$  by experience.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To verify the effectiveness of our CDA, we evaluate CAM seed regions, pseudo-masks, and segmentation masks, respectively. In our experiments, the standard mean Intersection over Union (mIoU) is used on the training set for evaluating CAM seed area masks and pseudo-masks, and on the PASCAL VOC 2012 val and test sets for evaluating segmentation masks. For the sake of simplicity, since the three WSSS models are all based on CAM [51], we use one of the representative models (IRNet [1]) as a baseline to conduct several ablation studies on CAM in mIoU to illustrate the role of each component of our approach.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Random pasting vs. Other sophisticated augmenta",
+        "bbox": [
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+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/332f02ed8c691b0d922b55d6ee79cc1bfeb8cb7d73d14e262765f02b52e546e2.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>operation</td><td>mIoU (%)</td></tr><tr><td rowspan=\"2\">Conventional Augmentation</td><td>Rotation</td><td>48.5</td></tr><tr><td>Translation</td><td>48.4</td></tr><tr><td rowspan=\"3\">Mixup [49]</td><td>α = 0.3</td><td>48.7</td></tr><tr><td>α = 0.5</td><td>48.5</td></tr><tr><td>α = 0.8</td><td>49.0</td></tr><tr><td>CutOut [12]</td><td>Random</td><td>48.9</td></tr><tr><td>CutMix [48]</td><td>Random</td><td>49.2</td></tr><tr><td>Random pasting (ours)</td><td>Rescale</td><td>49.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b4cfb342d3dcfaea487689b30842ce9903ed829cc1b2a784fa00ae2c492ddd39.jpg",
+        "table_caption": [
+            "Table 1. Experiments of different augmentation methods. Here  $\\alpha$  is the intensity of the interpolation between the eigenvector and the target vector."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Baseline</td><td>Rescale</td><td>Rotation</td><td>Gaussian</td><td>mIoU (%)</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>48.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>49.8</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>50.8</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>49.6</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>50.4</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/767c15451922d1decb8a631bdc8504a42fc990cd880f289b9121d6cc76188e33.jpg",
+        "table_caption": [
+            "Table 2. The ablation study of the effect on different pasting methods. Baseline indicates the original CAM method without pasting new objects for augmentation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Training manner</td><td>mIoU (%)</td></tr><tr><td>Pairwise</td><td>50.8</td></tr><tr><td>None-pairwise</td><td>50.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Experiments of augmentation training manner.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tion methods: As for the traditional augmentation methods, we adopt the random rotation and translation to expand the dataset to three times the original size, however, they can not bring significant boost for the performance. We also compare Mixup [49], CutOut [12] and CutMix [48] methods to generate new augmented images. As shown in Table 1, random rescale pasting outperforms the other three methods achieving  $49.8\\%$  mIoU. These results demonstrate that random pasting is suitable for our CDA framework. We consider that proper occlusion helps the network to better mine the features of other areas of the objects, and the situation of complete occlusion is relatively rare which will not affect our learning process.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparison with baseline: We further explore the impact of different pasting methods on data augmentation. Table 2 shows that using random rescale pasting has a  $1.5\\%$  improvement compared to baseline. After combining rescale and rotation, we can get the best performance to  $50.8\\%$  mIoU on PASCAL VOC training set. The results show that applying Gaussian smoothing can not help to im",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/846acbf57d09529da8e73a05cf4b494d94e8874d5dd9efaae16a1238dc6d8003.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative visualization of CAMs. Our CDA framework not only suppresses over-activation  $(1^{st},2^{nd},3^{rd}$  row) of the high correlation contextual backgrounds of the objects and expands CAMs to cover the whole object regions  $(4^{th}$  row)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "prove the performance. Therefore, in subsequent experiments, unless otherwise specified, we will use the random rescale combining with the rotation method.",
+        "bbox": [
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+            518,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 shows the qualitative comparison between our CAM+Aug by CDA method and the original CAM. As shown in the first and second rows in the figure and the labels of objects are \"table\". The original CAM will activate background semantic information that is strongly related to the \"table\", such as \"chair\". However, by employing the decoupling augmentation training strategy, our method can focus on the target areas. For the image with the label of \"train\", CAM even pays attention not to the object itself, but the \"track\", which will be detrimental to the subsequent segmentation task. Moreover, CDA can also help the network expand and discover more comprehensive object features but not only the most discriminative regions like the \"cat\" shown in the last row.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The effect on pairwise training: Compared to merely using the augmented images to train the networks, we use the none-augmented images with the augmented images as pair images to jointly train the models as shown in Figure 2 stage-II. The results shown in Table 3 show that applying pairwise training strategy outperforms the one in single augmented images, which illustrates that this helps the network classifier to learn more discriminative features.",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/de6410bafd1311f8116546bc444bd81e206e89e80663ae8ec439b27e11017cc6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Network</td><td>Backbone</td><td>CAM</td><td>Pseudo-Masks</td><td>Seg. Masks (val-set)</td><td>Seg. Masks (test-set)</td></tr><tr><td rowspan=\"2\">AffinityNet [2] + CDA</td><td>ResNet-38</td><td>48.0</td><td>59.7</td><td>61.7</td><td>63.7</td></tr><tr><td>ResNet-38</td><td>48.9+0.9</td><td>63.3+3.6</td><td>64.2+2.5</td><td>65.8+2.1</td></tr><tr><td rowspan=\"2\">IRNet* [1] + CDA</td><td>ResNet-50</td><td>48.3</td><td>65.9</td><td>63.5</td><td>64.8</td></tr><tr><td>ResNet-50</td><td>50.8+2.5</td><td>67.7+1.8</td><td>65.8+2.3</td><td>66.4+1.6</td></tr><tr><td rowspan=\"2\">SEAM [43] + CDA</td><td>ResNet-38</td><td>55.4</td><td>63.4</td><td>64.5</td><td>65.7</td></tr><tr><td>ResNet-38</td><td>58.4+3.0</td><td>66.4+3.0</td><td>66.1+1.6</td><td>66.8+1.1</td></tr></table>",
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+        "table_caption": [
+            "Table 4. Different baselines with our CDA framework performance in mIoU on PASCAL VOC. *denotes our reimplemented results since the original code does not provided pre-trained weights."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Number of pasted objects</td><td>Same category objects</td><td>mIoU (%)</td></tr><tr><td>1</td><td>×</td><td>50.8</td></tr><tr><td>2</td><td>×</td><td>48.9</td></tr><tr><td>3</td><td>×</td><td>47.8</td></tr><tr><td>1</td><td>✓</td><td>50.2</td></tr><tr><td>2</td><td>✓</td><td>48.6</td></tr><tr><td>3</td><td>✓</td><td>47.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 5. Experiments of different number of pasted objects for augmentation.",
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+        "type": "text",
+        "text": "The effect on objects numbers: Under the default settings of our experiment, we only paste one new instance that does not exist in the original images. We further explore the effect of pasting multiple objects into the images to conduct augmentation. As shown in Table 5 above the solid line, when the number of object to be pasted increases from one to two, the mIoU performance will decrease. As the number of pasted objects changes to three, it will even worse than the baseline. The results show that over-pasted objects may cover the objects in the original image, making the noise sample dominant. This will confuse the classifier, which will bring negative effects. In addition, as depicted below the solid line in Table 5, when we allow the pasted object to be consistent with the object category in the original image, their general performance is worse than the former. This shows that forcing objects of different categories to be pasted into images can decouple the strong contextual dependence of objects in the original semantic environment.",
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+    {
+        "type": "text",
+        "text": "Analysis of pseudo labels and Segmentation masks: The overall results are shown in Table 4. We can observe that deploying CDA on different weakly supervised semantic segmentation models can improve all their performances. Specifically, SEAM [43] can achieve the best performance in Segmentation Masks on both validation set and testing set. Figure 6 shows that we can obtain more accurate and complete masks covering the object areas.",
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+    {
+        "type": "text",
+        "text": "4.4. Comparison with State-of-the-arts",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Finally, we compare our framework with state-of-the-art methods on the PASCAL VOC 2012 and COCO dataset in",
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+    {
+        "type": "image",
+        "img_path": "images/35a900d5d7e679cbeee2d9615b3b670696e2e2df8225add27d1a51f99f645573.jpg",
+        "image_caption": [
+            "Figure 6. Visualization of pseudo-masks (baseline: IRNet [1]). (a) Input images. (b) Ground-Truth labels. (c) Our CAM+Aug. (d) Original CAM."
+        ],
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+    {
+        "type": "text",
+        "text": "cluding both the validation set and the testing set. For a fair comparison, we adopt the same DeepLab [6, 7] architectures as reported in the original papers. On PASCAL VOC 2012, as is shown in Table 6, although different baselines already boosts performance compared to previous methods, when CDA is deployed in the models, SEAM [43] can achieve the best performance and outperform other state-of-the-arts by a large margin. IRNet [1] yield the second best performance and can beat its later published works. On COCO, CDA deployed on IRNet achieves  $33.7\\%$  mIoU on the val set, which surpasses the previous best model by  $1.1\\%$  mIoU. Figure 7 presents qualitative results of our CDA approach applying on IRNet baseline and compares them to itself. We can observe that CDA can make more accurate predictions on objects, which shows better demarcations in some coherent areas. Meanwhile, CDA can help to expand and discover more comprehensive object regions.",
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+    {
+        "type": "image",
+        "img_path": "images/da786e716fa7473f9651fb5bd513816e394a0c9dc93929be113165ab64d6a4d9.jpg",
+        "image_caption": [
+            "(a)",
+            "Figure 7. Qualitative results on the PASCAL VOC 2012 val set. (a) Input images. (b) Ground-truth labels. (c) Results obtained by IRNet [1] baseline. (d) Results of our IRNet + CDA. More results can be found in the supplementary material."
+        ],
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+        "type": "table",
+        "img_path": "images/4cdecb4225c098c0c2c37eef1f6cee20a8618129b53bef4dee70a4de65f0bd04.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Backbone</td><td>Saliency</td><td>val</td><td>test</td></tr><tr><td>CCNN [34]ICCV&#x27;15</td><td>VGG16</td><td>-</td><td>35.3</td><td>35.6</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>-</td><td>50.7</td><td>51.1</td></tr><tr><td>STC [45]TPAMI&#x27;17</td><td>VGG16</td><td>✓</td><td>49.8</td><td>51.2</td></tr><tr><td>AdvEra [44]CVPR&#x27;17</td><td>VGG16</td><td>✓</td><td>55.0</td><td>55.7</td></tr><tr><td>DCSP [5]BMVC&#x27;17</td><td>ResNet101</td><td>✓</td><td>60.8</td><td>61.9</td></tr><tr><td>MDC [46]CVPR&#x27;18</td><td>VGG16</td><td>✓</td><td>60.4</td><td>60.8</td></tr><tr><td>MCOF [42]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>60.3</td><td>61.2</td></tr><tr><td>DSRG [23]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>61.4</td><td>63.2</td></tr><tr><td>AffinityNet [2]CVPR&#x27;18</td><td>ResNet-38</td><td>-</td><td>61.7</td><td>63.7</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>-</td><td>63.5</td><td>64.8</td></tr><tr><td>FickleNet [28]CVPR&#x27;19</td><td>ResNet101</td><td>✓</td><td>64.9</td><td>65.3</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>-</td><td>64.5</td><td>65.7</td></tr><tr><td>ICD [16]CVPR&#x27;20</td><td>ResNet101</td><td>-</td><td>64.1</td><td>64.3</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>-</td><td>65.8</td><td>66.4</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>-</td><td>66.1</td><td>66.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a Context Decoupling Augmentation (CDA) method for WSSS and to narrow the gap with fully supervision. Specifically, through a two-stage training, the object instances provided by the network itself are copied and pasted into the input images to conduct augmentation. To further improve the ability of network for",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a8414ea5f113679d2f3fdf2811476bee8e9cd75456a43c28bba6af2eb76deb42.jpg",
+        "table_caption": [
+            "Table 6. Performance comparisons with other state-of-the-art WSSS methods on PASCAL VOC 2012 dataset. The best and second best performance under each set are marked with corresponding formats."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Backbone</td><td>val</td></tr><tr><td>BFBP [38]ECCV&#x27;16</td><td>VGG16</td><td>20.4</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>22.4</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>32.6</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>31.9</td></tr><tr><td>IAL [41]IJCV&#x27;20</td><td>VGG16</td><td>27.7</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>33.7</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>33.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 7. Performance comparisons with other state-of-the-art WSSS methods on COCO val in terms of mIoU.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "learning object features, we adopt pairwise training manner to help the classifier to distinguish more discriminative features. Experimental results show that CDA can help boost various WSSS methods to the new state-of-the-arts.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            500,
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported by National Natural Science Foundation of China (NSFC) 61876208, Key-Area Research and Development Program of Guangdong Province 2018B010108002, Central Universities of China under Grant D2192860, and the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG-RP-2018-003), and the MOE Tier-1 research grants: RG28/18 (S), RG22/19 (S) and RG95/20.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2209-2218, 2019. 1, 2, 3, 5, 7, 8",
+            "[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4981-4990, 2018. 1, 2, 5, 7, 8",
+            "[3] Relja Arandjelović and Andrew Zisserman. Object discovery with a copy-pasting gan. arXiv preprint arXiv:1905.11369, 2019. 3",
+            "[4] Amy Bearman, Olga Russakovsky, Vittorio Ferrari, and Li Fei-Fei. What's the point: Semantic segmentation with point supervision. In European conference on computer vision, pages 549-565. Springer, 2016. 1",
+            "[5] Arslan Chaudhry, Puneet K Dokania, and Philip HS Torr. Discovering class-specific pixels for weakly-supervised semantic segmentation. arXiv preprint arXiv:1707.05821, 2017. 8",
+            "[6] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv preprint arXiv:1412.7062, 2014. 7",
+            "[7] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4):834-848, 2017. 1, 5, 7",
+            "[8] 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. 1",
+            "[9] Wenqing Chu and Deng Cai. Deep feature based contextual model for object detection. Neurocomputing, 275:1035-1042, 2018. 5",
+            "[10] Jifeng Dai, Kaiming He, and Jian Sun. Boxsup: Exploiting bounding boxes to supervise convolutional networks for semantic segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1635-1643, 2015. 1",
+            "[11] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. IEEE, 2009. 5",
+            "[12] Terrance DeVries and Graham W Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552, 2017. 3, 6",
+            "[13] Nikita Dvornik, Julien Mairal, and Cordelia Schmid. Modeling visual context is key to augmenting object detection datasets. In Proceedings of the European Conference on Computer Vision (ECCV), pages 364-380, 2018. 2, 3, 4, 5"
+        ],
+        "bbox": [
+            78,
+            114,
+            470,
+            898
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[14] Debidatta Dwibedi, Ishan Misra, and Martial Hebert. Cut, paste and learn: Surprisingly easy synthesis for instance detection. In Proceedings of the IEEE International Conference on Computer Vision, pages 1301-1310, 2017. 3, 4",
+            "[15] Mark Everingham, SM Ali Eslami, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The Pascal visual object classes challenge: A retrospective. International journal of computer vision, 111(1):98-136, 2015. 2, 5",
+            "[16] Junsong Fan, Zhaoxiang Zhang, Chunfeng Song, and Tieniu Tan. Learning integral objects with intra-class discriminator for weakly-supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4283-4292, 2020. 8",
+            "[17] Maayan Frid-Adar, Eyal Klang, Michal Amitai, Jacob Goldberger, and Hayit Greenspan. Synthetic data augmentation using gan for improved liver lesion classification. In 2018 IEEE 15th international symposium on biomedical imaging (ISBI 2018), pages 289–293. IEEE, 2018. 3",
+            "[18] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A Wichmann, and Wieland Brendel. Imagenet-trained cnns are biased towards texture; increasing shape bias improves accuracy and robustness. arXiv preprint arXiv:1811.12231, 2018. 3",
+            "[19] Bharath Hariharan, Pablo Arbeláez, Lubomir Bourdev, Subhransu Maji, and Jitendra Malik. Semantic contours from inverse detectors. In 2011 International Conference on Computer Vision, pages 991–998. IEEE, 2011. 5",
+            "[20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 5",
+            "[21] Seunghoon Hong, Donghun Yeo, Suha Kwak, Honglak Lee, and Bohyung Han. Weakly supervised semantic segmentation using web-crawled videos. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7322-7330, 2017. 1, 2",
+            "[22] Qibin Hou, PengTao Jiang, Yunchao Wei, and Ming-Ming Cheng. Self-erasing network for integral object attention. In Advances in Neural Information Processing Systems, pages 549–559, 2018. 2",
+            "[23] Zilong Huang, Xinggang Wang, Jiasi Wang, Wenyu Liu, and Jingdong Wang. Weakly-supervised semantic segmentation network with deep seeded region growing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7014-7023, 2018. 8",
+            "[24] Anna Khoreva, Rodrigo Benenson, Jan Hosang, Matthias Hein, and Bernt Schiele. Simple does it: Weakly supervised instance and semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 876-885, 2017. 1",
+            "[25] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 5",
+            "[26] Alexander Kolesnikov and Christoph H Lampert. Seed, expand and constrain: Three principles for weakly-supervised image segmentation. In European conference on computer vision, pages 695-711. Springer, 2016. 8"
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            900
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[27] Philipp Krahenbuhl and Vladlen Koltun. Efficient inference in fully connected crfs with gaussian edge potentials. In Advances in neural information processing systems, pages 109-117, 2011. 5",
+            "[28] Jungbeom Lee, Eunji Kim, Sungmin Lee, Jangho Lee, and Sungroh Yoon. Ficklenet: Weakly and semi-supervised semantic image segmentation using stochastic inference. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5267-5276, 2019. 8",
+            "[29] Kunpeng Li, Ziyan Wu, Kuan-Chuan Peng, Jan Ernst, and Yun Fu. Tell me where to look: Guided attention inference network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9215-9223, 2018. 2",
+            "[30] Di Lin, Jifeng Dai, Jiaya Jia, Kaiming He, and Jian Sun. Scribblesup: Scribble-supervised convolutional networks for semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3159-3167, 2016. 1",
+            "[31] Guosheng Lin, Chunhua Shen, Anton Van Den Hengel, and Ian Reid. Efficient piecewise training of deep structured models for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3194-3203, 2016. 1",
+            "[32] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dálár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 2, 5",
+            "[33] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3431-3440, 2015. 1",
+            "[34] Deepak Pathak, Philipp Krahenbuhl, and Trevor Darrell. Constrained convolutional neural networks for weakly supervised segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1796-1804, 2015. 8",
+            "[35] Xingchao Peng, Baochen Sun, Karim Ali, and Kate Saenko. Learning deep object detectors from 3d models. In Proceedings of the IEEE International Conference on Computer Vision, pages 1278-1286, 2015. 3",
+            "[36] Tal Remez, Jonathan Huang, and Matthew Brown. Learning to segment via cut-and-paste. In Proceedings of the European conference on computer vision (ECCV), pages 37-52, 2018. 3",
+            "[37] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. arXiv preprint arXiv:1506.01497, 2015. 3",
+            "[38] Fatemehsadat Saleh, Mohammad Sadegh Aliakbarian, Mathieu Salzmann, Lars Petersson, Stephen Gould, and Jose M Alvarez. Built-in foreground/background prior for weakly-supervised semantic segmentation. In European conference on computer vision, pages 413-432. Springer, 2016. 8",
+            "[39] Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In Proceedings of the IEEE conference on"
+        ],
+        "bbox": [
+            78,
+            90,
+            470,
+            900
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "computer vision and pattern recognition, pages 761-769, 2016.5",
+            "[40] Paul Vernaza and Manmohan Chandraker. Learning random-walk label propagation for weakly-supervised semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7158-7166, 2017. 1",
+            "[41] Xiang Wang, Sifei Liu, Huimin Ma, and Ming-Hsuan Yang. Weakly-supervised semantic segmentation by iterative affinity learning. International Journal of Computer Vision, 128(6):1736-1749, 2020. 8",
+            "[42] Xiang Wang, Shaodi You, Xi Li, and Huimin Ma. Weakly-supervised semantic segmentation by iteratively mining common object features. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1354-1362, 2018. 8",
+            "[43] Yude Wang, Jie Zhang, Meina Kan, Shiguang Shan, and Xilin Chen. Self-supervised equivariant attention mechanism for weakly supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12275–12284, 2020. 1, 5, 7, 8",
+            "[44] Yunchao Wei, Jiashi Feng, Xiaodan Liang, Ming-Ming Cheng, Yao Zhao, and Shuicheng Yan. Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1568-1576, 2017. 2, 4, 8",
+            "[45] Yunchao Wei, Xiaodan Liang, Yunpeng Chen, Xiaohui Shen, Ming-Ming Cheng, Jiashi Feng, Yao Zhao, and Shuicheng Yan. Stc: A simple to complex framework for weakly-supervised semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(11):2314-2320, 2016. 8",
+            "[46] Yunchao Wei, Huaxin Xiao, Honghui Shi, Zequn Jie, Jiashi Feng, and Thomas S Huang. Revisiting dilated convolution: A simple approach for weakly-and semi-supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7268-7277, 2018. 8",
+            "[47] Fisher Yu and Vladlen Koltun. Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122, 2015. 2",
+            "[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023-6032, 2019. 6",
+            "[49] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 3, 6",
+            "[50] Tianyi Zhang, Guosheng Lin, Weide Liu, Jianfei Cai, and Alex Kot. Splitting vs. merging: Mining object regions with discrepancy and intersection loss for weakly supervised semantic segmentation. In European Conference on Computer Vision, 2020. 1",
+            "[51] Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discrimina"
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            900
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "tive localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 2, 5",
+            "[52] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 3"
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
+            204
+        ],
+        "page_idx": 10
+    }
+]

2103.01xxx/2103.01795/1e3bf6e0-c43c-48a3-b6bc-e85850389c17_model.json

@@ -0,0 +1,1839 @@
+[
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.145,
+                0.13,
+                0.828,
+                0.176
+            ],
+            "angle": 0,
+            "content": "Context Decoupling Augmentation for Weakly Supervised Semantic Segmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.22,
+                0.223,
+                0.747,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Yukun Su\\(^{1,2}\\), Ruizhou Sun\\(^{1,2}\\), Guosheng Lin\\(^{3\\dagger}\\), and Qingyao Wu\\(^{1,2\\dagger}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.182,
+                0.254,
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+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)School of Software and Engineering, South China University of Technology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.192,
+                0.273,
+                0.776,
+                0.29
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)Key Laboratory of Big Data and Intelligent Robot, Ministry of Education"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.131,
+                0.29,
+                0.842,
+                0.326
+            ],
+            "angle": 0,
+            "content": "\\(^{3}\\)School of Computer Science and Engineering, Nanyang Technological University suyukun666@gmail.com, ruizhousun@foxmail.com, gslin@ntu.edu.sg, qyw@scut.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.371,
+                0.314,
+                0.387
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.402,
+                0.474,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Data augmentation is vital for deep learning neural networks. By providing massive training samples, it helps to improve the generalization ability of the model. Weakly supervised semantic segmentation (WSSS) is a challenging problem that has been deeply studied in recent years, conventional data augmentation approaches for WSSS usually employ geometrical transformations, random cropping and color jittering. However, merely increasing the same contextual semantic data does not bring much gain to the networks to distinguish the objects, e.g., the correct image-level classification of \"aeroplane\" may be not only due to the recognition of the object itself, but also its cooccurrence context like \"sky\", which will cause the model to focus less on the object features. To this end, we present a Context Decoupling Augmentation (CDA) method, to change the inherent context in which the objects appear and thus drive the network to remove the dependence between object instances and contextual information. To validate the effectiveness of the proposed method, extensive experiments on PASCAL VOC 2012 and COCO datasets with several alternative network architectures demonstrate that CDA can boost various popular WSSS methods to the new state-of-the-art by a large margin. Code is available at https://github.com/suyukun666/CDA"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.793,
+                0.21,
+                0.809
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.818,
+                0.47,
+                0.88
+            ],
+            "angle": 0,
+            "content": "Semantic segmentation is a foundation in the computer vision field, which aims to predict the pixel-wise classification of the images and it enjoys a wide range of applications. Recently, benefiting from the deep neural net"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.371,
+                0.895,
+                0.567
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.581,
+                0.895,
+                0.68
+            ],
+            "angle": 0,
+            "content": "Figure 1. Illustration of the difference between conventional augmentation approaches and our method. Classical data augmentation consists of generating images obtained by basic geometrical transformations or color changes of original training images. Context Decoupling Augmentation (CDA) aims to randomly paste the given object instances into the scenes, so as to decouple the inherent context position of the original objects in the image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.885
+            ],
+            "angle": 0,
+            "content": "works, modern semantic segmentation models [7, 8, 31, 33] have achieved remarkable progress with massive human-annotated labeled data. However, collecting pixel-level labels is very time-consuming and labor-intensive, which shifts much research attention to weakly supervised semantic segmentation (WSSS). There exist various types of weak supervision for semantic segmentation like using bounding boxes [10, 24], scribbles [30, 40], points [4], and image-level labels [21, 2, 1, 43, 50]. Among them, image-level class labels have been widely used since they demand the least annotation efforts and are already provided in existing large-scale image datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this paper, we focus on augmentation for WSSS with"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.228,
+                0.9
+            ],
+            "angle": 0,
+            "content": "†Corresponding authors."
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.395
+            ],
+            "angle": 0,
+            "content": "image-level labels, which is crucial for deep learning networks. As shown in Figure 1 upper part, given a training image, traditional data augmentation methods utilize some geometrical transformations, such as rotation, scaling, flipping, and even some color conversions to increase the diversity of images to avoid overfitting. However, for weakly supervised semantic segmentation, adjusting the image as a whole and maintain the same contextual semantic relation will not significantly help the networks to mine the object areas. For example, \"sofa\" always appears in the room in the datasets, therefore, the trained network may not only recognize the objects depending on the instance features but also their co-occurrence context information [29]. Specifically, when object instances often appear at the same time with some accompanying backgrounds, it will cause the networks to yield confounding bias. Namely, the networks can perform classification task well is not due to successfully distinguishing the characteristics of objects, but to being aware of the appearance of certain contextual semantic information, which is harmful to mine the object regions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.398,
+                0.473,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Based on this observation, we propose a Context Decoupling Augmentation (CDA) method, designing for disassembling the inherent contextual information of the original image. As shown in Figure 1 bottom half, the \"cat\" shows in the \"sky\", and the \"sofa\" falls on the \"road\". Although some of these scene collocations rarely appear in life, the models can pay more attention to the objects corresponding to the classification labels. Unlike the fully-supervised data augmentation approaches [13], we cannot access the object instance labels to extract the objects under the weakly supervised setting. Therefore, we first adopt off-the-shelf WSSS approaches to obtain the object instances that have been well-segmented. Secondly, we randomly paste the selected foreground instances into the input images to get the new enhanced images and put them into the model for training together with the original ones without augmentation. In this way, we can break the dependency between objects and contextual background, and the models will focus on the internal information of the foreground instances rather than the context information to predict the categories they belong to. Besides, we use an online training technique to conduct data augmentation, which means that the combination of the raw input images and the object instances to be pasted are different each time. This greatly increases the diversity of combinations of various scenes and object instances, and thus enhance the decoupling capability of the networks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.811,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In the proposed context decoupling augmentation framework, we utilize different WSSS networks as our baselines. To verify the effectiveness of our proposed method, extensive experiments show that CDA can improve pseudomasks more than \\(2.8\\%\\) mIoU on average. We achieve new state-of-the-art performance by \\(66.1\\%\\) mIoU on the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.151
+            ],
+            "angle": 0,
+            "content": "val set and \\(66.8\\%\\) mIoU on the test set of PASCAL VOC 2012 [15], and \\(33.7\\%\\) mIoU on the val set of COCO [32]. The main contributions of our paper can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.157,
+                0.892,
+                0.218
+            ],
+            "angle": 0,
+            "content": "- We present a generally applicable data augmentation approach for weakly supervised semantic segmentation, which, to the best of our knowledge, has not been well explored."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.225,
+                0.892,
+                0.316
+            ],
+            "angle": 0,
+            "content": "- The proposed context decoupling augmentation (CDA) method does not require additional data and it can remove the correlation between foreground object instances and background context information, which can drive the network focus on object regions rather than the background."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.323,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": "- Experiments on PASCAL VOC 2012 and COCO show the effectiveness of our proposed method and CDA can boost the performance of different WSSS methods to the new state-of-the-art by a large margin."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.157,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.4,
+                0.642,
+                0.416
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.425,
+                0.587,
+                0.439
+            ],
+            "angle": 0,
+            "content": "2.1.WSSS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.448,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Image labels as the weak supervision for segmentation have been widely studied in the past few years. Many approaches [44, 2, 1] use CAM [51] to mine the object seed regions by predicting image labels. To solve the problem that only the discriminative regions can be highlighted, researchers designed to expand the object seed regions in various ways. For example, in [47], the target regions are expanded by fusing different discriminative regions generated by convolutional layers with different expansion rates. [44] drives the network to learn the rest parts of the objects by iteratively erasing the target areas. In addition, some previous works [21, 22] use additional data, such as videos and saliency maps, to explore the objects areas."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.646,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Although object expansion technologies emerge endlessly, they all use CAM [51] as the cornerstone. The effect of subsequent diffusion depends on the first step of the CAM learning features. As only image-level labels are provided, when objects are closely coupled with contextual backgrounds, such as \"boat\" and \"water\", \"aeroplane\" and \"sky\", \"train\" and \"track\", CAM will mistakenly recognize the background together with foreground objects. As mentioned in [29], the training networks have no incentive to focus attention only on the foreground class as there may be bias towards other contextual factors as a distractor with high correlation. Thus, this is an issue that's worth thinking about and that needs to be solved."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.688,
+                0.864
+            ],
+            "angle": 0,
+            "content": "2.2. Data Augmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Data augmentation is a major trick to train deep neural networks, which aims to increase the diversity of the data"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.135,
+                0.09,
+                0.841,
+                0.407
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.424,
+                0.895,
+                0.467
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of the proposed augmentation scheme. Stage-I: use the off-the-shelf weakly supervised semantic segmentation methods to obtain some simple object instances with good segmentation. Stage-II: paste the object instances randomly into the raw images to form the new input images, and perform online data augmentation training in a pairwise way with the original input images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.491,
+                0.473,
+                0.748
+            ],
+            "angle": 0,
+            "content": "by increasing the training samples and avoid overfitting to a certain extent. Conventional data augmentation approaches perform a series of operations on the basic data, such as rotation, flipping, adding Gaussian noise, etc. Some works have explored synthesizing training data [17, 35] for further generalizability. Generating new training samples by Stylizing ImageNet [18] can lead to better classification performances. Recently, GAN [52] has been employed to transfer the style of the images and to make the content of the images from one domain to another, which can enrich the semantic information of the images to train the deep neural networks. Furthermore, [49] introduced a method to mix two random samples and divide the classification results proportionally to enhance images. [12] conducted augmentation by randomly cutting out some areas in the sample and filled it with 0 pixel value, and keep the result of classification unchanged."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "For object detection and segmentation, a popular data augmentation way is \"copy-and-paste\" [13, 14]. These works pasted real segmented objects into natural images, which is beneficial to increase the object complexity of the internal images and can help to solve the problem of small target detection. However, obtaining these segmented objects requires pixel-wise instance labels. [36] used box-supervision and the off-the-shelf faster-RCNN [37] method to segment and generate masks via cut-and-paste. [3] adopted the unsupervised cut-and-paste learning method to"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.491,
+                0.895,
+                0.584
+            ],
+            "angle": 0,
+            "content": "generate new combined images, but this kind of method is only applicable to the image of single object. It is the first time that we employ copy-and-paste in the WSSS field and it does not require the help of pixel-wise labels and other auxiliary approaches. Thus, for WSSS, such a data augmentation scheme is significant and has not been well explored."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.597,
+                0.625,
+                0.613
+            ],
+            "angle": 0,
+            "content": "3. Framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.623,
+                0.895,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Our approach mainly consists of two stages: (1) we first collect the easy examples of well-segmented objects by using off-the-shelf WSSS methods; (2) then we train the network in a pairwise manner with online augmentation. In this section, we will describe these two stages in details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.71,
+                0.75,
+                0.728
+            ],
+            "angle": 0,
+            "content": "3.1. Object Instances Collecting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.734,
+                0.894,
+                0.856
+            ],
+            "angle": 0,
+            "content": "We aim to apply data augmentation on one of the WSSS models (i.e., IRNet [1]). To some extent, the WSSS method can successfully predict good masks for some easy objects with class labels. Therefore, as shown in Figure 2, in the first stage, we train the original network and we are able to select qualified object instances through the scene complexity of the image, the scope of the object and the semantic relevance by setting some criteria."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Specifically, for the inferring phase after training the network, we follow two main criteria for collecting object instances: (i) the current image should only have a single"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.091,
+                0.473,
+                0.177
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.192,
+                0.47,
+                0.248
+            ],
+            "angle": 0,
+            "content": "Figure 3. Different kinds of pasting methods used in experiments. (a) Raw input, (b) Random rescale pasting, (c) Random rescale + rotation pasting, (d) Random rescale + rotation + Gaussian smoothing pasting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.274,
+                0.473,
+                0.518
+            ],
+            "angle": 0,
+            "content": "class. The intuition behind this is that in the case of only a single class, the image information should be simple and without a complex semantic environment, the segmentation results of the model should be more accurate; (ii) the segmentation result of the current image should meet the condition, \\(\\epsilon_1 < \\frac{m}{n} < \\epsilon_2\\), where \\(\\epsilon_1\\) and \\(\\epsilon_2\\) are two threshold factors, respectively. \\(m\\) is the number of pixels belonging to the foreground object, \\(n\\) is the number of pixels of the entire image. The reason lies that if the scale value of \\(\\frac{m}{n}\\) is too large, it should be that the background is incorrectly identified as the foreground. In contrast, if the scale value is too small, it should be that the model has not been able to recognize enough foreground object pixel information. Different from existing synthesis approaches [13, 14], our method is based on self-provided masks to obtain qualified object instances images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.528,
+                0.351,
+                0.545
+            ],
+            "angle": 0,
+            "content": "3.2. Online Augmentation Training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.553,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Blending. Before we take a step to train the network in the second stage, we first introduce how to blend the object instances into the natural images. As shown in Figure 3, we show different types of pasting skills in our experiments. It's worth mentioning that we only paste objects that have not appeared in the original images. The significance of this is that we can increase the diversity of objects of the images, while also reducing the dependence of the same objects in the inherent scene. By randomly rescaling the objects, we can paste them into the images appropriately to prevent them from being too large or too small. The addition of random rotation can change the inherent orientation properties of the objects. Adding Gaussian smoothing can help the added objects boundary blend more naturally."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In some cases, the blending may not be ideal, we elaborate on several possibilities for random pasting. As shown in Figure 4, we have listed several augmented images of random pasting and we call them \"perfect\", \"good\" and \"noise\" examples. As for the \"good\" example, the new object \"bird\" covers part of the \"dog\" in the original image, however, we argue that this could help to erase the discriminative regions and force the network to discover more object regions like the function in [44]. The noise example shows that the"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.091,
+                0.699,
+                0.191
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.571,
+                0.193,
+                0.63,
+                0.205
+            ],
+            "angle": 0,
+            "content": "(a) perfect"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.713,
+                0.091,
+                0.89,
+                0.191
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.787,
+                0.193,
+                0.835,
+                0.205
+            ],
+            "angle": 0,
+            "content": "(b) good"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.216,
+                0.698,
+                0.317
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.674,
+                0.319,
+                0.722,
+                0.331
+            ],
+            "angle": 0,
+            "content": "(c) noise"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.699,
+                0.216,
+                0.892,
+                0.317
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.348,
+                0.892,
+                0.376
+            ],
+            "angle": 0,
+            "content": "Figure 4. Examples of the input augmented images with varying degrees of occlusion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.402,
+                0.893,
+                0.568
+            ],
+            "angle": 0,
+            "content": "\"sofa\" completely covers the \"aeroplane\" in the original image, which will cause confusion to network classification. However, we consider that such hard examples do not account for the majority. Most objects occupy in the middle or prominent location of the natural images. The random blending method we employ tends to paste the new objects into the off-center position of the images. Thus, this case does not affect learning. Hence, our framework is robust to the quality of augmentation. According to our experiments, this simple random blending method performs well in boosting the performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.893,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Online Training. The augmentation scheme is conducted online to enhance the network trained in stage-I to improve the ability to distinguish object features. Formally, in each batch, we sample \\( N / 2 \\) images from the training dataset and the same number object instances images from the subset which is provided from stage-I. Then we randomly paste the segmented objects into the input images, which creates a \\( N / 2 \\) batch new images. Thus, a batch of size \\( N \\) is generated online for each augmentation iteration. The construction process of the online augmentation learning is summarized in Algorithm 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Note that we train the online augmentation method in a pairwise manner as shown in Figure 2 stage-II left. We consider this can further help the networks to recognize the objects for the reason that some images have new blended objects, while some do not, which can help the classifier find more discriminative features. The motivation behind this is similar to \"finding the differences\" with the human visual system. When the two images have a different object but with a duplicated background, which can often leave a deep impression. For the same reason, this can make the network classifier learn better features of this kind of object."
+        }
+    ],
+    [
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.081,
+                0.092,
+                0.378,
+                0.106
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Stage-II: Online Augmentation."
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.081,
+                0.108,
+                0.47,
+                0.369
+            ],
+            "angle": 0,
+            "content": "Input: The training dataset images \\(\\mathcal{I}\\) and the corresponding labels \\(\\mathcal{L}\\); The object instances \\(\\mathcal{O}\\) and the corresponding labels \\(\\mathcal{T}\\).  \n1: while not done do  \n2: \\((\\mathcal{I}_i, \\mathcal{L}_i) \\gets\\) Draw one sample from training dataset;  \n3: \\((\\mathcal{O}_j, \\mathcal{T}_j) \\gets\\) Draw one sample from object instances subset;  \n4: while \\(\\mathcal{T}_j\\) in \\(\\mathcal{L}_i\\) do  \n5: \\((\\mathcal{O}_j, \\mathcal{T}_j) \\gets\\) Resample;  \n6: end while  \n7: \\(\\mathcal{I}_i' \\gets\\) Blend \\(\\mathcal{O}_j\\) into \\(\\mathcal{I}_i\\);  \n8: \\(\\mathcal{L}_i' \\gets\\) Append \\(\\mathcal{T}_j\\) in \\(\\mathcal{L}_i\\);  \n9: Train CAM \\(\\leftarrow\\) Loss(\\(\\mathbb{C}(\\mathcal{I}_i), \\mathcal{L}_i)\\) + Loss(\\(\\mathbb{C}(\\mathcal{I}_i')\\), \\(\\mathcal{L}_i'\\));  \n10: end while  \n11: Expansion."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.398,
+                0.195,
+                0.413
+            ],
+            "angle": 0,
+            "content": "3.3. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.421,
+                0.473,
+                0.695
+            ],
+            "angle": 0,
+            "content": "The proposed CDA framework contributes a new data augmentation learning strategy. Unlike the previous \"copy-and-paste\" works, we do not use additional pixel-wise labels. Specifically, by using the self-provided initial segmentation masks of the models, we can obtain the object instances for the next phase augmentation training. Furthermore, since our goal is to decouple the high correlation between objects and their contextual background, we don't need to consider much about visual context [13, 9], which can greatly improve the efficiency of pasting objects into the images. Besides, we adopt online augmentation training skills. Compared with static offline data augmentation, which merely enlarges the scale of the training dataset in linear-level. Namely, once a new dataset is formed, the number of images will remain unchanged. However, our method is able to obtain exponential-level augmentation, because the combination of object instances and natural images can be ever-changing in each round of training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.707,
+                0.21,
+                0.723
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.732,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "To demonstrate the contributions of the proposed method, we conduct several ablation studies to show the effectiveness of CDA and compare different baselines models to the state-of-the-arts. We will give the details of the datasets, evaluation metric, and baseline models in the following."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.833,
+                0.173,
+                0.847
+            ],
+            "angle": 0,
+            "content": "4.1. Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "All the networks in our framework are trained and evaluated on the PASCAL VOC 2012 [15] and COCO [32] segmentation benchmark for a fair comparison to previous"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "approaches. As for PASCAL VOC, the official dataset separation has 1464 images for training, 1449 for validation and 1456 for testing. Following the common practice, we take additional annotations to build an augmented training set with 10582 images presented in [19]. COCO is a more challenging benchmark with 81 semantic classes (one background class), 80k, and 40k images for training and validation. We use the standard mean Intersection-over-Union (mIoU) as the evaluation metric for all experiments."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.238,
+                0.719,
+                0.254
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.262,
+                0.892,
+                0.685
+            ],
+            "angle": 0,
+            "content": "To validate the applicability of CDA, we deploy it on three popular WSSS models including IRNet [1], AffinityNet [2] and SEAM [43]. The general training architecture components include a multi-label image classification step, a pseudo-mask generation step, and the final segmentation model (DeepLab-v2 [7]). We strictly follow the same settings as reported in the official codes. Specially, for SEAM [43] and AffinityNet [2] baselines, ResNet38 [20] that pre-trained on ImageNet [11] is adopted as backbone with batch size as 8 and 16, respectively. When training the networks, multi-scale and data augmentation techniques like horizontal flip, random cropping, and color jittering are deployed in both architectures. Following the poly policy \\(lr_{init} = lr_{init}(1 - itr / max\\_ itr)^{\\rho}\\) with \\(\\rho = 0.9\\) for decay, the models are trained with a fix input size as \\(448 \\times 448\\) using Adam optimizer [25]. Besides, online hard example mining [39] is employed on the training loss in SEAM. As for IRNet [1], ResNet50 [20] is used as the backbone network (pretrained on ImageNet). The batch size is set to 16 for the image classification model and 32 for the inter-pixel relation model. The input image is cropped into a fix size of \\(512 \\times 512\\) using zero padding if needed. The model is trained with the same polynomial decay strategy as in AffinityNet [2] using stochastic gradient descent (SGD) for optimization with 8,000 iterations. The fully-connected CRF [27] is used in three baselines to refine CAM, pseudo-mask, and segmentation mask with the default parameters in the public code. We set the threshold \\(\\epsilon_1 = 0.1\\) and \\(\\epsilon_2 = 0.7\\) by experience."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.696,
+                0.665,
+                0.71
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.885
+            ],
+            "angle": 0,
+            "content": "To verify the effectiveness of our CDA, we evaluate CAM seed regions, pseudo-masks, and segmentation masks, respectively. In our experiments, the standard mean Intersection over Union (mIoU) is used on the training set for evaluating CAM seed area masks and pseudo-masks, and on the PASCAL VOC 2012 val and test sets for evaluating segmentation masks. For the sake of simplicity, since the three WSSS models are all based on CAM [51], we use one of the representative models (IRNet [1]) as a baseline to conduct several ablation studies on CAM in mIoU to illustrate the role of each component of our approach."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.886,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Random pasting vs. Other sophisticated augmenta"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.099,
+                0.09,
+                0.454,
+                0.252
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>operation</td><td>mIoU (%)</td></tr><tr><td rowspan=\"2\">Conventional Augmentation</td><td>Rotation</td><td>48.5</td></tr><tr><td>Translation</td><td>48.4</td></tr><tr><td rowspan=\"3\">Mixup [49]</td><td>α = 0.3</td><td>48.7</td></tr><tr><td>α = 0.5</td><td>48.5</td></tr><tr><td>α = 0.8</td><td>49.0</td></tr><tr><td>CutOut [12]</td><td>Random</td><td>48.9</td></tr><tr><td>CutMix [48]</td><td>Random</td><td>49.2</td></tr><tr><td>Random pasting (ours)</td><td>Rescale</td><td>49.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.262,
+                0.47,
+                0.306
+            ],
+            "angle": 0,
+            "content": "Table 1. Experiments of different augmentation methods. Here \\(\\alpha\\) is the intensity of the interpolation between the eigenvector and the target vector."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.1,
+                0.32,
+                0.451,
+                0.419
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Baseline</td><td>Rescale</td><td>Rotation</td><td>Gaussian</td><td>mIoU (%)</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>48.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>49.8</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>50.8</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>49.6</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>50.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.429,
+                0.47,
+                0.471
+            ],
+            "angle": 0,
+            "content": "Table 2. The ablation study of the effect on different pasting methods. Baseline indicates the original CAM method without pasting new objects for augmentation."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.172,
+                0.486,
+                0.38,
+                0.546
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Training manner</td><td>mIoU (%)</td></tr><tr><td>Pairwise</td><td>50.8</td></tr><tr><td>None-pairwise</td><td>50.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.109,
+                0.556,
+                0.438,
+                0.57
+            ],
+            "angle": 0,
+            "content": "Table 3. Experiments of augmentation training manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.794
+            ],
+            "angle": 0,
+            "content": "tion methods: As for the traditional augmentation methods, we adopt the random rotation and translation to expand the dataset to three times the original size, however, they can not bring significant boost for the performance. We also compare Mixup [49], CutOut [12] and CutMix [48] methods to generate new augmented images. As shown in Table 1, random rescale pasting outperforms the other three methods achieving \\(49.8\\%\\) mIoU. These results demonstrate that random pasting is suitable for our CDA framework. We consider that proper occlusion helps the network to better mine the features of other areas of the objects, and the situation of complete occlusion is relatively rare which will not affect our learning process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Comparison with baseline: We further explore the impact of different pasting methods on data augmentation. Table 2 shows that using random rescale pasting has a \\(1.5\\%\\) improvement compared to baseline. After combining rescale and rotation, we can get the best performance to \\(50.8\\%\\) mIoU on PASCAL VOC training set. The results show that applying Gaussian smoothing can not help to im"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.092,
+                0.892,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.433,
+                0.894,
+                0.492
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative visualization of CAMs. Our CDA framework not only suppresses over-activation \\((1^{st},2^{nd},3^{rd}\\) row) of the high correlation contextual backgrounds of the objects and expands CAMs to cover the whole object regions \\((4^{th}\\) row)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.519,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "prove the performance. Therefore, in subsequent experiments, unless otherwise specified, we will use the random rescale combining with the rotation method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.567,
+                0.893,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Figure 5 shows the qualitative comparison between our CAM+Aug by CDA method and the original CAM. As shown in the first and second rows in the figure and the labels of objects are \"table\". The original CAM will activate background semantic information that is strongly related to the \"table\", such as \"chair\". However, by employing the decoupling augmentation training strategy, our method can focus on the target areas. For the image with the label of \"train\", CAM even pays attention not to the object itself, but the \"track\", which will be detrimental to the subsequent segmentation task. Moreover, CDA can also help the network expand and discover more comprehensive object features but not only the most discriminative regions like the \"cat\" shown in the last row."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The effect on pairwise training: Compared to merely using the augmented images to train the networks, we use the none-augmented images with the augmented images as pair images to jointly train the models as shown in Figure 2 stage-II. The results shown in Table 3 show that applying pairwise training strategy outperforms the one in single augmented images, which illustrates that this helps the network classifier to learn more discriminative features."
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.151,
+                0.09,
+                0.825,
+                0.213
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Network</td><td>Backbone</td><td>CAM</td><td>Pseudo-Masks</td><td>Seg. Masks (val-set)</td><td>Seg. Masks (test-set)</td></tr><tr><td rowspan=\"2\">AffinityNet [2] + CDA</td><td>ResNet-38</td><td>48.0</td><td>59.7</td><td>61.7</td><td>63.7</td></tr><tr><td>ResNet-38</td><td>48.9+0.9</td><td>63.3+3.6</td><td>64.2+2.5</td><td>65.8+2.1</td></tr><tr><td rowspan=\"2\">IRNet* [1] + CDA</td><td>ResNet-50</td><td>48.3</td><td>65.9</td><td>63.5</td><td>64.8</td></tr><tr><td>ResNet-50</td><td>50.8+2.5</td><td>67.7+1.8</td><td>65.8+2.3</td><td>66.4+1.6</td></tr><tr><td rowspan=\"2\">SEAM [43] + CDA</td><td>ResNet-38</td><td>55.4</td><td>63.4</td><td>64.5</td><td>65.7</td></tr><tr><td>ResNet-38</td><td>58.4+3.0</td><td>66.4+3.0</td><td>66.1+1.6</td><td>66.8+1.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.224,
+                0.893,
+                0.253
+            ],
+            "angle": 0,
+            "content": "Table 4. Different baselines with our CDA framework performance in mIoU on PASCAL VOC. *denotes our reimplemented results since the original code does not provided pre-trained weights."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.275,
+                0.465,
+                0.384
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Number of pasted objects</td><td>Same category objects</td><td>mIoU (%)</td></tr><tr><td>1</td><td>×</td><td>50.8</td></tr><tr><td>2</td><td>×</td><td>48.9</td></tr><tr><td>3</td><td>×</td><td>47.8</td></tr><tr><td>1</td><td>✓</td><td>50.2</td></tr><tr><td>2</td><td>✓</td><td>48.6</td></tr><tr><td>3</td><td>✓</td><td>47.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.395,
+                0.47,
+                0.423
+            ],
+            "angle": 0,
+            "content": "Table 5. Experiments of different number of pasted objects for augmentation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.446,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "The effect on objects numbers: Under the default settings of our experiment, we only paste one new instance that does not exist in the original images. We further explore the effect of pasting multiple objects into the images to conduct augmentation. As shown in Table 5 above the solid line, when the number of object to be pasted increases from one to two, the mIoU performance will decrease. As the number of pasted objects changes to three, it will even worse than the baseline. The results show that over-pasted objects may cover the objects in the original image, making the noise sample dominant. This will confuse the classifier, which will bring negative effects. In addition, as depicted below the solid line in Table 5, when we allow the pasted object to be consistent with the object category in the original image, their general performance is worse than the former. This shows that forcing objects of different categories to be pasted into images can decouple the strong contextual dependence of objects in the original semantic environment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.719,
+                0.469,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Analysis of pseudo labels and Segmentation masks: The overall results are shown in Table 4. We can observe that deploying CDA on different weakly supervised semantic segmentation models can improve all their performances. Specifically, SEAM [43] can achieve the best performance in Segmentation Masks on both validation set and testing set. Figure 6 shows that we can obtain more accurate and complete masks covering the object areas."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.379,
+                0.863
+            ],
+            "angle": 0,
+            "content": "4.4. Comparison with State-of-the-arts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Finally, we compare our framework with state-of-the-art methods on the PASCAL VOC 2012 and COCO dataset in"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.278,
+                0.891,
+                0.56
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.575,
+                0.892,
+                0.618
+            ],
+            "angle": 0,
+            "content": "Figure 6. Visualization of pseudo-masks (baseline: IRNet [1]). (a) Input images. (b) Ground-Truth labels. (c) Our CAM+Aug. (d) Original CAM."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "cluding both the validation set and the testing set. For a fair comparison, we adopt the same DeepLab [6, 7] architectures as reported in the original papers. On PASCAL VOC 2012, as is shown in Table 6, although different baselines already boosts performance compared to previous methods, when CDA is deployed in the models, SEAM [43] can achieve the best performance and outperform other state-of-the-arts by a large margin. IRNet [1] yield the second best performance and can beat its later published works. On COCO, CDA deployed on IRNet achieves \\(33.7\\%\\) mIoU on the val set, which surpasses the previous best model by \\(1.1\\%\\) mIoU. Figure 7 presents qualitative results of our CDA approach applying on IRNet baseline and compares them to itself. We can observe that CDA can make more accurate predictions on objects, which shows better demarcations in some coherent areas. Meanwhile, CDA can help to expand and discover more comprehensive object regions."
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.132,
+                0.123,
+                0.151,
+                0.135
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.156,
+                0.089,
+                0.837,
+                0.384
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.402,
+                0.893,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Figure 7. Qualitative results on the PASCAL VOC 2012 val set. (a) Input images. (b) Ground-truth labels. (c) Results obtained by IRNet [1] baseline. (d) Results of our IRNet + CDA. More results can be found in the supplementary material."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.453,
+                0.466,
+                0.689
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Backbone</td><td>Saliency</td><td>val</td><td>test</td></tr><tr><td>CCNN [34]ICCV&#x27;15</td><td>VGG16</td><td>-</td><td>35.3</td><td>35.6</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>-</td><td>50.7</td><td>51.1</td></tr><tr><td>STC [45]TPAMI&#x27;17</td><td>VGG16</td><td>✓</td><td>49.8</td><td>51.2</td></tr><tr><td>AdvEra [44]CVPR&#x27;17</td><td>VGG16</td><td>✓</td><td>55.0</td><td>55.7</td></tr><tr><td>DCSP [5]BMVC&#x27;17</td><td>ResNet101</td><td>✓</td><td>60.8</td><td>61.9</td></tr><tr><td>MDC [46]CVPR&#x27;18</td><td>VGG16</td><td>✓</td><td>60.4</td><td>60.8</td></tr><tr><td>MCOF [42]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>60.3</td><td>61.2</td></tr><tr><td>DSRG [23]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>61.4</td><td>63.2</td></tr><tr><td>AffinityNet [2]CVPR&#x27;18</td><td>ResNet-38</td><td>-</td><td>61.7</td><td>63.7</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>-</td><td>63.5</td><td>64.8</td></tr><tr><td>FickleNet [28]CVPR&#x27;19</td><td>ResNet101</td><td>✓</td><td>64.9</td><td>65.3</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>-</td><td>64.5</td><td>65.7</td></tr><tr><td>ICD [16]CVPR&#x27;20</td><td>ResNet101</td><td>-</td><td>64.1</td><td>64.3</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>-</td><td>65.8</td><td>66.4</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>-</td><td>66.1</td><td>66.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.699,
+                0.47,
+                0.755
+            ],
+            "angle": 0,
+            "content": "Table 6. Performance comparisons with other state-of-the-art WSSS methods on PASCAL VOC 2012 dataset. The best and second best performance under each set are marked with corresponding formats."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.782,
+                0.196,
+                0.798
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a Context Decoupling Augmentation (CDA) method for WSSS and to narrow the gap with fully supervision. Specifically, through a two-stage training, the object instances provided by the network itself are copied and pasted into the input images to conduct augmentation. To further improve the ability of network for"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.562,
+                0.453,
+                0.837,
+                0.587
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Backbone</td><td>val</td></tr><tr><td>BFBP [38]ECCV&#x27;16</td><td>VGG16</td><td>20.4</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>22.4</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>32.6</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>31.9</td></tr><tr><td>IAL [41]IJCV&#x27;20</td><td>VGG16</td><td>27.7</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>33.7</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>33.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.596,
+                0.892,
+                0.622
+            ],
+            "angle": 0,
+            "content": "Table 7. Performance comparisons with other state-of-the-art WSSS methods on COCO val in terms of mIoU."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.658,
+                0.892,
+                0.718
+            ],
+            "angle": 0,
+            "content": "learning object features, we adopt pairwise training manner to help the classifier to distinguish more discriminative features. Experimental results show that CDA can help boost various WSSS methods to the new state-of-the-arts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.749,
+                0.661,
+                0.767
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "This work was supported by National Natural Science Foundation of China (NSFC) 61876208, Key-Area Research and Development Program of Guangdong Province 2018B010108002, Central Universities of China under Grant D2192860, and the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG-RP-2018-003), and the MOE Tier-1 research grants: RG28/18 (S), RG22/19 (S) and RG95/20."
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.115,
+                0.47,
+                0.184
+            ],
+            "angle": 0,
+            "content": "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2209-2218, 2019. 1, 2, 3, 5, 7, 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.185,
+                0.472,
+                0.254
+            ],
+            "angle": 0,
+            "content": "[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4981-4990, 2018. 1, 2, 5, 7, 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.256,
+                0.471,
+                0.295
+            ],
+            "angle": 0,
+            "content": "[3] Relja Arandjelović and Andrew Zisserman. Object discovery with a copy-pasting gan. arXiv preprint arXiv:1905.11369, 2019. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.297,
+                0.471,
+                0.354
+            ],
+            "angle": 0,
+            "content": "[4] Amy Bearman, Olga Russakovsky, Vittorio Ferrari, and Li Fei-Fei. What's the point: Semantic segmentation with point supervision. In European conference on computer vision, pages 549-565. Springer, 2016. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.355,
+                0.47,
+                0.408
+            ],
+            "angle": 0,
+            "content": "[5] Arslan Chaudhry, Puneet K Dokania, and Philip HS Torr. Discovering class-specific pixels for weakly-supervised semantic segmentation. arXiv preprint arXiv:1707.05821, 2017. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.41,
+                0.47,
+                0.466
+            ],
+            "angle": 0,
+            "content": "[6] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv preprint arXiv:1412.7062, 2014. 7"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.467,
+                0.47,
+                0.548
+            ],
+            "angle": 0,
+            "content": "[7] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4):834-848, 2017. 1, 5, 7"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.551,
+                0.47,
+                0.62
+            ],
+            "angle": 0,
+            "content": "[8] 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. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.621,
+                0.47,
+                0.661
+            ],
+            "angle": 0,
+            "content": "[9] Wenqing Chu and Deng Cai. Deep feature based contextual model for object detection. Neurocomputing, 275:1035-1042, 2018. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.663,
+                0.47,
+                0.732
+            ],
+            "angle": 0,
+            "content": "[10] Jifeng Dai, Kaiming He, and Jian Sun. Boxsup: Exploiting bounding boxes to supervise convolutional networks for semantic segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1635-1643, 2015. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.733,
+                0.47,
+                0.789
+            ],
+            "angle": 0,
+            "content": "[11] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. IEEE, 2009. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.79,
+                0.47,
+                0.831
+            ],
+            "angle": 0,
+            "content": "[12] Terrance DeVries and Graham W Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552, 2017. 3, 6"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.832,
+                0.47,
+                0.899
+            ],
+            "angle": 0,
+            "content": "[13] Nikita Dvornik, Julien Mairal, and Cordelia Schmid. Modeling visual context is key to augmenting object detection datasets. In Proceedings of the European Conference on Computer Vision (ECCV), pages 364-380, 2018. 2, 3, 4, 5"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.08,
+                0.115,
+                0.472,
+                0.899
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.093,
+                0.892,
+                0.148
+            ],
+            "angle": 0,
+            "content": "[14] Debidatta Dwibedi, Ishan Misra, and Martial Hebert. Cut, paste and learn: Surprisingly easy synthesis for instance detection. In Proceedings of the IEEE International Conference on Computer Vision, pages 1301-1310, 2017. 3, 4"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.149,
+                0.892,
+                0.216
+            ],
+            "angle": 0,
+            "content": "[15] Mark Everingham, SM Ali Eslami, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The Pascal visual object classes challenge: A retrospective. International journal of computer vision, 111(1):98-136, 2015. 2, 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.218,
+                0.892,
+                0.288
+            ],
+            "angle": 0,
+            "content": "[16] Junsong Fan, Zhaoxiang Zhang, Chunfeng Song, and Tieniu Tan. Learning integral objects with intra-class discriminator for weakly-supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4283-4292, 2020. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.289,
+                0.892,
+                0.357
+            ],
+            "angle": 0,
+            "content": "[17] Maayan Frid-Adar, Eyal Klang, Michal Amitai, Jacob Goldberger, and Hayit Greenspan. Synthetic data augmentation using gan for improved liver lesion classification. In 2018 IEEE 15th international symposium on biomedical imaging (ISBI 2018), pages 289–293. IEEE, 2018. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.358,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "[18] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A Wichmann, and Wieland Brendel. Imagenet-trained cnns are biased towards texture; increasing shape bias improves accuracy and robustness. arXiv preprint arXiv:1811.12231, 2018. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.427,
+                0.892,
+                0.483
+            ],
+            "angle": 0,
+            "content": "[19] Bharath Hariharan, Pablo Arbeláez, Lubomir Bourdev, Subhransu Maji, and Jitendra Malik. Semantic contours from inverse detectors. In 2011 International Conference on Computer Vision, pages 991–998. IEEE, 2011. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.484,
+                0.892,
+                0.538
+            ],
+            "angle": 0,
+            "content": "[20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.539,
+                0.892,
+                0.608
+            ],
+            "angle": 0,
+            "content": "[21] Seunghoon Hong, Donghun Yeo, Suha Kwak, Honglak Lee, and Bohyung Han. Weakly supervised semantic segmentation using web-crawled videos. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7322-7330, 2017. 1, 2"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.609,
+                0.892,
+                0.662
+            ],
+            "angle": 0,
+            "content": "[22] Qibin Hou, PengTao Jiang, Yunchao Wei, and Ming-Ming Cheng. Self-erasing network for integral object attention. In Advances in Neural Information Processing Systems, pages 549–559, 2018. 2"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.664,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "[23] Zilong Huang, Xinggang Wang, Jiasi Wang, Wenyu Liu, and Jingdong Wang. Weakly-supervised semantic segmentation network with deep seeded region growing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7014-7023, 2018. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.735,
+                0.892,
+                0.803
+            ],
+            "angle": 0,
+            "content": "[24] Anna Khoreva, Rodrigo Benenson, Jan Hosang, Matthias Hein, and Bernt Schiele. Simple does it: Weakly supervised instance and semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 876-885, 2017. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.804,
+                0.892,
+                0.843
+            ],
+            "angle": 0,
+            "content": "[25] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.845,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "[26] Alexander Kolesnikov and Christoph H Lampert. Seed, expand and constrain: Three principles for weakly-supervised image segmentation. In European conference on computer vision, pages 695-711. Springer, 2016. 8"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
+                0.093,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        }
+    ],
+    [
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.47,
+                0.147
+            ],
+            "angle": 0,
+            "content": "[27] Philipp Krahenbuhl and Vladlen Koltun. Efficient inference in fully connected crfs with gaussian edge potentials. In Advances in neural information processing systems, pages 109-117, 2011. 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.148,
+                0.471,
+                0.218
+            ],
+            "angle": 0,
+            "content": "[28] Jungbeom Lee, Eunji Kim, Sungmin Lee, Jangho Lee, and Sungroh Yoon. Ficklenet: Weakly and semi-supervised semantic image segmentation using stochastic inference. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5267-5276, 2019. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.218,
+                0.471,
+                0.286
+            ],
+            "angle": 0,
+            "content": "[29] Kunpeng Li, Ziyan Wu, Kuan-Chuan Peng, Jan Ernst, and Yun Fu. Tell me where to look: Guided attention inference network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9215-9223, 2018. 2"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.288,
+                0.471,
+                0.356
+            ],
+            "angle": 0,
+            "content": "[30] Di Lin, Jifeng Dai, Jiaya Jia, Kaiming He, and Jian Sun. Scribblesup: Scribble-supervised convolutional networks for semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3159-3167, 2016. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.357,
+                0.471,
+                0.426
+            ],
+            "angle": 0,
+            "content": "[31] Guosheng Lin, Chunhua Shen, Anton Van Den Hengel, and Ian Reid. Efficient piecewise training of deep structured models for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3194-3203, 2016. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.427,
+                0.471,
+                0.496
+            ],
+            "angle": 0,
+            "content": "[32] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dálár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 2, 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.497,
+                0.471,
+                0.552
+            ],
+            "angle": 0,
+            "content": "[33] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3431-3440, 2015. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.553,
+                0.471,
+                0.62
+            ],
+            "angle": 0,
+            "content": "[34] Deepak Pathak, Philipp Krahenbuhl, and Trevor Darrell. Constrained convolutional neural networks for weakly supervised segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1796-1804, 2015. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.622,
+                0.471,
+                0.677
+            ],
+            "angle": 0,
+            "content": "[35] Xingchao Peng, Baochen Sun, Karim Ali, and Kate Saenko. Learning deep object detectors from 3d models. In Proceedings of the IEEE International Conference on Computer Vision, pages 1278-1286, 2015. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.678,
+                0.471,
+                0.733
+            ],
+            "angle": 0,
+            "content": "[36] Tal Remez, Jonathan Huang, and Matthew Brown. Learning to segment via cut-and-paste. In Proceedings of the European conference on computer vision (ECCV), pages 37-52, 2018. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.734,
+                0.471,
+                0.787
+            ],
+            "angle": 0,
+            "content": "[37] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. arXiv preprint arXiv:1506.01497, 2015. 3"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.789,
+                0.471,
+                0.859
+            ],
+            "angle": 0,
+            "content": "[38] Fatemehsadat Saleh, Mohammad Sadegh Aliakbarian, Mathieu Salzmann, Lars Petersson, Stephen Gould, and Jose M Alvarez. Built-in foreground/background prior for weakly-supervised semantic segmentation. In European conference on computer vision, pages 413-432. Springer, 2016. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.86,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "[39] Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In Proceedings of the IEEE conference on"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.08,
+                0.092,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.535,
+                0.093,
+                0.892,
+                0.119
+            ],
+            "angle": 0,
+            "content": "computer vision and pattern recognition, pages 761-769, 2016.5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.121,
+                0.892,
+                0.188
+            ],
+            "angle": 0,
+            "content": "[40] Paul Vernaza and Manmohan Chandraker. Learning random-walk label propagation for weakly-supervised semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7158-7166, 2017. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.19,
+                0.892,
+                0.245
+            ],
+            "angle": 0,
+            "content": "[41] Xiang Wang, Sifei Liu, Huimin Ma, and Ming-Hsuan Yang. Weakly-supervised semantic segmentation by iterative affinity learning. International Journal of Computer Vision, 128(6):1736-1749, 2020. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.246,
+                0.892,
+                0.314
+            ],
+            "angle": 0,
+            "content": "[42] Xiang Wang, Shaodi You, Xi Li, and Huimin Ma. Weakly-supervised semantic segmentation by iteratively mining common object features. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1354-1362, 2018. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.316,
+                0.892,
+                0.397
+            ],
+            "angle": 0,
+            "content": "[43] Yude Wang, Jie Zhang, Meina Kan, Shiguang Shan, and Xilin Chen. Self-supervised equivariant attention mechanism for weakly supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12275–12284, 2020. 1, 5, 7, 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.399,
+                0.892,
+                0.481
+            ],
+            "angle": 0,
+            "content": "[44] Yunchao Wei, Jiashi Feng, Xiaodan Liang, Ming-Ming Cheng, Yao Zhao, and Shuicheng Yan. Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1568-1576, 2017. 2, 4, 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.483,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "[45] Yunchao Wei, Xiaodan Liang, Yunpeng Chen, Xiaohui Shen, Ming-Ming Cheng, Jiashi Feng, Yao Zhao, and Shuicheng Yan. Stc: A simple to complex framework for weakly-supervised semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(11):2314-2320, 2016. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.567,
+                0.892,
+                0.648
+            ],
+            "angle": 0,
+            "content": "[46] Yunchao Wei, Huaxin Xiao, Honghui Shi, Zequn Jie, Jiashi Feng, and Thomas S Huang. Revisiting dilated convolution: A simple approach for weakly-and semi-supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7268-7277, 2018. 8"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.65,
+                0.892,
+                0.69
+            ],
+            "angle": 0,
+            "content": "[47] Fisher Yu and Vladlen Koltun. Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122, 2015. 2"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.692,
+                0.892,
+                0.761
+            ],
+            "angle": 0,
+            "content": "[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023-6032, 2019. 6"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.762,
+                0.892,
+                0.802
+            ],
+            "angle": 0,
+            "content": "[49] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 3, 6"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.803,
+                0.892,
+                0.871
+            ],
+            "angle": 0,
+            "content": "[50] Tianyi Zhang, Guosheng Lin, Weide Liu, Jianfei Cai, and Alex Kot. Splitting vs. merging: Mining object regions with discrepancy and intersection loss for weakly supervised semantic segmentation. In European Conference on Computer Vision, 2020. 1"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.873,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "[51] Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discrimina"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
+                0.093,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        }
+    ],
+    [
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.11,
+                0.092,
+                0.47,
+                0.134
+            ],
+            "angle": 0,
+            "content": "tive localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 2, 5"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.08,
+                0.136,
+                0.47,
+                0.205
+            ],
+            "angle": 0,
+            "content": "[52] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 3"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.08,
+                0.092,
+                0.47,
+                0.205
+            ],
+            "angle": 0,
+            "content": null
+        }
+    ]
+]

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+# Context Decoupling Augmentation for Weakly Supervised Semantic Segmentation
+
+Yukun Su $^{1,2}$ , Ruizhou Sun $^{1,2}$ , Guosheng Lin $^{3\dagger}$ , and Qingyao Wu $^{1,2\dagger}$
+
+$^{1}$ School of Software and Engineering, South China University of Technology
+
+$^{2}$ Key Laboratory of Big Data and Intelligent Robot, Ministry of Education
+
+$^{3}$ School of Computer Science and Engineering, Nanyang Technological University suyukun666@gmail.com, ruizhousun@foxmail.com, gslin@ntu.edu.sg, qyw@scut.edu.cn
+
+# Abstract
+
+Data augmentation is vital for deep learning neural networks. By providing massive training samples, it helps to improve the generalization ability of the model. Weakly supervised semantic segmentation (WSSS) is a challenging problem that has been deeply studied in recent years, conventional data augmentation approaches for WSSS usually employ geometrical transformations, random cropping and color jittering. However, merely increasing the same contextual semantic data does not bring much gain to the networks to distinguish the objects, e.g., the correct image-level classification of "aeroplane" may be not only due to the recognition of the object itself, but also its cooccurrence context like "sky", which will cause the model to focus less on the object features. To this end, we present a Context Decoupling Augmentation (CDA) method, to change the inherent context in which the objects appear and thus drive the network to remove the dependence between object instances and contextual information. To validate the effectiveness of the proposed method, extensive experiments on PASCAL VOC 2012 and COCO datasets with several alternative network architectures demonstrate that CDA can boost various popular WSSS methods to the new state-of-the-art by a large margin. Code is available at https://github.com/suyukun666/CDA
+
+# 1. Introduction
+
+Semantic segmentation is a foundation in the computer vision field, which aims to predict the pixel-wise classification of the images and it enjoys a wide range of applications. Recently, benefiting from the deep neural net
+
+![](images/e0eeda510bd4138b48e188ad1a2299330eccfcac73b334784dda355943302189.jpg)  
+Figure 1. Illustration of the difference between conventional augmentation approaches and our method. Classical data augmentation consists of generating images obtained by basic geometrical transformations or color changes of original training images. Context Decoupling Augmentation (CDA) aims to randomly paste the given object instances into the scenes, so as to decouple the inherent context position of the original objects in the image.
+
+works, modern semantic segmentation models [7, 8, 31, 33] have achieved remarkable progress with massive human-annotated labeled data. However, collecting pixel-level labels is very time-consuming and labor-intensive, which shifts much research attention to weakly supervised semantic segmentation (WSSS). There exist various types of weak supervision for semantic segmentation like using bounding boxes [10, 24], scribbles [30, 40], points [4], and image-level labels [21, 2, 1, 43, 50]. Among them, image-level class labels have been widely used since they demand the least annotation efforts and are already provided in existing large-scale image datasets.
+
+In this paper, we focus on augmentation for WSSS with
+
+image-level labels, which is crucial for deep learning networks. As shown in Figure 1 upper part, given a training image, traditional data augmentation methods utilize some geometrical transformations, such as rotation, scaling, flipping, and even some color conversions to increase the diversity of images to avoid overfitting. However, for weakly supervised semantic segmentation, adjusting the image as a whole and maintain the same contextual semantic relation will not significantly help the networks to mine the object areas. For example, "sofa" always appears in the room in the datasets, therefore, the trained network may not only recognize the objects depending on the instance features but also their co-occurrence context information [29]. Specifically, when object instances often appear at the same time with some accompanying backgrounds, it will cause the networks to yield confounding bias. Namely, the networks can perform classification task well is not due to successfully distinguishing the characteristics of objects, but to being aware of the appearance of certain contextual semantic information, which is harmful to mine the object regions.
+
+Based on this observation, we propose a Context Decoupling Augmentation (CDA) method, designing for disassembling the inherent contextual information of the original image. As shown in Figure 1 bottom half, the "cat" shows in the "sky", and the "sofa" falls on the "road". Although some of these scene collocations rarely appear in life, the models can pay more attention to the objects corresponding to the classification labels. Unlike the fully-supervised data augmentation approaches [13], we cannot access the object instance labels to extract the objects under the weakly supervised setting. Therefore, we first adopt off-the-shelf WSSS approaches to obtain the object instances that have been well-segmented. Secondly, we randomly paste the selected foreground instances into the input images to get the new enhanced images and put them into the model for training together with the original ones without augmentation. In this way, we can break the dependency between objects and contextual background, and the models will focus on the internal information of the foreground instances rather than the context information to predict the categories they belong to. Besides, we use an online training technique to conduct data augmentation, which means that the combination of the raw input images and the object instances to be pasted are different each time. This greatly increases the diversity of combinations of various scenes and object instances, and thus enhance the decoupling capability of the networks.
+
+In the proposed context decoupling augmentation framework, we utilize different WSSS networks as our baselines. To verify the effectiveness of our proposed method, extensive experiments show that CDA can improve pseudomasks more than  $2.8\%$  mIoU on average. We achieve new state-of-the-art performance by  $66.1\%$  mIoU on the
+
+val set and  $66.8\%$  mIoU on the test set of PASCAL VOC 2012 [15], and  $33.7\%$  mIoU on the val set of COCO [32]. The main contributions of our paper can be summarized as follows:
+
+- We present a generally applicable data augmentation approach for weakly supervised semantic segmentation, which, to the best of our knowledge, has not been well explored.  
+- The proposed context decoupling augmentation (CDA) method does not require additional data and it can remove the correlation between foreground object instances and background context information, which can drive the network focus on object regions rather than the background.  
+- Experiments on PASCAL VOC 2012 and COCO show the effectiveness of our proposed method and CDA can boost the performance of different WSSS methods to the new state-of-the-art by a large margin.
+
+# 2. Related Work
+
+# 2.1.WSSS
+
+Image labels as the weak supervision for segmentation have been widely studied in the past few years. Many approaches [44, 2, 1] use CAM [51] to mine the object seed regions by predicting image labels. To solve the problem that only the discriminative regions can be highlighted, researchers designed to expand the object seed regions in various ways. For example, in [47], the target regions are expanded by fusing different discriminative regions generated by convolutional layers with different expansion rates. [44] drives the network to learn the rest parts of the objects by iteratively erasing the target areas. In addition, some previous works [21, 22] use additional data, such as videos and saliency maps, to explore the objects areas.
+
+Although object expansion technologies emerge endlessly, they all use CAM [51] as the cornerstone. The effect of subsequent diffusion depends on the first step of the CAM learning features. As only image-level labels are provided, when objects are closely coupled with contextual backgrounds, such as "boat" and "water", "aeroplane" and "sky", "train" and "track", CAM will mistakenly recognize the background together with foreground objects. As mentioned in [29], the training networks have no incentive to focus attention only on the foreground class as there may be bias towards other contextual factors as a distractor with high correlation. Thus, this is an issue that's worth thinking about and that needs to be solved.
+
+# 2.2. Data Augmentation
+
+Data augmentation is a major trick to train deep neural networks, which aims to increase the diversity of the data
+
+![](images/2fea338e16860079098092b21ea0d10d6d9c597c99e2c7bf0c2f6c10519dcff4.jpg)  
+Figure 2. Overview of the proposed augmentation scheme. Stage-I: use the off-the-shelf weakly supervised semantic segmentation methods to obtain some simple object instances with good segmentation. Stage-II: paste the object instances randomly into the raw images to form the new input images, and perform online data augmentation training in a pairwise way with the original input images.
+
+by increasing the training samples and avoid overfitting to a certain extent. Conventional data augmentation approaches perform a series of operations on the basic data, such as rotation, flipping, adding Gaussian noise, etc. Some works have explored synthesizing training data [17, 35] for further generalizability. Generating new training samples by Stylizing ImageNet [18] can lead to better classification performances. Recently, GAN [52] has been employed to transfer the style of the images and to make the content of the images from one domain to another, which can enrich the semantic information of the images to train the deep neural networks. Furthermore, [49] introduced a method to mix two random samples and divide the classification results proportionally to enhance images. [12] conducted augmentation by randomly cutting out some areas in the sample and filled it with 0 pixel value, and keep the result of classification unchanged.
+
+For object detection and segmentation, a popular data augmentation way is "copy-and-paste" [13, 14]. These works pasted real segmented objects into natural images, which is beneficial to increase the object complexity of the internal images and can help to solve the problem of small target detection. However, obtaining these segmented objects requires pixel-wise instance labels. [36] used box-supervision and the off-the-shelf faster-RCNN [37] method to segment and generate masks via cut-and-paste. [3] adopted the unsupervised cut-and-paste learning method to
+
+generate new combined images, but this kind of method is only applicable to the image of single object. It is the first time that we employ copy-and-paste in the WSSS field and it does not require the help of pixel-wise labels and other auxiliary approaches. Thus, for WSSS, such a data augmentation scheme is significant and has not been well explored.
+
+# 3. Framework
+
+Our approach mainly consists of two stages: (1) we first collect the easy examples of well-segmented objects by using off-the-shelf WSSS methods; (2) then we train the network in a pairwise manner with online augmentation. In this section, we will describe these two stages in details.
+
+# 3.1. Object Instances Collecting
+
+We aim to apply data augmentation on one of the WSSS models (i.e., IRNet [1]). To some extent, the WSSS method can successfully predict good masks for some easy objects with class labels. Therefore, as shown in Figure 2, in the first stage, we train the original network and we are able to select qualified object instances through the scene complexity of the image, the scope of the object and the semantic relevance by setting some criteria.
+
+Specifically, for the inferring phase after training the network, we follow two main criteria for collecting object instances: (i) the current image should only have a single
+
+![](images/8ff2c6873eea62cdb3dcaa0e832a23a2f00e1e07964a17f609897ce8ed0ce9e9.jpg)  
+Figure 3. Different kinds of pasting methods used in experiments. (a) Raw input, (b) Random rescale pasting, (c) Random rescale + rotation pasting, (d) Random rescale + rotation + Gaussian smoothing pasting.
+
+class. The intuition behind this is that in the case of only a single class, the image information should be simple and without a complex semantic environment, the segmentation results of the model should be more accurate; (ii) the segmentation result of the current image should meet the condition,  $\epsilon_1 < \frac{m}{n} < \epsilon_2$ , where  $\epsilon_1$  and  $\epsilon_2$  are two threshold factors, respectively.  $m$  is the number of pixels belonging to the foreground object,  $n$  is the number of pixels of the entire image. The reason lies that if the scale value of  $\frac{m}{n}$  is too large, it should be that the background is incorrectly identified as the foreground. In contrast, if the scale value is too small, it should be that the model has not been able to recognize enough foreground object pixel information. Different from existing synthesis approaches [13, 14], our method is based on self-provided masks to obtain qualified object instances images.
+
+# 3.2. Online Augmentation Training
+
+Blending. Before we take a step to train the network in the second stage, we first introduce how to blend the object instances into the natural images. As shown in Figure 3, we show different types of pasting skills in our experiments. It's worth mentioning that we only paste objects that have not appeared in the original images. The significance of this is that we can increase the diversity of objects of the images, while also reducing the dependence of the same objects in the inherent scene. By randomly rescaling the objects, we can paste them into the images appropriately to prevent them from being too large or too small. The addition of random rotation can change the inherent orientation properties of the objects. Adding Gaussian smoothing can help the added objects boundary blend more naturally.
+
+In some cases, the blending may not be ideal, we elaborate on several possibilities for random pasting. As shown in Figure 4, we have listed several augmented images of random pasting and we call them "perfect", "good" and "noise" examples. As for the "good" example, the new object "bird" covers part of the "dog" in the original image, however, we argue that this could help to erase the discriminative regions and force the network to discover more object regions like the function in [44]. The noise example shows that the
+
+![](images/e94b503f8e97b5f5bfc6f5753253b75aa354fb452481be23d233e7160e7d1812.jpg)  
+(a) perfect
+
+![](images/532b965eb88241768233cac61775e4ebb1602af9667f24c13a17c0f9f03665a5.jpg)  
+(b) good
+
+![](images/9650832bdc63a7b09bbd44a2b3fc06ee888601bba252c29b5c7dd83227432b6f.jpg)  
+(c) noise
+
+![](images/4bd65e7b9983c3b1a30aadd31f8a58642ea57a7d77660881fdb940eb2d5d2d78.jpg)  
+Figure 4. Examples of the input augmented images with varying degrees of occlusion.
+
+"sofa" completely covers the "aeroplane" in the original image, which will cause confusion to network classification. However, we consider that such hard examples do not account for the majority. Most objects occupy in the middle or prominent location of the natural images. The random blending method we employ tends to paste the new objects into the off-center position of the images. Thus, this case does not affect learning. Hence, our framework is robust to the quality of augmentation. According to our experiments, this simple random blending method performs well in boosting the performance.
+
+Online Training. The augmentation scheme is conducted online to enhance the network trained in stage-I to improve the ability to distinguish object features. Formally, in each batch, we sample  $N / 2$  images from the training dataset and the same number object instances images from the subset which is provided from stage-I. Then we randomly paste the segmented objects into the input images, which creates a  $N / 2$  batch new images. Thus, a batch of size  $N$  is generated online for each augmentation iteration. The construction process of the online augmentation learning is summarized in Algorithm 1.
+
+Note that we train the online augmentation method in a pairwise manner as shown in Figure 2 stage-II left. We consider this can further help the networks to recognize the objects for the reason that some images have new blended objects, while some do not, which can help the classifier find more discriminative features. The motivation behind this is similar to "finding the differences" with the human visual system. When the two images have a different object but with a duplicated background, which can often leave a deep impression. For the same reason, this can make the network classifier learn better features of this kind of object.
+
+Algorithm 1 Stage-II: Online Augmentation.  
+Input: The training dataset images  $\mathcal{I}$  and the corresponding labels  $\mathcal{L}$ ; The object instances  $\mathcal{O}$  and the corresponding labels  $\mathcal{T}$ .  
+1: while not done do  
+2:  $(\mathcal{I}_i, \mathcal{L}_i) \gets$  Draw one sample from training dataset;  
+3:  $(\mathcal{O}_j, \mathcal{T}_j) \gets$  Draw one sample from object instances subset;  
+4: while  $\mathcal{T}_j$  in  $\mathcal{L}_i$  do  
+5:  $(\mathcal{O}_j, \mathcal{T}_j) \gets$  Resample;  
+6: end while  
+7:  $\mathcal{I}_i' \gets$  Blend  $\mathcal{O}_j$  into  $\mathcal{I}_i$ ;  
+8:  $\mathcal{L}_i' \gets$  Append  $\mathcal{T}_j$  in  $\mathcal{L}_i$ ;  
+9: Train CAM  $\leftarrow$  Loss( $\mathbb{C}(\mathcal{I}_i), \mathcal{L}_i)$  + Loss( $\mathbb{C}(\mathcal{I}_i')$ ,  $\mathcal{L}_i'$ );  
+10: end while  
+11: Expansion.
+
+# 3.3. Discussion
+
+The proposed CDA framework contributes a new data augmentation learning strategy. Unlike the previous "copy-and-paste" works, we do not use additional pixel-wise labels. Specifically, by using the self-provided initial segmentation masks of the models, we can obtain the object instances for the next phase augmentation training. Furthermore, since our goal is to decouple the high correlation between objects and their contextual background, we don't need to consider much about visual context [13, 9], which can greatly improve the efficiency of pasting objects into the images. Besides, we adopt online augmentation training skills. Compared with static offline data augmentation, which merely enlarges the scale of the training dataset in linear-level. Namely, once a new dataset is formed, the number of images will remain unchanged. However, our method is able to obtain exponential-level augmentation, because the combination of object instances and natural images can be ever-changing in each round of training.
+
+# 4. Experiments
+
+To demonstrate the contributions of the proposed method, we conduct several ablation studies to show the effectiveness of CDA and compare different baselines models to the state-of-the-arts. We will give the details of the datasets, evaluation metric, and baseline models in the following.
+
+# 4.1. Dataset
+
+All the networks in our framework are trained and evaluated on the PASCAL VOC 2012 [15] and COCO [32] segmentation benchmark for a fair comparison to previous
+
+approaches. As for PASCAL VOC, the official dataset separation has 1464 images for training, 1449 for validation and 1456 for testing. Following the common practice, we take additional annotations to build an augmented training set with 10582 images presented in [19]. COCO is a more challenging benchmark with 81 semantic classes (one background class), 80k, and 40k images for training and validation. We use the standard mean Intersection-over-Union (mIoU) as the evaluation metric for all experiments.
+
+# 4.2. Implementation Details
+
+To validate the applicability of CDA, we deploy it on three popular WSSS models including IRNet [1], AffinityNet [2] and SEAM [43]. The general training architecture components include a multi-label image classification step, a pseudo-mask generation step, and the final segmentation model (DeepLab-v2 [7]). We strictly follow the same settings as reported in the official codes. Specially, for SEAM [43] and AffinityNet [2] baselines, ResNet38 [20] that pre-trained on ImageNet [11] is adopted as backbone with batch size as 8 and 16, respectively. When training the networks, multi-scale and data augmentation techniques like horizontal flip, random cropping, and color jittering are deployed in both architectures. Following the poly policy  $lr_{init} = lr_{init}(1 - itr / max\_ itr)^{\rho}$  with  $\rho = 0.9$  for decay, the models are trained with a fix input size as  $448 \times 448$  using Adam optimizer [25]. Besides, online hard example mining [39] is employed on the training loss in SEAM. As for IRNet [1], ResNet50 [20] is used as the backbone network (pretrained on ImageNet). The batch size is set to 16 for the image classification model and 32 for the inter-pixel relation model. The input image is cropped into a fix size of  $512 \times 512$  using zero padding if needed. The model is trained with the same polynomial decay strategy as in AffinityNet [2] using stochastic gradient descent (SGD) for optimization with 8,000 iterations. The fully-connected CRF [27] is used in three baselines to refine CAM, pseudo-mask, and segmentation mask with the default parameters in the public code. We set the threshold  $\epsilon_1 = 0.1$  and  $\epsilon_2 = 0.7$  by experience.
+
+# 4.3. Ablation Studies
+
+To verify the effectiveness of our CDA, we evaluate CAM seed regions, pseudo-masks, and segmentation masks, respectively. In our experiments, the standard mean Intersection over Union (mIoU) is used on the training set for evaluating CAM seed area masks and pseudo-masks, and on the PASCAL VOC 2012 val and test sets for evaluating segmentation masks. For the sake of simplicity, since the three WSSS models are all based on CAM [51], we use one of the representative models (IRNet [1]) as a baseline to conduct several ablation studies on CAM in mIoU to illustrate the role of each component of our approach.
+
+Random pasting vs. Other sophisticated augmenta
+
+<table><tr><td>Method</td><td>operation</td><td>mIoU (%)</td></tr><tr><td rowspan="2">Conventional Augmentation</td><td>Rotation</td><td>48.5</td></tr><tr><td>Translation</td><td>48.4</td></tr><tr><td rowspan="3">Mixup [49]</td><td>α = 0.3</td><td>48.7</td></tr><tr><td>α = 0.5</td><td>48.5</td></tr><tr><td>α = 0.8</td><td>49.0</td></tr><tr><td>CutOut [12]</td><td>Random</td><td>48.9</td></tr><tr><td>CutMix [48]</td><td>Random</td><td>49.2</td></tr><tr><td>Random pasting (ours)</td><td>Rescale</td><td>49.8</td></tr></table>
+
+Table 1. Experiments of different augmentation methods. Here  $\alpha$  is the intensity of the interpolation between the eigenvector and the target vector.  
+
+<table><tr><td>Baseline</td><td>Rescale</td><td>Rotation</td><td>Gaussian</td><td>mIoU (%)</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>48.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>49.8</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>50.8</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>49.6</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>50.4</td></tr></table>
+
+Table 2. The ablation study of the effect on different pasting methods. Baseline indicates the original CAM method without pasting new objects for augmentation.  
+
+<table><tr><td>Training manner</td><td>mIoU (%)</td></tr><tr><td>Pairwise</td><td>50.8</td></tr><tr><td>None-pairwise</td><td>50.1</td></tr></table>
+
+Table 3. Experiments of augmentation training manner.
+
+tion methods: As for the traditional augmentation methods, we adopt the random rotation and translation to expand the dataset to three times the original size, however, they can not bring significant boost for the performance. We also compare Mixup [49], CutOut [12] and CutMix [48] methods to generate new augmented images. As shown in Table 1, random rescale pasting outperforms the other three methods achieving  $49.8\%$  mIoU. These results demonstrate that random pasting is suitable for our CDA framework. We consider that proper occlusion helps the network to better mine the features of other areas of the objects, and the situation of complete occlusion is relatively rare which will not affect our learning process.
+
+Comparison with baseline: We further explore the impact of different pasting methods on data augmentation. Table 2 shows that using random rescale pasting has a  $1.5\%$  improvement compared to baseline. After combining rescale and rotation, we can get the best performance to  $50.8\%$  mIoU on PASCAL VOC training set. The results show that applying Gaussian smoothing can not help to im
+
+![](images/846acbf57d09529da8e73a05cf4b494d94e8874d5dd9efaae16a1238dc6d8003.jpg)  
+Figure 5. Qualitative visualization of CAMs. Our CDA framework not only suppresses over-activation  $(1^{st},2^{nd},3^{rd}$  row) of the high correlation contextual backgrounds of the objects and expands CAMs to cover the whole object regions  $(4^{th}$  row).
+
+prove the performance. Therefore, in subsequent experiments, unless otherwise specified, we will use the random rescale combining with the rotation method.
+
+Figure 5 shows the qualitative comparison between our CAM+Aug by CDA method and the original CAM. As shown in the first and second rows in the figure and the labels of objects are "table". The original CAM will activate background semantic information that is strongly related to the "table", such as "chair". However, by employing the decoupling augmentation training strategy, our method can focus on the target areas. For the image with the label of "train", CAM even pays attention not to the object itself, but the "track", which will be detrimental to the subsequent segmentation task. Moreover, CDA can also help the network expand and discover more comprehensive object features but not only the most discriminative regions like the "cat" shown in the last row.
+
+The effect on pairwise training: Compared to merely using the augmented images to train the networks, we use the none-augmented images with the augmented images as pair images to jointly train the models as shown in Figure 2 stage-II. The results shown in Table 3 show that applying pairwise training strategy outperforms the one in single augmented images, which illustrates that this helps the network classifier to learn more discriminative features.
+
+<table><tr><td>Network</td><td>Backbone</td><td>CAM</td><td>Pseudo-Masks</td><td>Seg. Masks (val-set)</td><td>Seg. Masks (test-set)</td></tr><tr><td rowspan="2">AffinityNet [2] + CDA</td><td>ResNet-38</td><td>48.0</td><td>59.7</td><td>61.7</td><td>63.7</td></tr><tr><td>ResNet-38</td><td>48.9+0.9</td><td>63.3+3.6</td><td>64.2+2.5</td><td>65.8+2.1</td></tr><tr><td rowspan="2">IRNet* [1] + CDA</td><td>ResNet-50</td><td>48.3</td><td>65.9</td><td>63.5</td><td>64.8</td></tr><tr><td>ResNet-50</td><td>50.8+2.5</td><td>67.7+1.8</td><td>65.8+2.3</td><td>66.4+1.6</td></tr><tr><td rowspan="2">SEAM [43] + CDA</td><td>ResNet-38</td><td>55.4</td><td>63.4</td><td>64.5</td><td>65.7</td></tr><tr><td>ResNet-38</td><td>58.4+3.0</td><td>66.4+3.0</td><td>66.1+1.6</td><td>66.8+1.1</td></tr></table>
+
+Table 4. Different baselines with our CDA framework performance in mIoU on PASCAL VOC. *denotes our reimplemented results since the original code does not provided pre-trained weights.  
+
+<table><tr><td>Number of pasted objects</td><td>Same category objects</td><td>mIoU (%)</td></tr><tr><td>1</td><td>×</td><td>50.8</td></tr><tr><td>2</td><td>×</td><td>48.9</td></tr><tr><td>3</td><td>×</td><td>47.8</td></tr><tr><td>1</td><td>✓</td><td>50.2</td></tr><tr><td>2</td><td>✓</td><td>48.6</td></tr><tr><td>3</td><td>✓</td><td>47.4</td></tr></table>
+
+Table 5. Experiments of different number of pasted objects for augmentation.
+
+The effect on objects numbers: Under the default settings of our experiment, we only paste one new instance that does not exist in the original images. We further explore the effect of pasting multiple objects into the images to conduct augmentation. As shown in Table 5 above the solid line, when the number of object to be pasted increases from one to two, the mIoU performance will decrease. As the number of pasted objects changes to three, it will even worse than the baseline. The results show that over-pasted objects may cover the objects in the original image, making the noise sample dominant. This will confuse the classifier, which will bring negative effects. In addition, as depicted below the solid line in Table 5, when we allow the pasted object to be consistent with the object category in the original image, their general performance is worse than the former. This shows that forcing objects of different categories to be pasted into images can decouple the strong contextual dependence of objects in the original semantic environment.
+
+Analysis of pseudo labels and Segmentation masks: The overall results are shown in Table 4. We can observe that deploying CDA on different weakly supervised semantic segmentation models can improve all their performances. Specifically, SEAM [43] can achieve the best performance in Segmentation Masks on both validation set and testing set. Figure 6 shows that we can obtain more accurate and complete masks covering the object areas.
+
+# 4.4. Comparison with State-of-the-arts
+
+Finally, we compare our framework with state-of-the-art methods on the PASCAL VOC 2012 and COCO dataset in
+
+![](images/35a900d5d7e679cbeee2d9615b3b670696e2e2df8225add27d1a51f99f645573.jpg)  
+Figure 6. Visualization of pseudo-masks (baseline: IRNet [1]). (a) Input images. (b) Ground-Truth labels. (c) Our CAM+Aug. (d) Original CAM.
+
+cluding both the validation set and the testing set. For a fair comparison, we adopt the same DeepLab [6, 7] architectures as reported in the original papers. On PASCAL VOC 2012, as is shown in Table 6, although different baselines already boosts performance compared to previous methods, when CDA is deployed in the models, SEAM [43] can achieve the best performance and outperform other state-of-the-arts by a large margin. IRNet [1] yield the second best performance and can beat its later published works. On COCO, CDA deployed on IRNet achieves  $33.7\%$  mIoU on the val set, which surpasses the previous best model by  $1.1\%$  mIoU. Figure 7 presents qualitative results of our CDA approach applying on IRNet baseline and compares them to itself. We can observe that CDA can make more accurate predictions on objects, which shows better demarcations in some coherent areas. Meanwhile, CDA can help to expand and discover more comprehensive object regions.
+
+![](images/da786e716fa7473f9651fb5bd513816e394a0c9dc93929be113165ab64d6a4d9.jpg)  
+(a)  
+Figure 7. Qualitative results on the PASCAL VOC 2012 val set. (a) Input images. (b) Ground-truth labels. (c) Results obtained by IRNet [1] baseline. (d) Results of our IRNet + CDA. More results can be found in the supplementary material.
+
+<table><tr><td>Methods</td><td>Backbone</td><td>Saliency</td><td>val</td><td>test</td></tr><tr><td>CCNN [34]ICCV&#x27;15</td><td>VGG16</td><td>-</td><td>35.3</td><td>35.6</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>-</td><td>50.7</td><td>51.1</td></tr><tr><td>STC [45]TPAMI&#x27;17</td><td>VGG16</td><td>✓</td><td>49.8</td><td>51.2</td></tr><tr><td>AdvEra [44]CVPR&#x27;17</td><td>VGG16</td><td>✓</td><td>55.0</td><td>55.7</td></tr><tr><td>DCSP [5]BMVC&#x27;17</td><td>ResNet101</td><td>✓</td><td>60.8</td><td>61.9</td></tr><tr><td>MDC [46]CVPR&#x27;18</td><td>VGG16</td><td>✓</td><td>60.4</td><td>60.8</td></tr><tr><td>MCOF [42]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>60.3</td><td>61.2</td></tr><tr><td>DSRG [23]CVPR&#x27;18</td><td>ResNet101</td><td>✓</td><td>61.4</td><td>63.2</td></tr><tr><td>AffinityNet [2]CVPR&#x27;18</td><td>ResNet-38</td><td>-</td><td>61.7</td><td>63.7</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>-</td><td>63.5</td><td>64.8</td></tr><tr><td>FickleNet [28]CVPR&#x27;19</td><td>ResNet101</td><td>✓</td><td>64.9</td><td>65.3</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>-</td><td>64.5</td><td>65.7</td></tr><tr><td>ICD [16]CVPR&#x27;20</td><td>ResNet101</td><td>-</td><td>64.1</td><td>64.3</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>-</td><td>65.8</td><td>66.4</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>-</td><td>66.1</td><td>66.8</td></tr></table>
+
+# 5. Conclusion
+
+In this paper, we propose a Context Decoupling Augmentation (CDA) method for WSSS and to narrow the gap with fully supervision. Specifically, through a two-stage training, the object instances provided by the network itself are copied and pasted into the input images to conduct augmentation. To further improve the ability of network for
+
+Table 6. Performance comparisons with other state-of-the-art WSSS methods on PASCAL VOC 2012 dataset. The best and second best performance under each set are marked with corresponding formats.  
+
+<table><tr><td>Methods</td><td>Backbone</td><td>val</td></tr><tr><td>BFBP [38]ECCV&#x27;16</td><td>VGG16</td><td>20.4</td></tr><tr><td>SEC [26]ECCV&#x27;16</td><td>VGG16</td><td>22.4</td></tr><tr><td>IRNet [1]CVPR&#x27;19</td><td>ResNet50</td><td>32.6</td></tr><tr><td>SEAM [43]CVPR&#x27;20</td><td>ResNet38</td><td>31.9</td></tr><tr><td>IAL [41]IJCV&#x27;20</td><td>VGG16</td><td>27.7</td></tr><tr><td>IRNet + CDA (ours)</td><td>ResNet50</td><td>33.7</td></tr><tr><td>SEAM + CDA (ours)</td><td>ResNet38</td><td>33.2</td></tr></table>
+
+Table 7. Performance comparisons with other state-of-the-art WSSS methods on COCO val in terms of mIoU.
+
+learning object features, we adopt pairwise training manner to help the classifier to distinguish more discriminative features. Experimental results show that CDA can help boost various WSSS methods to the new state-of-the-arts.
+
+# Acknowledgement
+
+This work was supported by National Natural Science Foundation of China (NSFC) 61876208, Key-Area Research and Development Program of Guangdong Province 2018B010108002, Central Universities of China under Grant D2192860, and the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG-RP-2018-003), and the MOE Tier-1 research grants: RG28/18 (S), RG22/19 (S) and RG95/20.
+
+# References
+
+[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2209-2218, 2019. 1, 2, 3, 5, 7, 8  
+[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4981-4990, 2018. 1, 2, 5, 7, 8  
+[3] Relja Arandjelović and Andrew Zisserman. Object discovery with a copy-pasting gan. arXiv preprint arXiv:1905.11369, 2019. 3  
+[4] Amy Bearman, Olga Russakovsky, Vittorio Ferrari, and Li Fei-Fei. What's the point: Semantic segmentation with point supervision. In European conference on computer vision, pages 549-565. Springer, 2016. 1  
+[5] Arslan Chaudhry, Puneet K Dokania, and Philip HS Torr. Discovering class-specific pixels for weakly-supervised semantic segmentation. arXiv preprint arXiv:1707.05821, 2017. 8  
+[6] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv preprint arXiv:1412.7062, 2014. 7  
+[7] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4):834-848, 2017. 1, 5, 7  
+[8] 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. 1  
+[9] Wenqing Chu and Deng Cai. Deep feature based contextual model for object detection. Neurocomputing, 275:1035-1042, 2018. 5  
+[10] Jifeng Dai, Kaiming He, and Jian Sun. Boxsup: Exploiting bounding boxes to supervise convolutional networks for semantic segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1635-1643, 2015. 1  
+[11] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. IEEE, 2009. 5  
+[12] Terrance DeVries and Graham W Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552, 2017. 3, 6  
+[13] Nikita Dvornik, Julien Mairal, and Cordelia Schmid. Modeling visual context is key to augmenting object detection datasets. In Proceedings of the European Conference on Computer Vision (ECCV), pages 364-380, 2018. 2, 3, 4, 5
+
+[14] Debidatta Dwibedi, Ishan Misra, and Martial Hebert. Cut, paste and learn: Surprisingly easy synthesis for instance detection. In Proceedings of the IEEE International Conference on Computer Vision, pages 1301-1310, 2017. 3, 4  
+[15] Mark Everingham, SM Ali Eslami, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The Pascal visual object classes challenge: A retrospective. International journal of computer vision, 111(1):98-136, 2015. 2, 5  
+[16] Junsong Fan, Zhaoxiang Zhang, Chunfeng Song, and Tieniu Tan. Learning integral objects with intra-class discriminator for weakly-supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4283-4292, 2020. 8  
+[17] Maayan Frid-Adar, Eyal Klang, Michal Amitai, Jacob Goldberger, and Hayit Greenspan. Synthetic data augmentation using gan for improved liver lesion classification. In 2018 IEEE 15th international symposium on biomedical imaging (ISBI 2018), pages 289–293. IEEE, 2018. 3  
+[18] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A Wichmann, and Wieland Brendel. Imagenet-trained cnns are biased towards texture; increasing shape bias improves accuracy and robustness. arXiv preprint arXiv:1811.12231, 2018. 3  
+[19] Bharath Hariharan, Pablo Arbeláez, Lubomir Bourdev, Subhransu Maji, and Jitendra Malik. Semantic contours from inverse detectors. In 2011 International Conference on Computer Vision, pages 991–998. IEEE, 2011. 5  
+[20] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 5  
+[21] Seunghoon Hong, Donghun Yeo, Suha Kwak, Honglak Lee, and Bohyung Han. Weakly supervised semantic segmentation using web-crawled videos. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7322-7330, 2017. 1, 2  
+[22] Qibin Hou, PengTao Jiang, Yunchao Wei, and Ming-Ming Cheng. Self-erasing network for integral object attention. In Advances in Neural Information Processing Systems, pages 549–559, 2018. 2  
+[23] Zilong Huang, Xinggang Wang, Jiasi Wang, Wenyu Liu, and Jingdong Wang. Weakly-supervised semantic segmentation network with deep seeded region growing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7014-7023, 2018. 8  
+[24] Anna Khoreva, Rodrigo Benenson, Jan Hosang, Matthias Hein, and Bernt Schiele. Simple does it: Weakly supervised instance and semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 876-885, 2017. 1  
+[25] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. 5  
+[26] Alexander Kolesnikov and Christoph H Lampert. Seed, expand and constrain: Three principles for weakly-supervised image segmentation. In European conference on computer vision, pages 695-711. Springer, 2016. 8
+
+[27] Philipp Krahenbuhl and Vladlen Koltun. Efficient inference in fully connected crfs with gaussian edge potentials. In Advances in neural information processing systems, pages 109-117, 2011. 5  
+[28] Jungbeom Lee, Eunji Kim, Sungmin Lee, Jangho Lee, and Sungroh Yoon. Ficklenet: Weakly and semi-supervised semantic image segmentation using stochastic inference. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5267-5276, 2019. 8  
+[29] Kunpeng Li, Ziyan Wu, Kuan-Chuan Peng, Jan Ernst, and Yun Fu. Tell me where to look: Guided attention inference network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9215-9223, 2018. 2  
+[30] Di Lin, Jifeng Dai, Jiaya Jia, Kaiming He, and Jian Sun. Scribblesup: Scribble-supervised convolutional networks for semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3159-3167, 2016. 1  
+[31] Guosheng Lin, Chunhua Shen, Anton Van Den Hengel, and Ian Reid. Efficient piecewise training of deep structured models for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3194-3203, 2016. 1  
+[32] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dálár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 2, 5  
+[33] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3431-3440, 2015. 1  
+[34] Deepak Pathak, Philipp Krahenbuhl, and Trevor Darrell. Constrained convolutional neural networks for weakly supervised segmentation. In Proceedings of the IEEE international conference on computer vision, pages 1796-1804, 2015. 8  
+[35] Xingchao Peng, Baochen Sun, Karim Ali, and Kate Saenko. Learning deep object detectors from 3d models. In Proceedings of the IEEE International Conference on Computer Vision, pages 1278-1286, 2015. 3  
+[36] Tal Remez, Jonathan Huang, and Matthew Brown. Learning to segment via cut-and-paste. In Proceedings of the European conference on computer vision (ECCV), pages 37-52, 2018. 3  
+[37] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. arXiv preprint arXiv:1506.01497, 2015. 3  
+[38] Fatemehsadat Saleh, Mohammad Sadegh Aliakbarian, Mathieu Salzmann, Lars Petersson, Stephen Gould, and Jose M Alvarez. Built-in foreground/background prior for weakly-supervised semantic segmentation. In European conference on computer vision, pages 413-432. Springer, 2016. 8  
+[39] Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In Proceedings of the IEEE conference on
+
+computer vision and pattern recognition, pages 761-769, 2016.5  
+[40] Paul Vernaza and Manmohan Chandraker. Learning random-walk label propagation for weakly-supervised semantic segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7158-7166, 2017. 1  
+[41] Xiang Wang, Sifei Liu, Huimin Ma, and Ming-Hsuan Yang. Weakly-supervised semantic segmentation by iterative affinity learning. International Journal of Computer Vision, 128(6):1736-1749, 2020. 8  
+[42] Xiang Wang, Shaodi You, Xi Li, and Huimin Ma. Weakly-supervised semantic segmentation by iteratively mining common object features. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1354-1362, 2018. 8  
+[43] Yude Wang, Jie Zhang, Meina Kan, Shiguang Shan, and Xilin Chen. Self-supervised equivariant attention mechanism for weakly supervised semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12275–12284, 2020. 1, 5, 7, 8  
+[44] Yunchao Wei, Jiashi Feng, Xiaodan Liang, Ming-Ming Cheng, Yao Zhao, and Shuicheng Yan. Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1568-1576, 2017. 2, 4, 8  
+[45] Yunchao Wei, Xiaodan Liang, Yunpeng Chen, Xiaohui Shen, Ming-Ming Cheng, Jiashi Feng, Yao Zhao, and Shuicheng Yan. Stc: A simple to complex framework for weakly-supervised semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(11):2314-2320, 2016. 8  
+[46] Yunchao Wei, Huaxin Xiao, Honghui Shi, Zequn Jie, Jiashi Feng, and Thomas S Huang. Revisiting dilated convolution: A simple approach for weakly-and semi-supervised semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7268-7277, 2018. 8  
+[47] Fisher Yu and Vladlen Koltun. Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122, 2015. 2  
+[48] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023-6032, 2019. 6  
+[49] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 3, 6  
+[50] Tianyi Zhang, Guosheng Lin, Weide Liu, Jianfei Cai, and Alex Kot. Splitting vs. merging: Mining object regions with discrepancy and intersection loss for weakly supervised semantic segmentation. In European Conference on Computer Vision, 2020. 1  
+[51] Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discrimina
+
+tive localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2921-2929, 2016. 2, 5  
+[52] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 3

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+    {
+        "type": "text",
+        "text": "Strategic Classification Made Practical",
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+        "text": "Sagi Levanon<sup>1</sup> Nir Rosenfeld<sup>1</sup>",
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+        "text": "Strategic classification regards the problem of learning in settings where users can strategically modify their features to improve outcomes. This setting applies broadly and has received much recent attention. But despite its practical significance, work in this space has so far been predominantly theoretical. In this paper we present a learning framework for strategic classification that is practical. Our approach directly minimizes the \"strategic\" empirical risk, achieved by differentiating through the strategic response of users. This provides flexibility that allows us to extend beyond the original problem formulation and towards more realistic learning scenarios. A series of experiments demonstrates the effectiveness of our approach on various learning settings.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+        "text": "Across a multitude of domains—from loan approval to online dating to hiring and admissions—predictive machine learning models are becoming imperative for informing decisions that affect the lives of humans. But when people benefit from certain predictive outcomes, they are prone to act strategically to improve those outcomes. This has raised awareness as to the idea that standard learning algorithms may not be robust to such behavior, and there is a growing recognition as to the prevalence of this phenomena. Given the breadth of domains in which strategic user behavior is likely, practical tools for learning in strategic settings are of considerable importance.",
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+    {
+        "type": "text",
+        "text": "In this paper we study practical aspects of learning in the setting of strategic classification (Brückner & Scheffer, 2011; Hardt et al., 2016). In this problem, users respond to a published classifier by strategically modifying their features (at some cost) to improve their predicted outcomes. As a concrete example, consider a bank offering loans. The",
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+        "type": "text",
+        "text": "$^{1}$ Department of Computer Science, Technion - Israel Institute of Technology. Correspondence to: Nir Rosenfeld <nirr@cs.technion.ac.il>.",
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+    {
+        "type": "text",
+        "text": "Proceedings of the  $38^{th}$  International Conference on Machine Learning, PMLR 139, 2021. Copyright 2021 by the author(s).",
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+    {
+        "type": "text",
+        "text": "bank would like to approve a loan only if it is likely to be returned, and to aid in decision-making, the bank trains a classifier to predict loan returns. Applicants, however, would like their requests to be approved—regardless of their actual credibility. To promote their interests, they can modify their applications (at some cost) to best align with the bank's classification rule. From the bank's perspective, such modifications can invalidate model predictions, and the primary goal in strategic classification is to design learning algorithms that are robust to this form of 'gaming'.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that gaming is caused by the model itself, indirectly through how it shapes user incentives, and to its detriment. In this sense, strategic classification exemplifies how machine learning can be amenable to Goodhart's Law, a principle in policymaking stating that \"when a measure becomes a target, it ceases to be a good measure\". Strategic classification thus succinctly captures a natural form of tension that arises between a learning-based system and its users. There has been much recent work on this topic, studying aspects such as generalization (Sundaram et al., 2020; Zhang & Conitzer, 2021), equilibrium and dynamics (Perdomo et al., 2020; Brown et al., 2020; Izzo et al., 2021; Miller et al., 2021), online learning (Dong et al., 2018; Chen et al., 2019; Ahmadi et al., 2020), causality and decision outcomes (Kleinberg & Raghavan, 2019; Rosenfeld et al., 2020; Shavit et al., 2020; Bechavod et al., 2020; Miller et al., 2020), transparency (Ghalme et al., 2021; Bechavod et al., 2021), and social perspectives (Hu et al., 2019; Milli et al., 2019; Chen et al., 2020).",
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+        "type": "text",
+        "text": "But despite this flurry of recent work, algorithms for strategic classification are not in widespread use. The key reason for this is that work in this space has been predominantly theoretical. This has several practical implications. First, for mathematical tractability, strong assumptions are made (e.g., that the cost function is fixed and known). But the robustness of these methods to violations of their assumptions is not well understood. Second, methods tend to be crafted for very particular learning settings, and do not easily extend beyond the narrow context in which they are originally studied. Third, currently available algorithms lag far behind recent advances in machine learning methodology; they are prone to issues of scale, expressivity, and runtime, and lack the flexibility and modularity that current approaches readily provide (e.g., the ability to seamlessly \"add a layer\" or",
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+    {
+        "type": "aside_text",
+        "text": "arXiv:2103.01826v2 [cs.LG] 14 Jun 2021",
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+    },
+    {
+        "type": "text",
+        "text": "change the loss function). Combined, the above limitations indicate a clear need for an approach to learning in strategic classification that is effective and practical. Our work aims to take a first step towards addressing this need.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The core idea of our approach is to encode into the learning objective a response mapping that models how users respond to a given classification rule. By anticipating how inputs will be strategically modified under a given model, our approach optimizes directly for predictive performance under strategic behavior. We refer to this as *strategic empirical risk minimization*, or SERM. The challenge in optimizing the SERM objective is that models of user response typically involve an argmax operator, which can be nondifferentiable and even discontinuous. Our solution is to replace the argmax operator with a differentiable proxy, and for this we draw on recent advances in differentiable optimization solvers (Amos & Kolter, 2017; Djolonga & Krause, 2017; Agrawal et al., 2019a,b; Berthet et al., 2020; Tan et al., 2020; Agrawal & Boyd, 2020) and adapt them to our purpose. The resulting *strategic response layer* provides the main building-block of our framework.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Using the flexibility our framework provides, we propose and showcase multiple ways in which the framework can extend beyond the original formulation of strategic classification and towards more realistic learning scenarios. We make use of the modular nature of our approach and the flexibility it provides to explore various extensions aimed at addressing potential practical concerns. These include: supporting complex predictive models (e.g., recursive neural networks), supporting structured cost functions (e.g., constraining movement to a manifold), and relaxing the assumption of a fixed and known cost function (we handle adjustable and unknown costs).",
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+    {
+        "type": "text",
+        "text": "The primary goal in strategic classification is to learn strategically-robust predictive models, but several works have raised concern as to the adverse social outcomes this may entail (Milli et al., 2019; Hu et al., 2019; Chen et al., 2020). This may not be surprising given that learning focuses entirely on optimizing predictive accuracy. To address these concerns, here we argue for a broader perspective that considers the trade-off between system and user interests. Borrowing from welfare economics, we take the perspective of a 'social planner' tasked with balancing between these interests, and show how our approach can extend to target any operating point along the pareto front. To do this, we cast strategic classification as a problem of model selection, and propose novel forms of regularization that promote favorable social outcomes for various notions of 'social good'. Because strategic classification is not a zero-sum game, the incentives of the system and of its users are not entirely antagonistic. As we show, this permits much social benefit to be gained at only a small cost in accuracy.",
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+    {
+        "type": "text",
+        "text": "In summary, our paper makes the following contributions:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Practical framework. We propose a novel learning framework for strategic classification that is practical, effective, and flexible. Our approach allows to differentiate through strategic user responses, thus permitting end-to-end training.",
+            "- Flexible modeling. We show how the flexibility of our approach allows for learning in diverse strategic settings. We effectively apply our approach to multiple such settings of practical interest.",
+            "- Socially-aware learning. We propose several forms of regularization that encourage learned models to promote favorable social outcomes. By capitalizing on certain structural aspects of the problem, our regularization effectively balances between system and user interests."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "We conduct a series of experiments demonstrating the effectiveness of our approach. With respect to the above points, each of our experiments is designed to study a different practical aspect of learning. The experiments cover a range of learning environments using real and synthetic data. Our results show that learning in strategic classification can be practical, effective, and socially responsible.",
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+    {
+        "type": "text",
+        "text": "One of our main goals in this paper is to motivate and support future empirical research on strategic classification, Towards this end, we make publicly available a code repository with a flexible implementation of our approach, designed to support a wide range of strategic learning settings. Code can be found at https://github.com/SagiLevanon1/scmp.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The literature on strategic classification is growing at a rapid pace. Various formulations of the problem were studied in earlier works (Brückner & Scheffer, 2009; Brückner et al., 2012; Großhans et al., 2013), but most recent works adopt the core setup of Hardt et al. (2016), as we do here. Research in this space has mostly been oriented towards theory, with recent work introducing notions similar to SERM and extending PAC theory to this setting (Sundaram et al., 2020; Zhang & Conitzer, 2021). We complement these by placing emphasis on practical aspects of learning.",
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+    {
+        "type": "text",
+        "text": "Several papers consider the social impacts of strategic classification. Milli et al. (2019) study the social burden imposed by optimizing for accuracy. Chen et al. (2020) study the connection between strategically-aware learning and recourse. Hu et al. (2019) focus on fairness and show how classifiers can induce inequitable modification costs that affect utility. Our work ties these together, providing means to control",
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+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "the tradeoff between classifier's accuracy and the social outcomes it induces through regularization (see Sec. 3.4).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A parallel line of work studies how learned models affect actual (rather than predictive) outcomes. Some works analyze how models should promote users to invest effort effectively (Kleinberg & Raghavan, 2019; Alon et al., 2020), while others tie learning to the underlying casual mechanisms of the environment (Perdomo et al., 2020; Bechavod et al., 2020; Shavit et al., 2020; Miller et al., 2020). We remain within the original, purely predictive problem formulation, but view the extension of our approach to such settings to be intriguing as future work.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Learning setup. Denote by  $x \\in \\mathcal{X} \\subseteq \\mathbb{R}^d$  features representing user attributes (e.g., a loan application profile), and by  $y \\in \\mathcal{Y} = \\{-1, 1\\}$  their corresponding labels (e.g., loan returned or not). Let  $p(x, y)$  be a joint distribution over nonstrategic features and labels. The primary goal in learning is to find a classifier  $h: \\mathcal{X} \\to \\mathcal{Y}$  from a class  $H$  that achieves high expected accuracy. For this, we assume access to a sample set  $S = \\{(x_i, y_i)\\}_{i=1}^m$  sampled i.i.d. from  $p(x, y)$  on which we train. At test time, however,  $h$  is evaluated on data that is prone to modification by users. In strategic classification, users modify their features using the response mapping:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta_ {h} (x) \\triangleq \\underset {x ^ {\\prime} \\in \\mathcal {X}} {\\operatorname {a r g m a x}} h \\left(x ^ {\\prime}\\right) - c \\left(x, x ^ {\\prime}\\right) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $c$  is a known cost function. Test data includes pairs  $(\\Delta_h(x), y)$  where  $(x, y) \\sim p$ , and the goal in learning is to optimize predictive accuracy under this induced distribution.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As is common, the classifiers we consider will be based on score functions  $f: \\mathcal{X} \\to \\mathbb{R}$  via the decision rule  $h_f(x) = \\mathrm{sign}(f(x))$ , and learning will be concerned with optimizing over a class of parametrized score functions  $F$ . We write  $\\Delta_f$  to mean  $\\Delta_{h_f}$ , and for clarity, omit the notational dependence of the classifier  $h_f$  on  $f$  when clear from context.",
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+    {
+        "type": "text",
+        "text": "Game-theoretic formulation. Strategic classification can be formulated as a Stackelberg game between two players—the system and a population of users. First, the system learns from  $S$  a classifier  $h$ . Then, given  $h$ , users respond via  $\\Delta_h$ . The payoffs are:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {S y s t e m :} \\quad \\mathbb {P} [ y = h (\\Delta_ {h} (x)) ], \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {U s e r s :} \\quad \\mathbb {E} [ h (\\Delta_ {h} (x)) - c (x, \\Delta_ {h} (x)) ] \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Payoff to the system (Eq. (2)) is the probability of classifying manipulated points correctly. Payoff to the users (as a collective) is their expected utility (Eq. (3)), for which  $\\Delta$  as defined in Eq. (1) is a best-response.",
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+    {
+        "type": "text",
+        "text": "3.1. Strategic Empirical Risk Minimization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A naive approach would be to train a classifier to predict well on the (non-manipulated) input data, and use it at test time on manipulated data. The caveat in this approach is that strategic behavior causes a discrepancy between the (marginal) input distributions at train and test time. Strategic classification therefore introduces a form of distribution shift (Quionero-Candela et al., 2009), but with the unique property that shift is determined by the predictive model itself, albeit indirectly through its effect on user responses.",
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+    {
+        "type": "text",
+        "text": "Our approach will be to account for this shift by directly optimizing for the induced distribution. Noting that the system's payoff in Eq. (2) can be rewritten as  $1 - \\mathbb{E}[\\mathbb{1}\\{y\\neq h(\\Delta_h(x))\\} ]$  , we set our objective to the empirical loss over the strategically-modified training set:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {f \\in F} \\sum_ {i = 1} ^ {m} L \\left(\\Delta_ {f} \\left(x _ {i}\\right), y _ {i}, f\\right) + \\lambda R (f) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $L(z, y, f) = \\mathbb{1}\\{y \\neq h_f(z)\\}$  and  $R$  is an optional regularizer. In practice we replace  $L$  with a tractable surrogate (e.g., binary cross-entropy), and we will return to the role of regularization in Sec. 3.4. We refer to optimizing Eq. (4) as strategic empirical risk minimization (SERM). Note that  $f$  plays a dual role in the objective: it determines how inputs are modified (via  $\\Delta_f$ ) and how predictions are made on those modified inputs (via  $h_f$ ).",
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+    {
+        "type": "text",
+        "text": "3.2. Differentiating through strategic responses",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A natural way to approach the optimization of Eq. (4) is using gradient methods. The challenge in this approach is that  $\\Delta$  is an argmax operator and can therefore be nondifferentiable. Our solution to this will be to use a differentiable proxy for  $\\Delta$ , drawing inspiration from recent advances in differentibale optimization solvers. Such solvers map parametrized optimization problems to their (approximately) optimal solutions in a manner that is amenable to differentiation, and so can be used as optimization \"layers\" integrated into neural architectures.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our approach will be to implement the response mapping  $\\Delta$  as a differentiable optimization layer. In particular, we make use of convex optimization layers (Agrawal et al., 2019a), but since we seek to maximize, we will construct concave layers. A concave optimization layer  $g(\\theta)$  maps concave optimization problem instances to their argmax: the input to the layer,  $\\theta$ , defines the \"parameters\" (and hence the instance) of a template optimization problem, and the output of the layer is the solution under this parameterization. In our model,  $g$  will play the role of  $\\Delta$ , and  $\\theta$  will include features  $x$  and the learnable parameters of  $f$ .",
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+    {
+        "type": "text",
+        "text": "The response mapping  $\\Delta$  as defined in Eq. (1) is not concave, and to apply concave optimization, we construct a",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "concave proxy, denoted  $\\tilde{\\Delta}$ , as follows. To begin, assume for simplicity that  $h$  is linear, i.e.,  $h_w(x) = \\mathrm{sign}f_w(x)$  with  $f_w(x) = w^\\top x + b$ . Next, since sign is discontinuous, we replace it with a smooth sigmoid  $\\sigma^*$  of the following form:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {\\tau} ^ {*} (z) = \\frac {1}{2} \\sqrt {(\\tau^ {- 1} z + 1) ^ {2} + 1} - \\frac {1}{2} \\sqrt {(\\tau^ {- 1} z - 1) ^ {2} + 1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here  $\\tau$  is a temperature parameter: as  $\\tau$  decreases,  $\\sigma^{*}$  approaches sign. Our particular choice of sigmoid follows from the fact that  $\\sigma^{*}$  can be written as a sum of convex and concave functions. This motivates our final step, which is to apply the convex-concave procedure (CCP) (Yuille & Rangarajan, 2003). CCP is an approach to solving convex-concave optimization problems by iterating through a sequence of concave-relaxed problems, a process that guarantees convergence to local maxima. We focus on convex costs (e.g., linear or quadratic) so that CCP can be applied to the entire response function. Using CCP, we obtain reliable concave proxies of responses at each input. This gives us our differentiable proxy of the response mapping, which we refer to as a strategic response layer, defined as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\Delta} (x) = \\underset {x ^ {\\prime} \\in \\mathcal {X}} {\\operatorname {a r g m a x}} \\operatorname {C C P} \\left(\\sigma^ {*} \\left(w ^ {\\top} x ^ {\\prime} + b\\right)\\right) - c \\left(x, x ^ {\\prime}\\right) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here CCP denotes the concave proxy obtained at the last iteration of the procedure.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To compute the forward pass, we run the CCP procedure using any standard off-shelf convex solver, and compute the argmax w.r.t. the final proxy. For the backward pass, we plug the final proxy into the differentiable convex solver of Agrawal et al. (2019a) to get gradients for  $\\tilde{\\Delta}$  w.r.t.  $w, b$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Extensions",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3.1. NONLINEAR CLASSIFIERS",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The concave solver can handle only score functions  $f$  that are linear in the optimization variables. But  $f$  need not be linear in the input features  $x$ ; rather, it can be linear in any high-dimensional representation of the inputs,  $z = \\phi(x)$ ,  $z \\in \\mathcal{Z}$ , such as those obtained from the final hidden layers of neural networks. This holds as long as both  $f$  and  $c$  are defined over this representation (i.e., points move in representation-space). The response mapping becomes:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta (x) = \\operatorname * {a r g m a x} _ {z ^ {\\prime} \\in \\mathcal {Z}} \\sigma \\left(w ^ {\\top} z ^ {\\prime} + b\\right) - c (\\phi (x), z ^ {\\prime}) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "More generally,  $f$  must be linear in variables over which the cost function  $c$  is defined. For example, if  $c$  applies only to",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "a subset of the original features (for example, if only some features are manipulable), then  $f$  must be linear those features, but can be non-linear in all other features. Concretely, if  $x = (x_{\\mathrm{manip}}, x_{\\mathrm{non}})$  where  $x_{\\mathrm{manip}} \\in \\mathbb{R}^{d_1}$  and  $x_{\\mathrm{non}} \\in \\mathbb{R}^{d_2}$  are the manipulable and non-manipulable features, respectively, then our framework supports the following non-linear representational structure:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta (x) = \\operatorname * {a r g m a x} _ {x ^ {\\prime} \\in \\mathbb {R} ^ {d _ {1}}} \\sigma (w ^ {\\top} x ^ {\\prime} + v ^ {\\top} \\phi (x _ {\\text {n o n}}) + b) - c (x _ {\\text {m a n i p}}, x ^ {\\prime})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3.2. FLEXIBLE COSTS",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The core setting of strategic classification assumes costs are fixed. But in some settings, it is reasonable to assume that the system has some control over the cost function.<sup>4</sup> We model this as allowing the system to modify an initial cost function  $c_{0}$  to some other cost  $c \\in \\mathcal{C}$  from the class  $\\mathcal{C}$ , with this incurring a penalty of  $r(c_{0}, c)$ . The goal is now to jointly learn the classifier and the modified cost. Denoting by  $\\Delta_{f}^{c}$  the response mapping for classifier  $f$  and cost function  $c$ , we can extend the learning objective as follows:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {c \\in \\mathcal {C}} \\min  _ {f \\in F} \\sum_ {i = 1} ^ {m} L \\left(\\Delta_ {f} ^ {c} \\left(x _ {i}\\right), y _ {i}, f\\right) + r \\left(c _ {0}, c\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "By utilizing its flexibility in choosing  $c$ , in this setting the system has the capacity to obtain better predictive performance than when optimizing the objective in Eq. (4).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.3.3. UNKNOWN COSTS",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Strategic classification assumes that the cost function is known, but this may not hold in practice. Here we consider a setting in which the system does not know the true cost  $c^*$ , but has a reasonable estimate  $c_0$ . We model the system as believing that  $c^*$  lies in some set  $C \\subseteq \\mathcal{C}$  which includes  $c_0$  as well as nearby points, and which we view as a design parameter chosen by the learner. To learn in this setting, we propose a worst-case approach in which the system aims to perform well simultaneously on all  $c \\in C$ . We propose the following minmax objective:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {f \\in F} \\max  _ {c \\in C} \\sum_ {i = 1} ^ {m} L \\left(\\Delta_ {f} ^ {c} \\left(x _ {i}\\right), y _ {i}, f\\right) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3.4. MOVING ON A MANIFOLD",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The Manifold Hypothesis is a convention stating that high-dimensional data tend to lie on or near a low-dimensional manifold. Typically the manifold is unknown; but even if it",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
+            361,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>Most of the literature considers convex costs (and linear classifiers). This includes the experimental setting of Hardt et al. (2016).",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "There are many such tools available, and for reasonably-sized inputs, the computation overhead is small.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "${}^{3}$  Cost over representations are sensible,for example,when latent dimensions correspond to meaningful and manipulable realworld properties (e.g.,Chen et al. (2016)).",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>4</sup>For example, consider a bank offering loans, and assume one of the features is the number of credit cards a user has. If the bank itself issues credit cards, then by determining policies related to credit cards (e.g., eligibility criteria, commissions, rates), the bank achieves some control over costs.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "is known, common cost functions tend to permit arbitrary movement and so cannot account for this structure. Here we show how our approach can incorporate (approximate) manifold constraints into learning. We begin by learning a manifold bundle  $(M,T)$  composed of a manifold model  $M$  and a tangent function  $T(x)$  that returns the subspace tangent to  $M$  at  $x$ . Since tangents  $T(x)$  are linear objects that provide a first-order approximation to the manifold at  $x$ , our approach is to add them as linear constraints to the optimization of the response mapping (i.e., the argmax in  $\\Delta$  is taken over  $x' \\in T(x)$ ). This ensures points move only on the tangent, thus approximating movement on the manifold.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Regularizing for social good",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our discussion of strategic classification thus far has been focused on a single objective: predicting accurately in the face of strategic gaming. This promotes a clear interest of the system, but neglects to account for the effects of learning users. Returning to our loans example, note that any predictor inevitably determines the degree of recourse, defined as the ability of users that are denied a service (e.g., a loan) to take reasonable action to reverse this decision (Ustun et al., 2019; Gupta et al., 2019; Joshi et al., 2019; Chen et al., 2020; Karimi et al., 2020b). Recourse is clearly beneficial to users, but in many cases, its facilitation is also beneficial to the system (for discussion see Ustun et al. (2019); Venkatasubramanian & Alfano (2020); Karimi et al. (2020a)).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section we show how our framework can be used to train models that are both accurate and promote favorable social outcomes. Relying on the observation that different models can induce very different social outcomes (Heidari et al., 2019), we cast learning as a problem of model selection, where the selection criterion reflects some notion of 'social good' (e.g., recourse). Model selection is implemented through regularization and below we present novel forms of data-dependent regularizers  $R(f;S)$  targeting various notions of social good from the literature.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, we expect regularization to be useful because strategic classification is not a zero-sum game. In other words, predictive models that provide similar payoff to the system may differ considerably in their payoff to users; we argue that the system has the freedom, as well as the responsibility, to carefully choose between these. Viewing learning from the perspective of a 'social planner' interested in balancing between system and user interests, our regularization approach provides the means to achieve good balance. Varying the amount of regularization  $\\lambda$  provides solutions along the Pareto front, with  $\\lambda = 0$  corresponding to the strategic classification equilibrium in Eq. (2).",
+        "bbox": [
+            84,
+            683,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Expected utility. Since the payoff to users in Eq. (3) is given by their gained utility,  $u_{\\Delta}(x) = h(\\Delta(x)) - c(x, \\Delta(x))$ , a straightforward notion of social good is their expected utility,  $\\mathbb{E}[u_{\\Delta}(x)]$ . Note that  $\\Delta$  is a best-response but it is utility-optimal relative to  $h$ , and it is easy to construct an example showing that under the accuracy-optimal predictor utility can be arbitrarily low. To encourage models that provide users with high utility, we set:",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\text {u t i l}} (f; \\mathcal {S}) = - \\sum_ {i = 1} ^ {m} u _ {\\Delta} \\left(x _ {i}\\right) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and plug into the learning objective in (4), where in practice we again replace  $\\Delta$  with  $\\tilde{\\Delta}$  and optimize as in Sec. 3.2.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Social burden. In their paper on the social cost of strategic classification, Milli et al. (2019) study social burden, defined to be the minimum cost a positively-labeled user must incur in order to be classified correctly. Within our framework, we can regularize for social burden using:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\text {b u r d e n}} (f; \\mathcal {S}) = \\sum_ {i: y _ {i} = 1} \\min  _ {x ^ {\\prime}: f \\left(x ^ {\\prime}\\right) \\geq 0} c \\left(x, x ^ {\\prime}\\right) \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            401,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "which we can also implement as a convex optimization layer for linear  $f$  and convex  $c$  (the constraint is linear in  $x, w$ ).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Recourse. Recourse refers to the capacity of a user who is denied a service to restore approval through reasonable action (in our case, low-cost feature modification). Since  $\\Delta$  is a best-response, we say a user with  $h(x) = -1$  is granted recourse if  $h(\\Delta_h(x)) = 1$ . The random variable negating this condition is  $\\mathbb{1}\\{h(x) = -1 \\land h(\\Delta_h(x)) = -1\\}$ , and we regularize using its smoothed approximation:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\text {r e c o u r s e}} (f; \\mathcal {S}) = \\sum_ {i = 1} ^ {m} \\operatorname {s i g} (- f (x)) \\cdot \\operatorname {s i g} (- f (\\Delta_ {f} (x)))\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            501,
+            609,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Where  $\\operatorname{sig}(z) = \\frac{1}{1 + e^{-z}}$  is the standard sigmoid function. We calculate this regularization term using the same CCP approach on  $\\Delta_f(x)$ , and once again in practice use  $\\tilde{\\Delta}$  instead of  $\\Delta$  in training.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section we empirically demonstrate the utility and flexibility of our approach on a diverse set of tasks and settings. Our goal is to demonstrate how our framework supports learning in settings that extend beyond the basic setting of strategic classification, and each experiment extends",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
+            361,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "5 Many tools exist for learning bundles; e.g., Rifai et al. (2011a).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^6$  Consider  $d = 1$ , with points  $(- \\epsilon, -1)$  and  $(\\epsilon, 1)$ . Let  $c(x, x') = |x - x'|$ . The classifier  $h(x) = \\mathbb{1}\\{x \\geq 2\\}$  causes all positive points (and only positive points) to move. The payoff to negative points is  $-1$  and the payoff to positive points is  $-1 + \\epsilon$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/c9cf94fa2c6ef6b6ee7435f53438b1a41a49e21262ffd6577d8ec8388706e809.jpg",
+        "image_caption": [
+            "Figure 1. A comparison of our SERM approach to a 'strategy-blind' baseline across multiple datasets, predictive models, and settings. Left: A reproduction of the setting of Hardt et al. (2016) on the spam dataset with mixed linear-quadratic cost. Center: Learning RNNs for financial distress time-series data. Right: Comparing across multiple datasets and degrees of gaming (controlled by cost scale  $t$ )."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/40271d903c2f636f8ad194a7f24103c033ff76b8f0c592d1e51d40eb36c4e8c2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/21283a1d200ddbac37f59fd877219c5f878485ca771b87a34729638ed72674c6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the core setting of Hardt et al. (2016) in a way that targets a certain aspect of practical concern. The Appendix includes further details, additional experiments, and illustrations.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Experimental setup. Across all experiments we use four real datasets: (i) spam<sup>7</sup>, which includes features describing users of a large social network, some of which are spammers (used originally in Hardt et al. (2016)); (ii) credit<sup>8</sup>, which includes features describing credit card spending patterns, and labels indicating default on payment (we use the version from Ustun et al. (2019)); (iii) fraud<sup>9</sup>, which includes credit card transactions that are either genuine or fraudulent (Dal Pozzolo et al., 2015); and (iv) financial distress<sup>10</sup>, which includes time-series data describing businesses over time along with labels indicating their level of financial distress and whether they have gone bankrupt. All datasets include features that describe users and relate to tasks in which users have incentive to obtain positive predictive outcomes. Some experiments use synthetic environments, described below.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare our approach (SERM) to a strategy-blind baseline that falsely assumes points do not move, achieved by training on the same model class but using standard, non-strategic ERM. When appropriate, we also compare to the strategic algorithm of Hardt et al. (2016), and to other context-specific variants of our approach (e.g., naive or oracle models). All models train on non-strategic data, but are evaluated on strategic data. As a benchmark, we use the strategy-blind model evaluated on non-strategic data (i.e., where points do not move).",
+        "bbox": [
+            83,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our focus is mostly on linear classifiers as these are naturally interpretable and hence justify the form of strategic behavior considered in strategic classification. For time-series data, such as in experiment in Sec. 4.3, we use recursive neural networks (RNN). For optimizing our approach we use Adam with randomized batches and early stopping (most runs converged after at most 7 epochs). User responses were simulated using  $\\Delta$  from Eq. (1) with  $\\tau = 1$  for training and  $\\tau = 0.2$  for evaluation. Tolerance for CCP convergence was set to 0.01 (most attempts converged after at most 5 iterations). All methods use a 60-20-20 data split, and results are averaged over multiple random splits.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Core setting",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our first experiment begins with a reproduction of the experimental setting of Hardt et al. (2016). They use the spam dataset and consider linear-separable cost functions  $c_{\\mathrm{lin}}^v (x,x') = \\max \\{0,v^\\top (x' - x)\\}$  with a specific hand-coded  $v\\in \\mathbb{R}^d$ . Their algorithm only supports separable costs, and for linear-separable costs, returns a linear classifier. Linear costs, however, are unstable under evaluation since points can move at zero cost whenever  $v^{\\top}(x' - x)\\leq 0$ . Hence, they train with  $c_{\\mathrm{lin}}^v$ , but evaluate on a mixture cost:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nc _ {\\operatorname {m i x}} (x, x ^ {\\prime}; \\gamma , v) = (1 - \\gamma) \\cdot c _ {\\operatorname {l i n}} ^ {v} (x, x ^ {\\prime}) + \\gamma \\cdot c _ {\\operatorname {q u a d}} (x, x ^ {\\prime})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $c_{\\mathrm{quad}} = \\| x' - x\\| _2^2$  and  $\\gamma \\in (0,1]$  (they use  $\\gamma \\in \\{0.1,0.3\\}$ ). Our approach supports general convex costs and so is able to learn using the 'right' cost function (i.e., that is used in evaluation) for any  $\\gamma$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "7Data can be obtained from the authors of Costa et al. (2014). 8https://github.com/ustunb/ actionable-recourse 9https://www.kaggle.com/mlg-ulb/ creditcardfraud 10https://www.kaggle.com/shebrahimi/ financial-distress",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "11Linear costs are unstable at test time in the following way (see Hardt et al. (2016), Fig. 2 caption): if  $f$  is not precisely parallel to the cost vector  $v$  (i.e.,  $f(x) = v^\\top x + b$  for some  $b$ , where  $c(x, x') = \\max \\{0, v^\\top (x' - x)\\}$ ), then since any movement parallel to  $v$  is free, any  $x$  can move at zero cost to some  $x'$  for which  $f(x') > 0$  (and so all modified points are classified positively).",
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+    },
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+            "Figure 2. Trade-off curves of accuracy vs. various measures of social good: expected utility, social burden, and recourse. Points correspond to varying degrees of regularization  $(\\lambda)$ . For all measures, mild regularization improves social outcomes at little or no cost to accuracy."
+        ],
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+        "text": "Figure 1 (left) shows performance for increasing  $\\gamma$ . Benchmark accuracy on non-strategic data is  $81\\%$ , but once strategic movement is permitted, performance of the strategy-blind model drops to  $\\sim 54\\%$  (data is balanced so chance  $= \\% 50$ ). The algorithm of Hardt et al. (2016) anticipates strategic behavior but (wrongly) assumes costs are linear. Accuracy for  $\\gamma \\approx 0$  improves to some extent ( $\\sim 69\\%$ ), but remains far below the benchmark. However, as  $\\gamma$  increases, performance quickly drops to  $50\\%$ . In contrast, by correctly anticipating strategic behavior, SERM restores accuracy almost in full for  $\\gamma \\geq 0.2$  ( $\\sim 80\\%$ ).",
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+        "type": "text",
+        "text": "Next, we evaluate our method on additional datasets, focusing on quadratic cost (as it does not require hand-coded parameters), and varying the degree of 'gaming' by scaling the cost by a factor of  $t \\in \\{0.5, 1, 2\\}$ . Figure 1 (right) compares the performance of SERM to the strategy-blind baseline. As can be seen, SERM outperforms the blind model by a significant margin and closely matches the non-strategic benchmark for all datasets and degrees of gaming.",
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+        "type": "text",
+        "text": "4.2. Social good regularization",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate our approach of regularizing for social good (Sec. 3.4) on credit, which has been used in a recent paper on recourse by Ustun et al. (2019). Here we study how accuracy and social good trade-off under SERM by varying the amount of regularization  $\\lambda$ . Figure 2 shows results for expected utility (left), social burden (center), and recourse (right). Each point in the plots corresponds to a model trained with a different  $\\lambda$ . Results show that all three measures of social good exhibit a super-linear tradeoff curve: with mild regularization, a large increase in social good is obtained at little or no cost to accuracy. This highlights three interrelated points: that incentives in strategic classification are not fully discordant; that multiple models can achieve high accuracy; and that of these, our approach to model selection through regularization is effective at selecting models that promote favorable social outcomes.",
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+        "type": "text",
+        "text": "4.3. Beyond linear models",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We apply our approach to time-series data in financial distress and for our predictive model we use non-linear recurrent neural networks (RNN). Each example in the dataset describes a firm over  $t$  time steps using a sequence of feature vectors  $\\boldsymbol{x} = (x^{(1)},\\dots,x^{(t)})$ , where  $x^{(k)} \\in \\mathbb{R}^d$  describes the firm at time  $k \\leq t$  and  $t$  varies across examples  $(1 \\leq t \\leq 14)$ . Labels determine whether the firm has gone bankrupt at time  $t$ , and we assume users can modify features only at this final timepoint  $x^{(t)}$ . This mimics a setting in which the history of the firm is fixed, but its features at the time of arbitration can be manipulated (at some cost). We implement  $f$  as a fully-connected RNN with layers:",
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+        "type": "equation",
+        "text": "\n$$\nh ^ {(i)} = \\varphi (W x ^ {(i)} + V h ^ {(i - 1)} + a)\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where model parameters  $W, V, a$  are tied across layers and activations  $\\varphi$  are sigmoidal for all layers but the last, which is used for prediction. We set the embedded dimension to 10. Plugging into Eq. (1), the response mapping becomes:",
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+        "type": "equation",
+        "text": "\n$$\n\\Delta (\\boldsymbol {x}) = \\operatorname * {a r g m a x} _ {x ^ {\\prime} \\in \\mathcal {X}} \\operatorname {s i g n} (w ^ {\\top} x ^ {\\prime} + v ^ {\\top} h ^ {(t - 1)} + b) - c (x ^ {(t)}, x ^ {\\prime})\n$$\n",
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+    {
+        "type": "text",
+        "text": "with quadratic cost. This is a special case of Sec. 3.3.1 with  $\\phi(x) = (x^{(t)}, h^{(t-1)})$ . Since  $f$  is linear in  $x'$  and  $c$  is convex in  $x'$ , our CCP approach can be applied (Sec. 3.2).",
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+        "text": "We experiment with varying history lengths by taking suffixes of fixed size  $k$  of each  $x$ . Figure 1 (center) shows results for increasing suffix lengths  $k$ . As can be seen, SERM outperforms a blind RNN by roughly  $15\\%$  for all  $k$  and nearly matches the non-strategic benchmark for  $k \\geq 2$ .",
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+        "type": "text",
+        "text": "4.4. Beyond oracle cost functions",
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+        "text": "In this section we move beyond the assumption of a fixed and known ('oracle') cost function and study the extensions presented in Sec. 3.3. We use stylized 2D synthetic data that allows us to visually illustrate how our approach behaves in these extended settings. In each setting we compare SERM to appropriate naive and oracle baselines, specified below.",
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+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
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+        "image_caption": [
+            "Figure 3. An illustrations of various extensions of the role of the cost function  $c$ . (Left) Flexibility: cost is linear (arrows show direction) and is initially  $v_{0}$ , but the system can invest effort to change it. Learning produces a cost  $\\hat{v}$  that is near the optimal  $v^{*}$ , with which SERM achieves near-optimal accuracy. (Center) Robustness: Cost is quadratic (circles show diameter of maximal movement), but the system has only an estimate  $v_{0}$  of the true cost  $v^{*}$ . Learning aims to be minmax-optimal with respect to all costs  $v \\in V$  near  $v_{0}$  (ring shows the set  $V$ ). SERM again learns a near-optimal classifier. (Right) Manifold constraints: Points are allowed to move only on the quadratic manifold that is unknown (and hence not encoded in  $c$ ). Our approach is to first learn the manifold, and then use derived tangents as constraints in optimizing  $\\Delta$ . This approximates movement within the manifold and allows SERM to learn well."
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+    {
+        "type": "text",
+        "text": "Flexible cost functions. In this setting we assume that the system can modify an initial cost to some extent. Data is generated by a mixture of two 'narrow' MVN distributions with means  $\\mu = [-0.5, 0]$  (for  $y = -1$ ) and  $\\mu = [0.5, 0]$  ( $y = 1$ ) and diagonal covariances with  $\\Sigma_{11} = 0.1$  and  $\\Sigma_{22} = 1$ . We use linear-separable cost  $c_{\\mathrm{lin}}^v$  (for stability we mix using  $\\gamma = 0.005$ ) and set the initial cost to  $v_0 = [0.5, 0.5]$ . The learner has flexibility to choose any  $v \\in V = \\{v': \\| v' - v_0\\|_\\infty \\leq 2\\}$ . For a naive baseline we consider a model that does not modify the cost, i.e., uses  $v = v_0$ . The oracle baseline uses the optimal  $v^* = [2, 0] \\in V$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To learn with flexible costs, we use the approach presented in Sec. 3.3.2 and jointly optimize model parameters  $w$ ,  $b$  and cost parameters  $v$ . Results are shown in Figure 3 (left). If no strategic movement is allowed, then the optimal linear classifier having  $w = [1,0]$ ,  $b = 0$  achieves  $\\sim 100\\%$  (non-strategic) accuracy. However, with strategic movement under  $v_{0}$ , the strategically-optimal classifier has weights  $w = [0.5,0.5]$ ,  $b = 1$ . These are indeed the weights learned by the naïve baseline, which achieves  $0.72\\%$  accuracy. However, for  $v = [1,0]$ , the optimal classifier has  $w = [1,0]$ ,  $b = 1$ , and an oracle baseline that has  $v^{*} = [1,0]$  learns these weights and achieves  $100\\%$ . Our flexible approach learns a near-optimal cost  $(\\hat{v} = [2.3,0.6])$  along with the corresponding optimal model, achieving  $97\\%$  accuracy.",
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+    {
+        "type": "text",
+        "text": "Unknown cost functions. In this setting we assume that points move according to a ground-truth cost function that is unknown, and that the system has only an rough estimate of this cost. Data is generated by a mixture of two symmetric MVN distributions with means  $\\mu = [-0.6, 0]$  (for  $y = -1$ ) and  $\\mu = [0.6, 0]$  ( $y = 1$ ) and diagonal covariances  $\\Sigma_{11} = \\Sigma_{22} = 0.1$ . We use an a-symmetric quadratic cost in which",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "dimensions can differ in scale,  $c_{\\mathrm{quad}}^v (x,x') = \\sum_{i = 1}^d v_i(x_i - x_i')^2$ , parameterized by  $v\\in \\mathbb{R}^d$ . The ground-truth cost is set to  $v^{*} = (0.5,0.5)$  and the initial estimate to  $v_{0} = (2,2)$ . Here the oracle baseline learns using  $v^{*}$ , and naive baseline learns under the false assumption that  $v_{0} = v^{*}$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To learn under an unknown cost, we use the robust minmax approach presented in Sec. 3.3.3 and train a predictor  $f$  to be minmax-optimal w.r.t. a belief set  $V$ , which we set to  $V = \\{v \\in \\mathbb{R}^2 : \\| v_0 - v \\|_{\\infty} \\leq 1.7\\}$  (note that  $v^* \\in V$ ). In this setting optimization is simplified since it suffices to maximize  $v$  over the reduced set  $\\{v_{\\min}, v_{\\max}\\} \\subset V$ , where in our case  $v_{\\min} = [0.3, 0.3]$  and  $v_{\\max} = [3.7, 3.7]$ . Figure 3 (center) illustrates the results of learning in this setting. The benchmark on non-strategic data is  $\\sim 100\\%$ , as is the performance of the oracle model on strategic data. The naive model obtains  $74\\%$  accuracy using  $v_0$ . SERM optimized using the minmax objective achieves  $91\\%$  accuracy.",
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+    {
+        "type": "text",
+        "text": "Manifold constraints. In this setting we work with a cost function is known and fixed, but assume that points can move only within a low-dimensional manifold that is unknown to the system. We use a 1D manifold that satisfies  $x_{2} = -x_{1}^{2}$  and generate data points  $x = (x_{1},x_{2})$  using  $x_{1}\\sim U([-5,5])$  and set  $x_{2}$  according to the manifold constraints. Labels are  $y = \\mathrm{sign}(x_1)$  and the cost is quadratic.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To learn under unknown manifold constraints, we follow the approach outlined in Sec. 3.3.4, where in the response function  $\\Delta$  the (unknown) manifold constraints are approximated using (estimated) tangent constraints. Here, manifold tangents have a close form solution, but for completeness we pursue a more general approach and learn them. In particular, we learn the manifold using a contractive autoencoder",
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+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "(CAE) (Rifai et al., 2011b) with 2 stacked hidden layers of width 20 and sigmoidal activations. CAEs minimize reconstruction error under a regularization term that penalizes Jacobian absolute values. Balancing between these two forces encourages learned embeddings that permit movement only in directions that are useful for reconstruction, i.e., along the manifold. Jacobians also provide manifold tangents, and we compute these as proposed for manifold tangent classifiers (MTC) in Rifai et al. (2011a).",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 (right) shows results for this setting. The problem is separable and so optimal non-strategic accuracy is  $100\\%$ . A naive baseline which does not account for manifold constraints wrongly assumes points can move freely across the  $x_{1}$ -axis and places all weight on this axis. This false assumption reduces accuracy to  $52\\%$ —much lower than that of a blind baseline, which achieves  $89\\%$ . Our SERM approach augmented with MTC tangents over an estimated CAE manifold reaches  $98\\%$  accuracy.",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "5. Conclusions",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper we proposed a practical approach to learning in strategic classification. By differentiating through user responses, our approach allows for effective and efficient learning in diverse settings. Key to our approach were differentiable optimization solvers; we are hopeful that future advances in this field could be utilized within our framework to support more elaborate forms of user responses. Strategic classification has so far been mostly studied under a theoretical lens; our work takes a first step towards making learning practical, with the aim of promoting discussion amongst practitioners, applied researchers, and those interested in social aspects of learning. Our approach to regularization serves as a reminder that strategic classification is a game for two players, and that learning can, and should, aid in promoting the interests of all parties involved. We believe that a responsible approach to applied strategic classification can be beneficial to both systems and the users they serve.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            86,
+            685,
+            184,
+            700
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Agrawal, A. and Boyd, S. Differentiating through log-log convex programs. arXiv preprint arXiv:2004.12553, 2020.",
+            "Agrawal, A., Amos, B., Barratt, S., Boyd, S., Diamond, S., and Kolter, J. Z. Differentiable convex optimization layers. In Advances in neural information processing systems, pp. 9562-9574, 2019a.",
+            "Agrawal, A., Barratt, S., Boyd, S., Busseti, E., and Moursi, W. M. Differentiating through a cone program. arXiv preprint arXiv:1904.09043, 2019b.",
+            "Ahmadi, S., Beyhaghi, H., Blum, A., and Naggita, K. The"
+        ],
+        "bbox": [
+            86,
+            709,
+            478,
+            906
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "strategic perceptron. Available at https://arxiv.org/abs/2008.01710, 2020.",
+            "Alon, T., Dobson, M., Procaccia, A. D., Talgam-Cohen, I., and Tucker-Foltz, J. Multiagent evaluation mechanisms. In The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI), pp. 1774-1781, 2020.",
+            "Amos, B. and Kolter, J. Z. Optnet: Differentiable optimization as a layer in neural networks. In International Conference on Machine Learning, pp. 136-145, 2017.",
+            "Bechavod, Y., Ligett, K., Wu, Z. S., and Ziani, J. Causal feature discovery through strategic modification. Available at https://arxiv.org/abs/2002.07024, 2020.",
+            "Bechavod, Y., Podimata, C., Wu, Z. S., and Ziani, J. Information discrepancy in strategic learning. Available at https://arxiv.org/pdf/2103.01028.pdf, 2021.",
+            "Berthet, Q., Blondel, M., Teboul, O., Cuturi, M., Vert, J.-P., and Bach, F. Learning with differentiable perturbed optimizers. arXiv preprint arXiv:2002.08676, 2020.",
+            "Brown, G., Hod, S., and Kalemaj, I. Performative prediction in a stateful world. arXiv preprint arXiv:2011.03885, 2020.",
+            "Brückner, M. and Scheffer, T. Nash equilibria of static prediction games. In Advances in neural information processing systems, pp. 171-179, 2009.",
+            "Brückner, M. and Scheffer, T. Stackelberg games for adversarial prediction problems. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 547-555, 2011.",
+            "Brückner, M., Kanzow, C., and Scheffer, T. Static prediction games for adversarial learning problems. The Journal of Machine Learning Research, 13(1):2617-2654, 2012.",
+            "Chen, X., Duan, Y., Houthooft, R., Schulman, J., Sutskever, I., and Abbeel, P. Infogan: Interpretable representation learning by information maximizing generative adversarial nets. In Lee, D., Sugiyama, M., Luxburg, U., Guyon, I., and Garnett, R. (eds.), Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016. URL https://proceedings.neurips.cc/paper/2016/file/7c9d0b1f96aebd7b5eca8c3edaa19ebb-Paper.pdf.",
+            "Chen, Y., Liu, Y., and Podimata, C. Learning strategy-aware linear classifiers. arXiv preprint arXiv:1911.04004, 2019.",
+            "Chen, Y., Wang, J., and Liu, Y. Strategic recourse in linear classification. arXiv preprint arXiv:2011.00355, 2020."
+        ],
+        "bbox": [
+            500,
+            85,
+            895,
+            906
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
+            361,
+            56,
+            611,
+            71
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Costa, H., Merschmann, L. H., Barth, F., and Benevenuto, F. Pollution, bad-mouthing, and local marketing: The underground of location-based social networks. Information Sciences, 279:123-137, 2014.",
+            "Dal Pozzolo, A., Caelen, O., Johnson, R. A., and Bontempi, G. Calibrating probability with undersampling for unbalanced classification. In 2015 IEEE Symposium Series on Computational Intelligence, pp. 159-166. IEEE, 2015.",
+            "Djolonga, J. and Krause, A. Differentiable learning of submodular models. In Advances in Neural Information Processing Systems, pp. 1013-1023, 2017.",
+            "Dong, J., Roth, A., Schutzman, Z., Waggoner, B., and Wu, Z. S. Strategic classification from revealed preferences. In Proceedings of the 2018 ACM Conference on Economics and Computation (EC), pp. 55-70, 2018.",
+            "Ghalme, G., Nair, V., Eilat, I., Talgam-Cohen, I., and Rosenfeld, N. Strategic classification in the dark. In Proceedings of the 38th International Conference on Machine Learning (ICML), 2021.",
+            "Großhans, M., Sawade, C., Brückner, M., and Scheffer, T. Bayesian games for adversarial regression problems. In International Conference on Machine Learning, pp. 55-63, 2013.",
+            "Gupta, V., Nokhiz, P., Roy, C. D., and Venkatasubramanian, S. Equalizing recourse across groups. arXiv preprint arXiv:1909.03166, 2019.",
+            "Hardt, M., Megiddo, N., Papadimitriou, C., and Wootters, M. Strategic classification. In Proceedings of the 2016 ACM conference on innovations in theoretical computer science, pp. 111-122, 2016.",
+            "Heidari, H., Nanda, V., and Gummadi, K. On the long-term impact of algorithmic decision policies: Effort unfairness and feature segregation through social learning. In 36th International Conference on Machine Learning, pp. 2692-2701, 2019.",
+            "Hu, L., Immorlica, N., and Vaughan, J. W. The disparate effects of strategic manipulation. In Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT*), pp. 259-268, 2019.",
+            "Izzo, Z., Ying, L., and Zou, J. How to learn when data reacts to your model: performative gradient descent. arXiv preprint arXiv:2102.07698, 2021.",
+            "Joshi, S., Koyejo, O., Vijitbenjaronk, W., Kim, B., and Ghosh, J. Towards realistic individual recourse and actionable explanations in black-box decision making systems. arXiv preprint arXiv:1907.09615, 2019."
+        ],
+        "bbox": [
+            86,
+            84,
+            475,
+            906
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Karimi, A.-H., Barthe, G., Schölkopf, B., and Valera, I. A survey of algorithmic recourse: definitions, formulations, solutions, and prospects. arXiv preprint arXiv:2010.04050, 2020a.",
+            "Karimi, A.-H., von Kugelgen, J., Scholkopf, B., and Valera, I. Algorithmic recourse under imperfect causal knowledge: a probabilistic approach. Advances in Neural Information Processing Systems, 33, 2020b.",
+            "Kleinberg, J. M. and Raghavan, M. How do classifiers induce agents to invest effort strategically? In Proceedings of the 2019 ACM Conference on Economics and Computation, (EC), pp. 825-844, 2019.",
+            "Miller, J., Milli, S., and Hardt, M. Strategic classification is causal modeling in disguise. In International Conference on Machine Learning, pp. 6917-6926. PMLR, 2020.",
+            "Miller, J., Perdomo, J. C., and Zrnic, T. Outside the echo chamber: Optimizing the performative risk. arXiv preprint arXiv:2102.08570, 2021.",
+            "Milli, S., Miller, J., Dragan, A. D., and Hardt, M. The social cost of strategic classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT*), pp. 230-239, 2019.",
+            "Perdomo, J. C., Zrnic, T., Mendler-Dünner, C., and Hardt, M. Performative prediction. In Proceedings of the 37th International Conference on Machine Learning (ICML), 2020.",
+            "Quionero-Candela, J., Sugiyama, M., Schwaighofer, A., and Lawrence, N. D. Dataset shift in machine learning. The MIT Press, 2009.",
+            "Rifai, S., Dauphin, Y. N., Vincent, P., Bengio, Y., and Muller, X. The manifold tangent classifier. Advances in neural information processing systems, 24:2294-2302, 2011a.",
+            "Rifai, S., Vincent, P., Muller, X., Glorot, X., and Bengio, Y. Contractive auto-encoders: Explicit invariance during feature extraction. In Icml, 2011b.",
+            "Rosenfeld, N., Hilgard, A., Ravindranath, S. S., and Parkes, D. C. From predictions to decisions: Using lookahead regularization. Advances in Neural Information Processing Systems, 33, 2020.",
+            "Shavit, Y., Edelman, B., and Axelrod, B. Causal strategic linear regression. In International Conference on Machine Learning, pp. 8676-8686. PMLR, 2020.",
+            "Shen, X., Diamond, S., Gu, Y., and Boyd, S. Disciplined convex-concave programming. In 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 1009-1014. IEEE, 2016."
+        ],
+        "bbox": [
+            500,
+            84,
+            885,
+            906
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Sundaram, R., Vullikanti, A., Xu, H., and Yao, F. Pac-learning for strategic classification. arXiv preprint arXiv:2012.03310, 2020.",
+            "Tan, Y., Terekhov, D., and Delong, A. Learning linear programs from optimal decisions. Advances in Neural Information Processing Systems, 33, 2020.",
+            "Ustun, B., Spangher, A., and Liu, Y. Actionable recourse in linear classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pp. 10-19, 2019.",
+            "Venkatasubramanian, S. and Alfano, M. The philosophical basis of algorithmic recourse. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, pp. 284-293, 2020.",
+            "Yuille, A. L. and Rangarajan, A. The concave-convex procedure. Neural computation, 15(4):915-936, 2003.",
+            "Zhang, H. and Conitzer, V. Incentive-aware pac learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 2021."
+        ],
+        "bbox": [
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+        "type": "header",
+        "text": "Strategic Classification Made Practical",
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+    {
+        "type": "text",
+        "text": "A. Experimental details",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A.1.Data",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Across all experiments we use four real datasets:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- **Spam**<sup>12</sup>. This dataset includes features of authentic users and spammers from a large social network, and was used in Hardt et al. (2016). The data includes  $n = 7$ , 076 examples and  $d = 15$  features. Features include number of words in the post, number of phone numbers in the post and number of followers of the user. The data is balanced, i.e., there is an equal number of positive ( $y = 1$ ) and negative ( $y = -1$ ) examples.",
+            "- Credit<sup>13</sup>. This dataset includes features describing credit card spending patterns, along with labels indicating default on payment. We use the same version used in the recourse paper by Ustun et al. (2019), and adopt their preprocessing procedure (see link). The original dataset includes  $n = 30,000$  examples and  $d = 11$  Features. Features include age, amount of bill statement and history of past payments. For training time purposes, in our experiments we used a random balanced subset of 3,000 examples, as we did not notice any changes in performance for larger sample set sizes (which is plausible given that  $f$  is linear and  $d$  here is small).",
+            "- Fraud<sup>14</sup> (Dal Pozzolo et al., 2015). This dataset includes credit card transactions that are either genuine or fraudulent. The original data includes  $n = 284k$  examples and  $d = 29$  features. Due to confidentiality issues, feature information is not provided. The original dataset is highly imbalanced, and for our experiments we take all available negative examples and uniformly sample a matching number of positive examples, giving a total of  $n = 984$  balanced examples.",
+            "- Finance<sup>15</sup>. This dataset includes time-series data describing firms along with an indication of their level of financial distress (denoted fd). Each series ends either at the maximal time step of  $t = 14$  or earlier if the firm has gone bankrupt. Bankruptcy is declared when fd  $< -0.5$ , and we use this definition to determine labels  $y$ . The data includes  $n = 422$  time-series examples, with each time step within each example described using  $d = 83$  anonymized numerical features.<sup>16</sup> The ratio of positive (i.e., non-bankrupt) examples is  $67.7\\%$ . Time-series lengths are in the range  $t \\in \\{0, \\dots, 14\\}$  (inclusive), with mean  $= 8.7$  and median  $= 4.9$ ."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Features in all datasets were standardized (i.e., scaled to obtain a mean of zero and standard deviation of one) on the train set. To ensure consistent behavior in term of the effect of the cost function on movement, features in each datasets were further divided by  $\\sqrt{d}$  where  $d$  is the (per-dataset) number of features.",
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+    {
+        "type": "text",
+        "text": "A.2. Training and tuning",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "For all experiments we use a 60-20-20 split into train, validation, and test sets, respectively, and all results are averaged over multiple random splits. For optimization we use ADAM, where within each epoch we use randomize batches of size 24 for financial distress and fraud 64 for credit and 128 for spam chosen according to their respective number of examples, and early stop w.r.t. accuracy on the validation set. For all methods, learning rates were set according to the validation set. For  $\\sigma$  we set  $\\tau = 1$  for training and  $\\tau = 0.2$  for testing, and set the CCP tolerance to 0.001, but note results are robust to variations in these.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "A.3. CCP procedure",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We use our own implementation of CCP, based on Shen et al. (2016), and using the publicly-available SCS solver<sup>17</sup> for solving the concave sub-problems appearing in each iteration. Algorithm 1 includes pseudocode for our procedure. We use the notation:",
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+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {\\cup} (x; f) = \\frac {1}{2} \\sqrt {(\\tau^ {- 1} f (x) + 1) ^ {2} + 1}, \\qquad \\sigma_ {\\cap} (x; f) = - \\frac {1}{2} \\sqrt {(\\tau^ {- 1} f (x) - 1) ^ {2} + 1},\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "header",
+        "text": "Strategic Classification Made Practical",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{12}$ Data can be obtained from the authors of Costa et al. (2014).",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>13</sup>https://github.com/ustunb/actionable-recourse",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{14}$ https://www.kaggle.com/mlg-ulb/creditcardfraud",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "page_footnote",
+        "text": "15https://www.kaggle.com/shebrahimi/financial-distress",
+        "bbox": [
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+        "page_idx": 11
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+    {
+        "type": "page_footnote",
+        "text": "16The data includes a single categorical feature, which we discard.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "17https://web.stanford.edu/\\~boyd/papers/scs.html",
+        "bbox": [
+            102,
+            891,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "for the convex and concave parts of  $\\sigma$ , respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 CCP forward pass"
+        ],
+        "code_body": "1: Initialize  $t = 0, \\delta = \\infty$   \n2:  $x^0 = x$   \n3: repeat  \n4:  $t = t + 1$   \n5:  $g = \\nabla_x \\sigma_\\cup (x^{t-1}; f)$   \n6:  $x^t = \\operatorname{argmax}_{x'} g^\\top x' + \\sigma_\\cap (x'; f) - c(x, x')$   \n7: until convergence  \n8:  $g^t = \\nabla_x \\sigma_\\cup (x^t; f)$   \n9: return  $x^t, g^t$",
+        "bbox": [
+            94,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In practice we terminate when  $\\| x^t - x^{t-1} \\|_2 \\leq \\mathrm{tol}$  or after at most  $t = 100$  iterations. In our experiments we used  $\\mathrm{tol} = 0.001$ , but the vast majority of instances terminated after  $t = 5$  iterations. The algorithm returns two objects: the approximate argmax  $x^t$  used in the forward pass, and the linearization  $g^t$  (of which  $x^t$  is an exact argmax) used to parameterize the convex optimization layer to enable a backwards pass.",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4. Runtime evaluation",
+        "text_level": 1,
+        "bbox": [
+            86,
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section we present results on the runtime of our method. Presumably the main overhead in our approach is computing the CCP solution and surrogate in the forward pass. Note however that while each call to solver may be expensive, jointly solving for all examples in a batch (i.e., solving  $k$  independent problems in one call, where  $k$  is the batch size) can greatly reduce this overhead. All experiments were run on a single laptop (Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz 2.90 GHz, 16.0 GB RAM).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To evaluate this, we run an experiment on synthetic data and for varying batch sizes. We use scikit-learn's make_classification function, using 750 train samples, 250 validation samples,  $d = 5$  features, balanced classes, and 0.01 label noise. 4 (two left-most plots) show runtime results for increasing batch size  $k$  and training for 5 epochs. We consider two alternatives to setting the number of CCP iterations: (i) convergence to tolerance 0.001 on average across examples in the batch (left), and (ii) a slowly increasing, uniform number of iterations, with the number of iterations initialized at one and increased by one after each epoch (right). As can be seen, increasing the batch size greatly improves overall runtime, as well as the relative runtime of CCP.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We also report runtime on the real datasets used in Sec. 4.1. For equalized comparison we set the number of epochs to 7. Batch sizes were set per dataset as described in Sec. A.2 (as noted, these were not chosen to optimize for speed). Figure 4 (two right-most plots) show total train times and relative CCP times for all datasets for both stopping criteria.",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Code. Our code can be obtained at: https://github.com/SagiLevanon1/scmp.",
+        "bbox": [
+            84,
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+        "page_idx": 12
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+        "image_caption": [
+            "Figure 4. Runtime on synthetic data (varying CCP batch size) and real data (fixed batch size)."
+        ],
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+# Strategic Classification Made Practical
+
+Sagi Levanon<sup>1</sup> Nir Rosenfeld<sup>1</sup>
+
+# Abstract
+
+Strategic classification regards the problem of learning in settings where users can strategically modify their features to improve outcomes. This setting applies broadly and has received much recent attention. But despite its practical significance, work in this space has so far been predominantly theoretical. In this paper we present a learning framework for strategic classification that is practical. Our approach directly minimizes the "strategic" empirical risk, achieved by differentiating through the strategic response of users. This provides flexibility that allows us to extend beyond the original problem formulation and towards more realistic learning scenarios. A series of experiments demonstrates the effectiveness of our approach on various learning settings.
+
+# 1. Introduction
+
+Across a multitude of domains—from loan approval to online dating to hiring and admissions—predictive machine learning models are becoming imperative for informing decisions that affect the lives of humans. But when people benefit from certain predictive outcomes, they are prone to act strategically to improve those outcomes. This has raised awareness as to the idea that standard learning algorithms may not be robust to such behavior, and there is a growing recognition as to the prevalence of this phenomena. Given the breadth of domains in which strategic user behavior is likely, practical tools for learning in strategic settings are of considerable importance.
+
+In this paper we study practical aspects of learning in the setting of strategic classification (Brückner & Scheffer, 2011; Hardt et al., 2016). In this problem, users respond to a published classifier by strategically modifying their features (at some cost) to improve their predicted outcomes. As a concrete example, consider a bank offering loans. The
+
+$^{1}$ Department of Computer Science, Technion - Israel Institute of Technology. Correspondence to: Nir Rosenfeld <nirr@cs.technion.ac.il>.
+
+Proceedings of the  $38^{th}$  International Conference on Machine Learning, PMLR 139, 2021. Copyright 2021 by the author(s).
+
+bank would like to approve a loan only if it is likely to be returned, and to aid in decision-making, the bank trains a classifier to predict loan returns. Applicants, however, would like their requests to be approved—regardless of their actual credibility. To promote their interests, they can modify their applications (at some cost) to best align with the bank's classification rule. From the bank's perspective, such modifications can invalidate model predictions, and the primary goal in strategic classification is to design learning algorithms that are robust to this form of 'gaming'.
+
+Note that gaming is caused by the model itself, indirectly through how it shapes user incentives, and to its detriment. In this sense, strategic classification exemplifies how machine learning can be amenable to Goodhart's Law, a principle in policymaking stating that "when a measure becomes a target, it ceases to be a good measure". Strategic classification thus succinctly captures a natural form of tension that arises between a learning-based system and its users. There has been much recent work on this topic, studying aspects such as generalization (Sundaram et al., 2020; Zhang & Conitzer, 2021), equilibrium and dynamics (Perdomo et al., 2020; Brown et al., 2020; Izzo et al., 2021; Miller et al., 2021), online learning (Dong et al., 2018; Chen et al., 2019; Ahmadi et al., 2020), causality and decision outcomes (Kleinberg & Raghavan, 2019; Rosenfeld et al., 2020; Shavit et al., 2020; Bechavod et al., 2020; Miller et al., 2020), transparency (Ghalme et al., 2021; Bechavod et al., 2021), and social perspectives (Hu et al., 2019; Milli et al., 2019; Chen et al., 2020).
+
+But despite this flurry of recent work, algorithms for strategic classification are not in widespread use. The key reason for this is that work in this space has been predominantly theoretical. This has several practical implications. First, for mathematical tractability, strong assumptions are made (e.g., that the cost function is fixed and known). But the robustness of these methods to violations of their assumptions is not well understood. Second, methods tend to be crafted for very particular learning settings, and do not easily extend beyond the narrow context in which they are originally studied. Third, currently available algorithms lag far behind recent advances in machine learning methodology; they are prone to issues of scale, expressivity, and runtime, and lack the flexibility and modularity that current approaches readily provide (e.g., the ability to seamlessly "add a layer" or
+
+change the loss function). Combined, the above limitations indicate a clear need for an approach to learning in strategic classification that is effective and practical. Our work aims to take a first step towards addressing this need.
+
+The core idea of our approach is to encode into the learning objective a response mapping that models how users respond to a given classification rule. By anticipating how inputs will be strategically modified under a given model, our approach optimizes directly for predictive performance under strategic behavior. We refer to this as *strategic empirical risk minimization*, or SERM. The challenge in optimizing the SERM objective is that models of user response typically involve an argmax operator, which can be nondifferentiable and even discontinuous. Our solution is to replace the argmax operator with a differentiable proxy, and for this we draw on recent advances in differentiable optimization solvers (Amos & Kolter, 2017; Djolonga & Krause, 2017; Agrawal et al., 2019a,b; Berthet et al., 2020; Tan et al., 2020; Agrawal & Boyd, 2020) and adapt them to our purpose. The resulting *strategic response layer* provides the main building-block of our framework.
+
+Using the flexibility our framework provides, we propose and showcase multiple ways in which the framework can extend beyond the original formulation of strategic classification and towards more realistic learning scenarios. We make use of the modular nature of our approach and the flexibility it provides to explore various extensions aimed at addressing potential practical concerns. These include: supporting complex predictive models (e.g., recursive neural networks), supporting structured cost functions (e.g., constraining movement to a manifold), and relaxing the assumption of a fixed and known cost function (we handle adjustable and unknown costs).
+
+The primary goal in strategic classification is to learn strategically-robust predictive models, but several works have raised concern as to the adverse social outcomes this may entail (Milli et al., 2019; Hu et al., 2019; Chen et al., 2020). This may not be surprising given that learning focuses entirely on optimizing predictive accuracy. To address these concerns, here we argue for a broader perspective that considers the trade-off between system and user interests. Borrowing from welfare economics, we take the perspective of a 'social planner' tasked with balancing between these interests, and show how our approach can extend to target any operating point along the pareto front. To do this, we cast strategic classification as a problem of model selection, and propose novel forms of regularization that promote favorable social outcomes for various notions of 'social good'. Because strategic classification is not a zero-sum game, the incentives of the system and of its users are not entirely antagonistic. As we show, this permits much social benefit to be gained at only a small cost in accuracy.
+
+In summary, our paper makes the following contributions:
+
+- Practical framework. We propose a novel learning framework for strategic classification that is practical, effective, and flexible. Our approach allows to differentiate through strategic user responses, thus permitting end-to-end training.  
+- Flexible modeling. We show how the flexibility of our approach allows for learning in diverse strategic settings. We effectively apply our approach to multiple such settings of practical interest.  
+- Socially-aware learning. We propose several forms of regularization that encourage learned models to promote favorable social outcomes. By capitalizing on certain structural aspects of the problem, our regularization effectively balances between system and user interests.
+
+We conduct a series of experiments demonstrating the effectiveness of our approach. With respect to the above points, each of our experiments is designed to study a different practical aspect of learning. The experiments cover a range of learning environments using real and synthetic data. Our results show that learning in strategic classification can be practical, effective, and socially responsible.
+
+One of our main goals in this paper is to motivate and support future empirical research on strategic classification, Towards this end, we make publicly available a code repository with a flexible implementation of our approach, designed to support a wide range of strategic learning settings. Code can be found at https://github.com/SagiLevanon1/scmp.
+
+# 2. Related Work
+
+The literature on strategic classification is growing at a rapid pace. Various formulations of the problem were studied in earlier works (Brückner & Scheffer, 2009; Brückner et al., 2012; Großhans et al., 2013), but most recent works adopt the core setup of Hardt et al. (2016), as we do here. Research in this space has mostly been oriented towards theory, with recent work introducing notions similar to SERM and extending PAC theory to this setting (Sundaram et al., 2020; Zhang & Conitzer, 2021). We complement these by placing emphasis on practical aspects of learning.
+
+Several papers consider the social impacts of strategic classification. Milli et al. (2019) study the social burden imposed by optimizing for accuracy. Chen et al. (2020) study the connection between strategically-aware learning and recourse. Hu et al. (2019) focus on fairness and show how classifiers can induce inequitable modification costs that affect utility. Our work ties these together, providing means to control
+
+the tradeoff between classifier's accuracy and the social outcomes it induces through regularization (see Sec. 3.4).
+
+A parallel line of work studies how learned models affect actual (rather than predictive) outcomes. Some works analyze how models should promote users to invest effort effectively (Kleinberg & Raghavan, 2019; Alon et al., 2020), while others tie learning to the underlying casual mechanisms of the environment (Perdomo et al., 2020; Bechavod et al., 2020; Shavit et al., 2020; Miller et al., 2020). We remain within the original, purely predictive problem formulation, but view the extension of our approach to such settings to be intriguing as future work.
+
+# 3. Method
+
+Learning setup. Denote by  $x \in \mathcal{X} \subseteq \mathbb{R}^d$  features representing user attributes (e.g., a loan application profile), and by  $y \in \mathcal{Y} = \{-1, 1\}$  their corresponding labels (e.g., loan returned or not). Let  $p(x, y)$  be a joint distribution over nonstrategic features and labels. The primary goal in learning is to find a classifier  $h: \mathcal{X} \to \mathcal{Y}$  from a class  $H$  that achieves high expected accuracy. For this, we assume access to a sample set  $S = \{(x_i, y_i)\}_{i=1}^m$  sampled i.i.d. from  $p(x, y)$  on which we train. At test time, however,  $h$  is evaluated on data that is prone to modification by users. In strategic classification, users modify their features using the response mapping:
+
+$$
+\Delta_ {h} (x) \triangleq \underset {x ^ {\prime} \in \mathcal {X}} {\operatorname {a r g m a x}} h \left(x ^ {\prime}\right) - c \left(x, x ^ {\prime}\right) \tag {1}
+$$
+
+where  $c$  is a known cost function. Test data includes pairs  $(\Delta_h(x), y)$  where  $(x, y) \sim p$ , and the goal in learning is to optimize predictive accuracy under this induced distribution.
+
+As is common, the classifiers we consider will be based on score functions  $f: \mathcal{X} \to \mathbb{R}$  via the decision rule  $h_f(x) = \mathrm{sign}(f(x))$ , and learning will be concerned with optimizing over a class of parametrized score functions  $F$ . We write  $\Delta_f$  to mean  $\Delta_{h_f}$ , and for clarity, omit the notational dependence of the classifier  $h_f$  on  $f$  when clear from context.
+
+Game-theoretic formulation. Strategic classification can be formulated as a Stackelberg game between two players—the system and a population of users. First, the system learns from  $S$  a classifier  $h$ . Then, given  $h$ , users respond via  $\Delta_h$ . The payoffs are:
+
+$$
+\text {S y s t e m :} \quad \mathbb {P} [ y = h (\Delta_ {h} (x)) ], \tag {2}
+$$
+
+$$
+\text {U s e r s :} \quad \mathbb {E} [ h (\Delta_ {h} (x)) - c (x, \Delta_ {h} (x)) ] \tag {3}
+$$
+
+Payoff to the system (Eq. (2)) is the probability of classifying manipulated points correctly. Payoff to the users (as a collective) is their expected utility (Eq. (3)), for which  $\Delta$  as defined in Eq. (1) is a best-response.
+
+# 3.1. Strategic Empirical Risk Minimization
+
+A naive approach would be to train a classifier to predict well on the (non-manipulated) input data, and use it at test time on manipulated data. The caveat in this approach is that strategic behavior causes a discrepancy between the (marginal) input distributions at train and test time. Strategic classification therefore introduces a form of distribution shift (Quionero-Candela et al., 2009), but with the unique property that shift is determined by the predictive model itself, albeit indirectly through its effect on user responses.
+
+Our approach will be to account for this shift by directly optimizing for the induced distribution. Noting that the system's payoff in Eq. (2) can be rewritten as  $1 - \mathbb{E}[\mathbb{1}\{y\neq h(\Delta_h(x))\} ]$  , we set our objective to the empirical loss over the strategically-modified training set:
+
+$$
+\min  _ {f \in F} \sum_ {i = 1} ^ {m} L \left(\Delta_ {f} \left(x _ {i}\right), y _ {i}, f\right) + \lambda R (f) \tag {4}
+$$
+
+where  $L(z, y, f) = \mathbb{1}\{y \neq h_f(z)\}$  and  $R$  is an optional regularizer. In practice we replace  $L$  with a tractable surrogate (e.g., binary cross-entropy), and we will return to the role of regularization in Sec. 3.4. We refer to optimizing Eq. (4) as strategic empirical risk minimization (SERM). Note that  $f$  plays a dual role in the objective: it determines how inputs are modified (via  $\Delta_f$ ) and how predictions are made on those modified inputs (via  $h_f$ ).
+
+# 3.2. Differentiating through strategic responses
+
+A natural way to approach the optimization of Eq. (4) is using gradient methods. The challenge in this approach is that  $\Delta$  is an argmax operator and can therefore be nondifferentiable. Our solution to this will be to use a differentiable proxy for  $\Delta$ , drawing inspiration from recent advances in differentibale optimization solvers. Such solvers map parametrized optimization problems to their (approximately) optimal solutions in a manner that is amenable to differentiation, and so can be used as optimization "layers" integrated into neural architectures.
+
+Our approach will be to implement the response mapping  $\Delta$  as a differentiable optimization layer. In particular, we make use of convex optimization layers (Agrawal et al., 2019a), but since we seek to maximize, we will construct concave layers. A concave optimization layer  $g(\theta)$  maps concave optimization problem instances to their argmax: the input to the layer,  $\theta$ , defines the "parameters" (and hence the instance) of a template optimization problem, and the output of the layer is the solution under this parameterization. In our model,  $g$  will play the role of  $\Delta$ , and  $\theta$  will include features  $x$  and the learnable parameters of  $f$ .
+
+The response mapping  $\Delta$  as defined in Eq. (1) is not concave, and to apply concave optimization, we construct a
+
+concave proxy, denoted  $\tilde{\Delta}$ , as follows. To begin, assume for simplicity that  $h$  is linear, i.e.,  $h_w(x) = \mathrm{sign}f_w(x)$  with  $f_w(x) = w^\top x + b$ . Next, since sign is discontinuous, we replace it with a smooth sigmoid  $\sigma^*$  of the following form:
+
+$$
+\sigma_ {\tau} ^ {*} (z) = \frac {1}{2} \sqrt {(\tau^ {- 1} z + 1) ^ {2} + 1} - \frac {1}{2} \sqrt {(\tau^ {- 1} z - 1) ^ {2} + 1}
+$$
+
+Here  $\tau$  is a temperature parameter: as  $\tau$  decreases,  $\sigma^{*}$  approaches sign. Our particular choice of sigmoid follows from the fact that  $\sigma^{*}$  can be written as a sum of convex and concave functions. This motivates our final step, which is to apply the convex-concave procedure (CCP) (Yuille & Rangarajan, 2003). CCP is an approach to solving convex-concave optimization problems by iterating through a sequence of concave-relaxed problems, a process that guarantees convergence to local maxima. We focus on convex costs (e.g., linear or quadratic) so that CCP can be applied to the entire response function. Using CCP, we obtain reliable concave proxies of responses at each input. This gives us our differentiable proxy of the response mapping, which we refer to as a strategic response layer, defined as:
+
+$$
+\tilde {\Delta} (x) = \underset {x ^ {\prime} \in \mathcal {X}} {\operatorname {a r g m a x}} \operatorname {C C P} \left(\sigma^ {*} \left(w ^ {\top} x ^ {\prime} + b\right)\right) - c \left(x, x ^ {\prime}\right) \tag {5}
+$$
+
+Here CCP denotes the concave proxy obtained at the last iteration of the procedure.
+
+To compute the forward pass, we run the CCP procedure using any standard off-shelf convex solver, and compute the argmax w.r.t. the final proxy. For the backward pass, we plug the final proxy into the differentiable convex solver of Agrawal et al. (2019a) to get gradients for  $\tilde{\Delta}$  w.r.t.  $w, b$ .
+
+# 3.3. Extensions
+
+# 3.3.1. NONLINEAR CLASSIFIERS
+
+The concave solver can handle only score functions  $f$  that are linear in the optimization variables. But  $f$  need not be linear in the input features  $x$ ; rather, it can be linear in any high-dimensional representation of the inputs,  $z = \phi(x)$ ,  $z \in \mathcal{Z}$ , such as those obtained from the final hidden layers of neural networks. This holds as long as both  $f$  and  $c$  are defined over this representation (i.e., points move in representation-space). The response mapping becomes:
+
+$$
+\Delta (x) = \operatorname * {a r g m a x} _ {z ^ {\prime} \in \mathcal {Z}} \sigma \left(w ^ {\top} z ^ {\prime} + b\right) - c (\phi (x), z ^ {\prime}) \tag {6}
+$$
+
+More generally,  $f$  must be linear in variables over which the cost function  $c$  is defined. For example, if  $c$  applies only to
+
+a subset of the original features (for example, if only some features are manipulable), then  $f$  must be linear those features, but can be non-linear in all other features. Concretely, if  $x = (x_{\mathrm{manip}}, x_{\mathrm{non}})$  where  $x_{\mathrm{manip}} \in \mathbb{R}^{d_1}$  and  $x_{\mathrm{non}} \in \mathbb{R}^{d_2}$  are the manipulable and non-manipulable features, respectively, then our framework supports the following non-linear representational structure:
+
+$$
+\Delta (x) = \operatorname * {a r g m a x} _ {x ^ {\prime} \in \mathbb {R} ^ {d _ {1}}} \sigma (w ^ {\top} x ^ {\prime} + v ^ {\top} \phi (x _ {\text {n o n}}) + b) - c (x _ {\text {m a n i p}}, x ^ {\prime})
+$$
+
+# 3.3.2. FLEXIBLE COSTS
+
+The core setting of strategic classification assumes costs are fixed. But in some settings, it is reasonable to assume that the system has some control over the cost function.<sup>4</sup> We model this as allowing the system to modify an initial cost function  $c_{0}$  to some other cost  $c \in \mathcal{C}$  from the class  $\mathcal{C}$ , with this incurring a penalty of  $r(c_{0}, c)$ . The goal is now to jointly learn the classifier and the modified cost. Denoting by  $\Delta_{f}^{c}$  the response mapping for classifier  $f$  and cost function  $c$ , we can extend the learning objective as follows:
+
+$$
+\min  _ {c \in \mathcal {C}} \min  _ {f \in F} \sum_ {i = 1} ^ {m} L \left(\Delta_ {f} ^ {c} \left(x _ {i}\right), y _ {i}, f\right) + r \left(c _ {0}, c\right) \tag {7}
+$$
+
+By utilizing its flexibility in choosing  $c$ , in this setting the system has the capacity to obtain better predictive performance than when optimizing the objective in Eq. (4).
+
+# 3.3.3. UNKNOWN COSTS
+
+Strategic classification assumes that the cost function is known, but this may not hold in practice. Here we consider a setting in which the system does not know the true cost  $c^*$ , but has a reasonable estimate  $c_0$ . We model the system as believing that  $c^*$  lies in some set  $C \subseteq \mathcal{C}$  which includes  $c_0$  as well as nearby points, and which we view as a design parameter chosen by the learner. To learn in this setting, we propose a worst-case approach in which the system aims to perform well simultaneously on all  $c \in C$ . We propose the following minmax objective:
+
+$$
+\min  _ {f \in F} \max  _ {c \in C} \sum_ {i = 1} ^ {m} L \left(\Delta_ {f} ^ {c} \left(x _ {i}\right), y _ {i}, f\right) \tag {8}
+$$
+
+# 3.3.4. MOVING ON A MANIFOLD
+
+The Manifold Hypothesis is a convention stating that high-dimensional data tend to lie on or near a low-dimensional manifold. Typically the manifold is unknown; but even if it
+
+is known, common cost functions tend to permit arbitrary movement and so cannot account for this structure. Here we show how our approach can incorporate (approximate) manifold constraints into learning. We begin by learning a manifold bundle  $(M,T)$  composed of a manifold model  $M$  and a tangent function  $T(x)$  that returns the subspace tangent to  $M$  at  $x$ . Since tangents  $T(x)$  are linear objects that provide a first-order approximation to the manifold at  $x$ , our approach is to add them as linear constraints to the optimization of the response mapping (i.e., the argmax in  $\Delta$  is taken over  $x' \in T(x)$ ). This ensures points move only on the tangent, thus approximating movement on the manifold.
+
+# 3.4. Regularizing for social good
+
+Our discussion of strategic classification thus far has been focused on a single objective: predicting accurately in the face of strategic gaming. This promotes a clear interest of the system, but neglects to account for the effects of learning users. Returning to our loans example, note that any predictor inevitably determines the degree of recourse, defined as the ability of users that are denied a service (e.g., a loan) to take reasonable action to reverse this decision (Ustun et al., 2019; Gupta et al., 2019; Joshi et al., 2019; Chen et al., 2020; Karimi et al., 2020b). Recourse is clearly beneficial to users, but in many cases, its facilitation is also beneficial to the system (for discussion see Ustun et al. (2019); Venkatasubramanian & Alfano (2020); Karimi et al. (2020a)).
+
+In this section we show how our framework can be used to train models that are both accurate and promote favorable social outcomes. Relying on the observation that different models can induce very different social outcomes (Heidari et al., 2019), we cast learning as a problem of model selection, where the selection criterion reflects some notion of 'social good' (e.g., recourse). Model selection is implemented through regularization and below we present novel forms of data-dependent regularizers  $R(f;S)$  targeting various notions of social good from the literature.
+
+Intuitively, we expect regularization to be useful because strategic classification is not a zero-sum game. In other words, predictive models that provide similar payoff to the system may differ considerably in their payoff to users; we argue that the system has the freedom, as well as the responsibility, to carefully choose between these. Viewing learning from the perspective of a 'social planner' interested in balancing between system and user interests, our regularization approach provides the means to achieve good balance. Varying the amount of regularization  $\lambda$  provides solutions along the Pareto front, with  $\lambda = 0$  corresponding to the strategic classification equilibrium in Eq. (2).
+
+Expected utility. Since the payoff to users in Eq. (3) is given by their gained utility,  $u_{\Delta}(x) = h(\Delta(x)) - c(x, \Delta(x))$ , a straightforward notion of social good is their expected utility,  $\mathbb{E}[u_{\Delta}(x)]$ . Note that  $\Delta$  is a best-response but it is utility-optimal relative to  $h$ , and it is easy to construct an example showing that under the accuracy-optimal predictor utility can be arbitrarily low. To encourage models that provide users with high utility, we set:
+
+$$
+R _ {\text {u t i l}} (f; \mathcal {S}) = - \sum_ {i = 1} ^ {m} u _ {\Delta} \left(x _ {i}\right) \tag {9}
+$$
+
+and plug into the learning objective in (4), where in practice we again replace  $\Delta$  with  $\tilde{\Delta}$  and optimize as in Sec. 3.2.
+
+Social burden. In their paper on the social cost of strategic classification, Milli et al. (2019) study social burden, defined to be the minimum cost a positively-labeled user must incur in order to be classified correctly. Within our framework, we can regularize for social burden using:
+
+$$
+R _ {\text {b u r d e n}} (f; \mathcal {S}) = \sum_ {i: y _ {i} = 1} \min  _ {x ^ {\prime}: f \left(x ^ {\prime}\right) \geq 0} c \left(x, x ^ {\prime}\right) \tag {10}
+$$
+
+which we can also implement as a convex optimization layer for linear  $f$  and convex  $c$  (the constraint is linear in  $x, w$ ).
+
+Recourse. Recourse refers to the capacity of a user who is denied a service to restore approval through reasonable action (in our case, low-cost feature modification). Since  $\Delta$  is a best-response, we say a user with  $h(x) = -1$  is granted recourse if  $h(\Delta_h(x)) = 1$ . The random variable negating this condition is  $\mathbb{1}\{h(x) = -1 \land h(\Delta_h(x)) = -1\}$ , and we regularize using its smoothed approximation:
+
+$$
+R _ {\text {r e c o u r s e}} (f; \mathcal {S}) = \sum_ {i = 1} ^ {m} \operatorname {s i g} (- f (x)) \cdot \operatorname {s i g} (- f (\Delta_ {f} (x)))
+$$
+
+Where  $\operatorname{sig}(z) = \frac{1}{1 + e^{-z}}$  is the standard sigmoid function. We calculate this regularization term using the same CCP approach on  $\Delta_f(x)$ , and once again in practice use  $\tilde{\Delta}$  instead of  $\Delta$  in training.
+
+# 4. Experiments
+
+In this section we empirically demonstrate the utility and flexibility of our approach on a diverse set of tasks and settings. Our goal is to demonstrate how our framework supports learning in settings that extend beyond the basic setting of strategic classification, and each experiment extends
+
+![](images/c9cf94fa2c6ef6b6ee7435f53438b1a41a49e21262ffd6577d8ec8388706e809.jpg)  
+Figure 1. A comparison of our SERM approach to a 'strategy-blind' baseline across multiple datasets, predictive models, and settings. Left: A reproduction of the setting of Hardt et al. (2016) on the spam dataset with mixed linear-quadratic cost. Center: Learning RNNs for financial distress time-series data. Right: Comparing across multiple datasets and degrees of gaming (controlled by cost scale  $t$ ).
+
+![](images/40271d903c2f636f8ad194a7f24103c033ff76b8f0c592d1e51d40eb36c4e8c2.jpg)
+
+![](images/21283a1d200ddbac37f59fd877219c5f878485ca771b87a34729638ed72674c6.jpg)
+
+the core setting of Hardt et al. (2016) in a way that targets a certain aspect of practical concern. The Appendix includes further details, additional experiments, and illustrations.
+
+Experimental setup. Across all experiments we use four real datasets: (i) spam<sup>7</sup>, which includes features describing users of a large social network, some of which are spammers (used originally in Hardt et al. (2016)); (ii) credit<sup>8</sup>, which includes features describing credit card spending patterns, and labels indicating default on payment (we use the version from Ustun et al. (2019)); (iii) fraud<sup>9</sup>, which includes credit card transactions that are either genuine or fraudulent (Dal Pozzolo et al., 2015); and (iv) financial distress<sup>10</sup>, which includes time-series data describing businesses over time along with labels indicating their level of financial distress and whether they have gone bankrupt. All datasets include features that describe users and relate to tasks in which users have incentive to obtain positive predictive outcomes. Some experiments use synthetic environments, described below.
+
+We compare our approach (SERM) to a strategy-blind baseline that falsely assumes points do not move, achieved by training on the same model class but using standard, non-strategic ERM. When appropriate, we also compare to the strategic algorithm of Hardt et al. (2016), and to other context-specific variants of our approach (e.g., naive or oracle models). All models train on non-strategic data, but are evaluated on strategic data. As a benchmark, we use the strategy-blind model evaluated on non-strategic data (i.e., where points do not move).
+
+Our focus is mostly on linear classifiers as these are naturally interpretable and hence justify the form of strategic behavior considered in strategic classification. For time-series data, such as in experiment in Sec. 4.3, we use recursive neural networks (RNN). For optimizing our approach we use Adam with randomized batches and early stopping (most runs converged after at most 7 epochs). User responses were simulated using  $\Delta$  from Eq. (1) with  $\tau = 1$  for training and  $\tau = 0.2$  for evaluation. Tolerance for CCP convergence was set to 0.01 (most attempts converged after at most 5 iterations). All methods use a 60-20-20 data split, and results are averaged over multiple random splits.
+
+# 4.1. Core setting
+
+Our first experiment begins with a reproduction of the experimental setting of Hardt et al. (2016). They use the spam dataset and consider linear-separable cost functions  $c_{\mathrm{lin}}^v (x,x') = \max \{0,v^\top (x' - x)\}$  with a specific hand-coded  $v\in \mathbb{R}^d$ . Their algorithm only supports separable costs, and for linear-separable costs, returns a linear classifier. Linear costs, however, are unstable under evaluation since points can move at zero cost whenever  $v^{\top}(x' - x)\leq 0$ . Hence, they train with  $c_{\mathrm{lin}}^v$ , but evaluate on a mixture cost:
+
+$$
+c _ {\operatorname {m i x}} (x, x ^ {\prime}; \gamma , v) = (1 - \gamma) \cdot c _ {\operatorname {l i n}} ^ {v} (x, x ^ {\prime}) + \gamma \cdot c _ {\operatorname {q u a d}} (x, x ^ {\prime})
+$$
+
+where  $c_{\mathrm{quad}} = \| x' - x\| _2^2$  and  $\gamma \in (0,1]$  (they use  $\gamma \in \{0.1,0.3\}$ ). Our approach supports general convex costs and so is able to learn using the 'right' cost function (i.e., that is used in evaluation) for any  $\gamma$ .
+
+![](images/9fd296a2a07f0ee56e3827d16f099462b341c04a30db9083ce73765c8291db8f.jpg)  
+Figure 2. Trade-off curves of accuracy vs. various measures of social good: expected utility, social burden, and recourse. Points correspond to varying degrees of regularization  $(\lambda)$ . For all measures, mild regularization improves social outcomes at little or no cost to accuracy.
+
+![](images/e09c336447a1e883ce70ddfe1f570df567e0ce81777c27d633fbedc15bd4e890.jpg)
+
+![](images/283241175748bc4c0b84b3138076745a2536ffb5948b163bdd841f31d9bcd40e.jpg)
+
+Figure 1 (left) shows performance for increasing  $\gamma$ . Benchmark accuracy on non-strategic data is  $81\%$ , but once strategic movement is permitted, performance of the strategy-blind model drops to  $\sim 54\%$  (data is balanced so chance  $= \% 50$ ). The algorithm of Hardt et al. (2016) anticipates strategic behavior but (wrongly) assumes costs are linear. Accuracy for  $\gamma \approx 0$  improves to some extent ( $\sim 69\%$ ), but remains far below the benchmark. However, as  $\gamma$  increases, performance quickly drops to  $50\%$ . In contrast, by correctly anticipating strategic behavior, SERM restores accuracy almost in full for  $\gamma \geq 0.2$  ( $\sim 80\%$ ).
+
+Next, we evaluate our method on additional datasets, focusing on quadratic cost (as it does not require hand-coded parameters), and varying the degree of 'gaming' by scaling the cost by a factor of  $t \in \{0.5, 1, 2\}$ . Figure 1 (right) compares the performance of SERM to the strategy-blind baseline. As can be seen, SERM outperforms the blind model by a significant margin and closely matches the non-strategic benchmark for all datasets and degrees of gaming.
+
+# 4.2. Social good regularization
+
+We evaluate our approach of regularizing for social good (Sec. 3.4) on credit, which has been used in a recent paper on recourse by Ustun et al. (2019). Here we study how accuracy and social good trade-off under SERM by varying the amount of regularization  $\lambda$ . Figure 2 shows results for expected utility (left), social burden (center), and recourse (right). Each point in the plots corresponds to a model trained with a different  $\lambda$ . Results show that all three measures of social good exhibit a super-linear tradeoff curve: with mild regularization, a large increase in social good is obtained at little or no cost to accuracy. This highlights three interrelated points: that incentives in strategic classification are not fully discordant; that multiple models can achieve high accuracy; and that of these, our approach to model selection through regularization is effective at selecting models that promote favorable social outcomes.
+
+# 4.3. Beyond linear models
+
+We apply our approach to time-series data in financial distress and for our predictive model we use non-linear recurrent neural networks (RNN). Each example in the dataset describes a firm over  $t$  time steps using a sequence of feature vectors  $\boldsymbol{x} = (x^{(1)},\dots,x^{(t)})$ , where  $x^{(k)} \in \mathbb{R}^d$  describes the firm at time  $k \leq t$  and  $t$  varies across examples  $(1 \leq t \leq 14)$ . Labels determine whether the firm has gone bankrupt at time  $t$ , and we assume users can modify features only at this final timepoint  $x^{(t)}$ . This mimics a setting in which the history of the firm is fixed, but its features at the time of arbitration can be manipulated (at some cost). We implement  $f$  as a fully-connected RNN with layers:
+
+$$
+h ^ {(i)} = \varphi (W x ^ {(i)} + V h ^ {(i - 1)} + a)
+$$
+
+where model parameters  $W, V, a$  are tied across layers and activations  $\varphi$  are sigmoidal for all layers but the last, which is used for prediction. We set the embedded dimension to 10. Plugging into Eq. (1), the response mapping becomes:
+
+$$
+\Delta (\boldsymbol {x}) = \operatorname * {a r g m a x} _ {x ^ {\prime} \in \mathcal {X}} \operatorname {s i g n} (w ^ {\top} x ^ {\prime} + v ^ {\top} h ^ {(t - 1)} + b) - c (x ^ {(t)}, x ^ {\prime})
+$$
+
+with quadratic cost. This is a special case of Sec. 3.3.1 with  $\phi(x) = (x^{(t)}, h^{(t-1)})$ . Since  $f$  is linear in  $x'$  and  $c$  is convex in  $x'$ , our CCP approach can be applied (Sec. 3.2).
+
+We experiment with varying history lengths by taking suffixes of fixed size  $k$  of each  $x$ . Figure 1 (center) shows results for increasing suffix lengths  $k$ . As can be seen, SERM outperforms a blind RNN by roughly  $15\%$  for all  $k$  and nearly matches the non-strategic benchmark for  $k \geq 2$ .
+
+# 4.4. Beyond oracle cost functions
+
+In this section we move beyond the assumption of a fixed and known ('oracle') cost function and study the extensions presented in Sec. 3.3. We use stylized 2D synthetic data that allows us to visually illustrate how our approach behaves in these extended settings. In each setting we compare SERM to appropriate naive and oracle baselines, specified below.
+
+![](images/f471f8bd470209daca8c988ccdec79d27bb5d0a8815452f0d1972c5d8f8ec804.jpg)  
+Figure 3. An illustrations of various extensions of the role of the cost function  $c$ . (Left) Flexibility: cost is linear (arrows show direction) and is initially  $v_{0}$ , but the system can invest effort to change it. Learning produces a cost  $\hat{v}$  that is near the optimal  $v^{*}$ , with which SERM achieves near-optimal accuracy. (Center) Robustness: Cost is quadratic (circles show diameter of maximal movement), but the system has only an estimate  $v_{0}$  of the true cost  $v^{*}$ . Learning aims to be minmax-optimal with respect to all costs  $v \in V$  near  $v_{0}$  (ring shows the set  $V$ ). SERM again learns a near-optimal classifier. (Right) Manifold constraints: Points are allowed to move only on the quadratic manifold that is unknown (and hence not encoded in  $c$ ). Our approach is to first learn the manifold, and then use derived tangents as constraints in optimizing  $\Delta$ . This approximates movement within the manifold and allows SERM to learn well.
+
+![](images/aea979c109b79792e4efbba9a640037f9c579751d485bc6bfb2c269ce0c0cd9e.jpg)
+
+![](images/0ac1d3216be237e54a13f4b5286e05183670c3862fc7ee51f6e41672fe9eb2f5.jpg)
+
+Flexible cost functions. In this setting we assume that the system can modify an initial cost to some extent. Data is generated by a mixture of two 'narrow' MVN distributions with means  $\mu = [-0.5, 0]$  (for  $y = -1$ ) and  $\mu = [0.5, 0]$  ( $y = 1$ ) and diagonal covariances with  $\Sigma_{11} = 0.1$  and  $\Sigma_{22} = 1$ . We use linear-separable cost  $c_{\mathrm{lin}}^v$  (for stability we mix using  $\gamma = 0.005$ ) and set the initial cost to  $v_0 = [0.5, 0.5]$ . The learner has flexibility to choose any  $v \in V = \{v': \| v' - v_0\|_\infty \leq 2\}$ . For a naive baseline we consider a model that does not modify the cost, i.e., uses  $v = v_0$ . The oracle baseline uses the optimal  $v^* = [2, 0] \in V$ .
+
+To learn with flexible costs, we use the approach presented in Sec. 3.3.2 and jointly optimize model parameters  $w$ ,  $b$  and cost parameters  $v$ . Results are shown in Figure 3 (left). If no strategic movement is allowed, then the optimal linear classifier having  $w = [1,0]$ ,  $b = 0$  achieves  $\sim 100\%$  (non-strategic) accuracy. However, with strategic movement under  $v_{0}$ , the strategically-optimal classifier has weights  $w = [0.5,0.5]$ ,  $b = 1$ . These are indeed the weights learned by the naïve baseline, which achieves  $0.72\%$  accuracy. However, for  $v = [1,0]$ , the optimal classifier has  $w = [1,0]$ ,  $b = 1$ , and an oracle baseline that has  $v^{*} = [1,0]$  learns these weights and achieves  $100\%$ . Our flexible approach learns a near-optimal cost  $(\hat{v} = [2.3,0.6])$  along with the corresponding optimal model, achieving  $97\%$  accuracy.
+
+Unknown cost functions. In this setting we assume that points move according to a ground-truth cost function that is unknown, and that the system has only an rough estimate of this cost. Data is generated by a mixture of two symmetric MVN distributions with means  $\mu = [-0.6, 0]$  (for  $y = -1$ ) and  $\mu = [0.6, 0]$  ( $y = 1$ ) and diagonal covariances  $\Sigma_{11} = \Sigma_{22} = 0.1$ . We use an a-symmetric quadratic cost in which
+
+dimensions can differ in scale,  $c_{\mathrm{quad}}^v (x,x') = \sum_{i = 1}^d v_i(x_i - x_i')^2$ , parameterized by  $v\in \mathbb{R}^d$ . The ground-truth cost is set to  $v^{*} = (0.5,0.5)$  and the initial estimate to  $v_{0} = (2,2)$ . Here the oracle baseline learns using  $v^{*}$ , and naive baseline learns under the false assumption that  $v_{0} = v^{*}$ .
+
+To learn under an unknown cost, we use the robust minmax approach presented in Sec. 3.3.3 and train a predictor  $f$  to be minmax-optimal w.r.t. a belief set  $V$ , which we set to  $V = \{v \in \mathbb{R}^2 : \| v_0 - v \|_{\infty} \leq 1.7\}$  (note that  $v^* \in V$ ). In this setting optimization is simplified since it suffices to maximize  $v$  over the reduced set  $\{v_{\min}, v_{\max}\} \subset V$ , where in our case  $v_{\min} = [0.3, 0.3]$  and  $v_{\max} = [3.7, 3.7]$ . Figure 3 (center) illustrates the results of learning in this setting. The benchmark on non-strategic data is  $\sim 100\%$ , as is the performance of the oracle model on strategic data. The naive model obtains  $74\%$  accuracy using  $v_0$ . SERM optimized using the minmax objective achieves  $91\%$  accuracy.
+
+Manifold constraints. In this setting we work with a cost function is known and fixed, but assume that points can move only within a low-dimensional manifold that is unknown to the system. We use a 1D manifold that satisfies  $x_{2} = -x_{1}^{2}$  and generate data points  $x = (x_{1},x_{2})$  using  $x_{1}\sim U([-5,5])$  and set  $x_{2}$  according to the manifold constraints. Labels are  $y = \mathrm{sign}(x_1)$  and the cost is quadratic.
+
+To learn under unknown manifold constraints, we follow the approach outlined in Sec. 3.3.4, where in the response function  $\Delta$  the (unknown) manifold constraints are approximated using (estimated) tangent constraints. Here, manifold tangents have a close form solution, but for completeness we pursue a more general approach and learn them. In particular, we learn the manifold using a contractive autoencoder
+
+(CAE) (Rifai et al., 2011b) with 2 stacked hidden layers of width 20 and sigmoidal activations. CAEs minimize reconstruction error under a regularization term that penalizes Jacobian absolute values. Balancing between these two forces encourages learned embeddings that permit movement only in directions that are useful for reconstruction, i.e., along the manifold. Jacobians also provide manifold tangents, and we compute these as proposed for manifold tangent classifiers (MTC) in Rifai et al. (2011a).
+
+Figure 3 (right) shows results for this setting. The problem is separable and so optimal non-strategic accuracy is  $100\%$ . A naive baseline which does not account for manifold constraints wrongly assumes points can move freely across the  $x_{1}$ -axis and places all weight on this axis. This false assumption reduces accuracy to  $52\%$ —much lower than that of a blind baseline, which achieves  $89\%$ . Our SERM approach augmented with MTC tangents over an estimated CAE manifold reaches  $98\%$  accuracy.
+
+# 5. Conclusions
+
+In this paper we proposed a practical approach to learning in strategic classification. By differentiating through user responses, our approach allows for effective and efficient learning in diverse settings. Key to our approach were differentiable optimization solvers; we are hopeful that future advances in this field could be utilized within our framework to support more elaborate forms of user responses. Strategic classification has so far been mostly studied under a theoretical lens; our work takes a first step towards making learning practical, with the aim of promoting discussion amongst practitioners, applied researchers, and those interested in social aspects of learning. Our approach to regularization serves as a reminder that strategic classification is a game for two players, and that learning can, and should, aid in promoting the interests of all parties involved. We believe that a responsible approach to applied strategic classification can be beneficial to both systems and the users they serve.
+
+# References
+
+Agrawal, A. and Boyd, S. Differentiating through log-log convex programs. arXiv preprint arXiv:2004.12553, 2020.  
+Agrawal, A., Amos, B., Barratt, S., Boyd, S., Diamond, S., and Kolter, J. Z. Differentiable convex optimization layers. In Advances in neural information processing systems, pp. 9562-9574, 2019a.  
+Agrawal, A., Barratt, S., Boyd, S., Busseti, E., and Moursi, W. M. Differentiating through a cone program. arXiv preprint arXiv:1904.09043, 2019b.  
+Ahmadi, S., Beyhaghi, H., Blum, A., and Naggita, K. The
+
+strategic perceptron. Available at https://arxiv.org/abs/2008.01710, 2020.  
+Alon, T., Dobson, M., Procaccia, A. D., Talgam-Cohen, I., and Tucker-Foltz, J. Multiagent evaluation mechanisms. In The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI), pp. 1774-1781, 2020.  
+Amos, B. and Kolter, J. Z. Optnet: Differentiable optimization as a layer in neural networks. In International Conference on Machine Learning, pp. 136-145, 2017.  
+Bechavod, Y., Ligett, K., Wu, Z. S., and Ziani, J. Causal feature discovery through strategic modification. Available at https://arxiv.org/abs/2002.07024, 2020.  
+Bechavod, Y., Podimata, C., Wu, Z. S., and Ziani, J. Information discrepancy in strategic learning. Available at https://arxiv.org/pdf/2103.01028.pdf, 2021.  
+Berthet, Q., Blondel, M., Teboul, O., Cuturi, M., Vert, J.-P., and Bach, F. Learning with differentiable perturbed optimizers. arXiv preprint arXiv:2002.08676, 2020.  
+Brown, G., Hod, S., and Kalemaj, I. Performative prediction in a stateful world. arXiv preprint arXiv:2011.03885, 2020.  
+Brückner, M. and Scheffer, T. Nash equilibria of static prediction games. In Advances in neural information processing systems, pp. 171-179, 2009.  
+Brückner, M. and Scheffer, T. Stackelberg games for adversarial prediction problems. In Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 547-555, 2011.  
+Brückner, M., Kanzow, C., and Scheffer, T. Static prediction games for adversarial learning problems. The Journal of Machine Learning Research, 13(1):2617-2654, 2012.  
+Chen, X., Duan, Y., Houthooft, R., Schulman, J., Sutskever, I., and Abbeel, P. Infogan: Interpretable representation learning by information maximizing generative adversarial nets. In Lee, D., Sugiyama, M., Luxburg, U., Guyon, I., and Garnett, R. (eds.), Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016. URL https://proceedings.neurips.cc/paper/2016/file/7c9d0b1f96aebd7b5eca8c3edaa19ebb-Paper.pdf.  
+Chen, Y., Liu, Y., and Podimata, C. Learning strategy-aware linear classifiers. arXiv preprint arXiv:1911.04004, 2019.  
+Chen, Y., Wang, J., and Liu, Y. Strategic recourse in linear classification. arXiv preprint arXiv:2011.00355, 2020.
+
+Costa, H., Merschmann, L. H., Barth, F., and Benevenuto, F. Pollution, bad-mouthing, and local marketing: The underground of location-based social networks. Information Sciences, 279:123-137, 2014.  
+Dal Pozzolo, A., Caelen, O., Johnson, R. A., and Bontempi, G. Calibrating probability with undersampling for unbalanced classification. In 2015 IEEE Symposium Series on Computational Intelligence, pp. 159-166. IEEE, 2015.  
+Djolonga, J. and Krause, A. Differentiable learning of submodular models. In Advances in Neural Information Processing Systems, pp. 1013-1023, 2017.  
+Dong, J., Roth, A., Schutzman, Z., Waggoner, B., and Wu, Z. S. Strategic classification from revealed preferences. In Proceedings of the 2018 ACM Conference on Economics and Computation (EC), pp. 55-70, 2018.  
+Ghalme, G., Nair, V., Eilat, I., Talgam-Cohen, I., and Rosenfeld, N. Strategic classification in the dark. In Proceedings of the 38th International Conference on Machine Learning (ICML), 2021.  
+Großhans, M., Sawade, C., Brückner, M., and Scheffer, T. Bayesian games for adversarial regression problems. In International Conference on Machine Learning, pp. 55-63, 2013.  
+Gupta, V., Nokhiz, P., Roy, C. D., and Venkatasubramanian, S. Equalizing recourse across groups. arXiv preprint arXiv:1909.03166, 2019.  
+Hardt, M., Megiddo, N., Papadimitriou, C., and Wootters, M. Strategic classification. In Proceedings of the 2016 ACM conference on innovations in theoretical computer science, pp. 111-122, 2016.  
+Heidari, H., Nanda, V., and Gummadi, K. On the long-term impact of algorithmic decision policies: Effort unfairness and feature segregation through social learning. In 36th International Conference on Machine Learning, pp. 2692-2701, 2019.  
+Hu, L., Immorlica, N., and Vaughan, J. W. The disparate effects of strategic manipulation. In Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT*), pp. 259-268, 2019.  
+Izzo, Z., Ying, L., and Zou, J. How to learn when data reacts to your model: performative gradient descent. arXiv preprint arXiv:2102.07698, 2021.  
+Joshi, S., Koyejo, O., Vijitbenjaronk, W., Kim, B., and Ghosh, J. Towards realistic individual recourse and actionable explanations in black-box decision making systems. arXiv preprint arXiv:1907.09615, 2019.
+
+Karimi, A.-H., Barthe, G., Schölkopf, B., and Valera, I. A survey of algorithmic recourse: definitions, formulations, solutions, and prospects. arXiv preprint arXiv:2010.04050, 2020a.  
+Karimi, A.-H., von Kugelgen, J., Scholkopf, B., and Valera, I. Algorithmic recourse under imperfect causal knowledge: a probabilistic approach. Advances in Neural Information Processing Systems, 33, 2020b.  
+Kleinberg, J. M. and Raghavan, M. How do classifiers induce agents to invest effort strategically? In Proceedings of the 2019 ACM Conference on Economics and Computation, (EC), pp. 825-844, 2019.  
+Miller, J., Milli, S., and Hardt, M. Strategic classification is causal modeling in disguise. In International Conference on Machine Learning, pp. 6917-6926. PMLR, 2020.  
+Miller, J., Perdomo, J. C., and Zrnic, T. Outside the echo chamber: Optimizing the performative risk. arXiv preprint arXiv:2102.08570, 2021.  
+Milli, S., Miller, J., Dragan, A. D., and Hardt, M. The social cost of strategic classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT*), pp. 230-239, 2019.  
+Perdomo, J. C., Zrnic, T., Mendler-Dünner, C., and Hardt, M. Performative prediction. In Proceedings of the 37th International Conference on Machine Learning (ICML), 2020.  
+Quionero-Candela, J., Sugiyama, M., Schwaighofer, A., and Lawrence, N. D. Dataset shift in machine learning. The MIT Press, 2009.  
+Rifai, S., Dauphin, Y. N., Vincent, P., Bengio, Y., and Muller, X. The manifold tangent classifier. Advances in neural information processing systems, 24:2294-2302, 2011a.  
+Rifai, S., Vincent, P., Muller, X., Glorot, X., and Bengio, Y. Contractive auto-encoders: Explicit invariance during feature extraction. In Icml, 2011b.  
+Rosenfeld, N., Hilgard, A., Ravindranath, S. S., and Parkes, D. C. From predictions to decisions: Using lookahead regularization. Advances in Neural Information Processing Systems, 33, 2020.  
+Shavit, Y., Edelman, B., and Axelrod, B. Causal strategic linear regression. In International Conference on Machine Learning, pp. 8676-8686. PMLR, 2020.  
+Shen, X., Diamond, S., Gu, Y., and Boyd, S. Disciplined convex-concave programming. In 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 1009-1014. IEEE, 2016.
+
+Sundaram, R., Vullikanti, A., Xu, H., and Yao, F. Pac-learning for strategic classification. arXiv preprint arXiv:2012.03310, 2020.  
+Tan, Y., Terekhov, D., and Delong, A. Learning linear programs from optimal decisions. Advances in Neural Information Processing Systems, 33, 2020.  
+Ustun, B., Spangher, A., and Liu, Y. Actionable recourse in linear classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pp. 10-19, 2019.  
+Venkatasubramanian, S. and Alfano, M. The philosophical basis of algorithmic recourse. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency, pp. 284-293, 2020.  
+Yuille, A. L. and Rangarajan, A. The concave-convex procedure. Neural computation, 15(4):915-936, 2003.  
+Zhang, H. and Conitzer, V. Incentive-aware pac learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 2021.
+
+# A. Experimental details
+
+# A.1.Data
+
+Across all experiments we use four real datasets:
+
+- **Spam**<sup>12</sup>. This dataset includes features of authentic users and spammers from a large social network, and was used in Hardt et al. (2016). The data includes  $n = 7$ , 076 examples and  $d = 15$  features. Features include number of words in the post, number of phone numbers in the post and number of followers of the user. The data is balanced, i.e., there is an equal number of positive ( $y = 1$ ) and negative ( $y = -1$ ) examples.  
+- Credit<sup>13</sup>. This dataset includes features describing credit card spending patterns, along with labels indicating default on payment. We use the same version used in the recourse paper by Ustun et al. (2019), and adopt their preprocessing procedure (see link). The original dataset includes  $n = 30,000$  examples and  $d = 11$  Features. Features include age, amount of bill statement and history of past payments. For training time purposes, in our experiments we used a random balanced subset of 3,000 examples, as we did not notice any changes in performance for larger sample set sizes (which is plausible given that  $f$  is linear and  $d$  here is small).  
+- Fraud<sup>14</sup> (Dal Pozzolo et al., 2015). This dataset includes credit card transactions that are either genuine or fraudulent. The original data includes  $n = 284k$  examples and  $d = 29$  features. Due to confidentiality issues, feature information is not provided. The original dataset is highly imbalanced, and for our experiments we take all available negative examples and uniformly sample a matching number of positive examples, giving a total of  $n = 984$  balanced examples.  
+- Finance<sup>15</sup>. This dataset includes time-series data describing firms along with an indication of their level of financial distress (denoted fd). Each series ends either at the maximal time step of  $t = 14$  or earlier if the firm has gone bankrupt. Bankruptcy is declared when fd  $< -0.5$ , and we use this definition to determine labels  $y$ . The data includes  $n = 422$  time-series examples, with each time step within each example described using  $d = 83$  anonymized numerical features.<sup>16</sup> The ratio of positive (i.e., non-bankrupt) examples is  $67.7\%$ . Time-series lengths are in the range  $t \in \{0, \dots, 14\}$  (inclusive), with mean  $= 8.7$  and median  $= 4.9$ .
+
+Features in all datasets were standardized (i.e., scaled to obtain a mean of zero and standard deviation of one) on the train set. To ensure consistent behavior in term of the effect of the cost function on movement, features in each datasets were further divided by  $\sqrt{d}$  where  $d$  is the (per-dataset) number of features.
+
+# A.2. Training and tuning
+
+For all experiments we use a 60-20-20 split into train, validation, and test sets, respectively, and all results are averaged over multiple random splits. For optimization we use ADAM, where within each epoch we use randomize batches of size 24 for financial distress and fraud 64 for credit and 128 for spam chosen according to their respective number of examples, and early stop w.r.t. accuracy on the validation set. For all methods, learning rates were set according to the validation set. For  $\sigma$  we set  $\tau = 1$  for training and  $\tau = 0.2$  for testing, and set the CCP tolerance to 0.001, but note results are robust to variations in these.
+
+# A.3. CCP procedure
+
+We use our own implementation of CCP, based on Shen et al. (2016), and using the publicly-available SCS solver<sup>17</sup> for solving the concave sub-problems appearing in each iteration. Algorithm 1 includes pseudocode for our procedure. We use the notation:
+
+$$
+\sigma_ {\cup} (x; f) = \frac {1}{2} \sqrt {(\tau^ {- 1} f (x) + 1) ^ {2} + 1}, \qquad \sigma_ {\cap} (x; f) = - \frac {1}{2} \sqrt {(\tau^ {- 1} f (x) - 1) ^ {2} + 1},
+$$
+
+for the convex and concave parts of  $\sigma$ , respectively.
+
+Algorithm 1 CCP forward pass  
+1: Initialize  $t = 0, \delta = \infty$   
+2:  $x^0 = x$   
+3: repeat  
+4:  $t = t + 1$   
+5:  $g = \nabla_x \sigma_\cup (x^{t-1}; f)$   
+6:  $x^t = \operatorname{argmax}_{x'} g^\top x' + \sigma_\cap (x'; f) - c(x, x')$   
+7: until convergence  
+8:  $g^t = \nabla_x \sigma_\cup (x^t; f)$   
+9: return  $x^t, g^t$
+
+In practice we terminate when  $\| x^t - x^{t-1} \|_2 \leq \mathrm{tol}$  or after at most  $t = 100$  iterations. In our experiments we used  $\mathrm{tol} = 0.001$ , but the vast majority of instances terminated after  $t = 5$  iterations. The algorithm returns two objects: the approximate argmax  $x^t$  used in the forward pass, and the linearization  $g^t$  (of which  $x^t$  is an exact argmax) used to parameterize the convex optimization layer to enable a backwards pass.
+
+# A.4. Runtime evaluation
+
+In this section we present results on the runtime of our method. Presumably the main overhead in our approach is computing the CCP solution and surrogate in the forward pass. Note however that while each call to solver may be expensive, jointly solving for all examples in a batch (i.e., solving  $k$  independent problems in one call, where  $k$  is the batch size) can greatly reduce this overhead. All experiments were run on a single laptop (Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz 2.90 GHz, 16.0 GB RAM).
+
+To evaluate this, we run an experiment on synthetic data and for varying batch sizes. We use scikit-learn's make_classification function, using 750 train samples, 250 validation samples,  $d = 5$  features, balanced classes, and 0.01 label noise. 4 (two left-most plots) show runtime results for increasing batch size  $k$  and training for 5 epochs. We consider two alternatives to setting the number of CCP iterations: (i) convergence to tolerance 0.001 on average across examples in the batch (left), and (ii) a slowly increasing, uniform number of iterations, with the number of iterations initialized at one and increased by one after each epoch (right). As can be seen, increasing the batch size greatly improves overall runtime, as well as the relative runtime of CCP.
+
+We also report runtime on the real datasets used in Sec. 4.1. For equalized comparison we set the number of epochs to 7. Batch sizes were set per dataset as described in Sec. A.2 (as noted, these were not chosen to optimize for speed). Figure 4 (two right-most plots) show total train times and relative CCP times for all datasets for both stopping criteria.
+
+Code. Our code can be obtained at: https://github.com/SagiLevanon1/scmp.
+
+![](images/e1b58dcda4f1e84ffc91a78635a2eeb32358e2c04283188c44b112d6d8ba17f7.jpg)  
+Figure 4. Runtime on synthetic data (varying CCP batch size) and real data (fixed batch size).
+
+![](images/51b00de4df7f6ef061e2212af59d7c70ec7a5b5b556b32be454383c5b941956a.jpg)
+
+![](images/d6eee7f6568bf00c14322385d82159953a87342067cdb57a2da89a141154b989.jpg)
+
+![](images/1ee25375a1ecf1e219a8a8b8d816679e480fb5503bd8bd47f154974a9e0d4d1e.jpg)

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+# HED-UNet: Combined Segmentation and Edge Detection for Monitoring the Antarctic Coastline
+
+Konrad Heidler, Lichao Mou, Celia Baumhoer, Andreas Dietz, and Xiao Xiang Zhu, Fellow, IEEE
+
+Abstract—This work has been accepted by IEEE TGRS for publication. Deep learning-based coastline detection algorithms have begun to outshine traditional statistical methods in recent years. However, they are usually trained only as single-purpose models to either segment land and water or delineate the coastline. In contrast to this, a human annotator will usually keep a mental map of both segmentation and delineation when performing manual coastline detection. To take into account this task duality, we therefore devise a new model to unite these two approaches in a deep learning model. By taking inspiration from the main building blocks of a semantic segmentation framework (UNet) and an edge detection framework (HED), both tasks are combined in a natural way. Training is made efficient by employing deep supervision on side predictions at multiple resolutions. Finally, a hierarchical attention mechanism is introduced to adaptively merge these multiscale predictions into the final model output. The advantages of this approach over other traditional and deep learning-based methods for coastline detection are demonstrated on a dataset of Sentinel-1 imagery covering parts of the Antarctic coast, where coastline detection is notoriously difficult. An implementation of our method is available at https://github.com/khdlr/HED-UNet.
+
+Index Terms—Semantic segmentation, edge detection, Antarctica, glacier front
+
+# I. INTRODUCTION
+
+CONTRARY to many other landmasses, Antarctica's coastline is fringed by dynamic glacier and ice shelf fronts continuously changing the coastline location by iceberg calving, which is influenced by both seasonal variations as well as global climate change. Tracking the advance and retreat of glacier and ice shelf fronts is an important factor for a better understanding of glaciological processes. Furthermore, it is essential to monitor calving front retreat as it enhances the sea level contribution of the Antarctic ice sheet due to decreased buttressing effects.
+
+This work is supported by the Helmholtz Association through the Helmholtz Information and Data Science Incubator project "Artificial Intelligence for Cold Regions", Acronym AI-Core, by Helmholtz Association's Initiative and Networking Fund through Helmholtz AI [grant number: ZT-I-PF-5-01] - Local Unit "Munich Unit @Aeronautics, Space and Transport (MASTr)", and by the German Federal Ministry of Education and Research (BMBF) in the framework of the international future AI lab "AI4EO - Artificial Intelligence for Earth Observation: Reasoning, Uncertainties, Ethics and Beyond" (Grant number: 01DD20001).  
+K. Heidler, L. Mou and X. Zhu are with the Remote Sensing Technology Institute (IMF), German Aerospace Center (DLR), 82234 Wessling, Germany, and also with the Data Science in Earth Observation (SiPEO, formerly Signal Processing in Earth Observation), Technical University of Munich (TUM), 80333 Munich, Germany. E-mails: konrad.heidler@dlr.de; lichao.mou@dlr.de; xiaoxiang.zhu@dlr.de  
+C. Baumhoer and A. Dietz are with the German Remote Sensing Data Center (DFD), German Aerospace Center (DLR), 82234 Wessling, Germany. E-mails: celia.baumhoer@dlr.de; andreas.dietz@dlr.de
+
+![](images/41c33121eaac44d203eddac03e263299396631742b1250820614f9429e0bdafa.jpg)  
+SAR imagery
+
+![](images/b73e35e9e0ae5cf143ff6a9970c509b13b09c010f4083e984ed29331d6631ddd.jpg)  
+Segmentation
+
+![](images/3493fd506f41ea157cf23549c8c5e041a1f0ef5cfbb24f54543c1a42cd678bdd.jpg)  
+Edge Detection  
+Fig. 1. In coastline detection, the vision tasks of segmentation and edge detection are inseparable.
+
+Overall, the length of the Antarctic coastline amounts to around  $40000\mathrm{km}$  [1], which renders manual delineation infeasible. Especially when observing the developments over multiple time steps for continuous tracking, an automated coastline extraction technique is needed. The recent advances in algorithms and sensing platforms open up new possibilities for the analysis of satellite imagery over large regions, which can be observed in fields as diverse as land cover mapping [2]–[4], bathymetry [5]–[7], urban applications [8]–[12], change detection [13]–[17], and cryosphere research [18]–[22].
+
+This kind of fine-grained analysis is possible because of the availability of satellite imagery with revisit times in the order of days. Regarding data sources, both optical and synthetic aperture radar (SAR) sensors produce imagery suitable for the delineation of the Antarctic coastline [23]. The use of optical imagery in the Antarctic comes with some major drawbacks. Apart from the usual problems with cloud cover, vision is further impeded by polar night and sensor saturation due to the high albedo of ice. To create continuous and gapless observations, data from the Sentinel-1 mission was chosen as the main imagery source. SAR data has often been found to be helpful with the analysis of the cryosphere [24]–[33]. In our case, it allows for near-realtime analysis at a high temporal resolution.
+
+Using SAR data for the task of coastline extraction also imposes some challenges. The speckle present in SAR images makes it harder to pinpoint the exact boundary between land and sea. Further, the backscatter characteristics of glacial ice vary throughout the year, making it hard to distinguish between e.g. open sea and the higher ice sheet. Therefore, a good model needs to pay additional attention to contextual clues and cannot rely on local information only.
+
+Existing studies for delineating coastlines in general, as well as the Antarctic one, often focus their predictions on either the area of land and sea (sea-land segmentation), or the coastline itself (coastline detection). But to the human eye, the two
+
+concepts of "area" and "edge" are closely intertwined, making it hard to imagine one without the other. When conducting manual coastline delineation, a human annotator will therefore mentally segment the scene into sea and land while searching for the edge between the two at the same time.
+
+We hypothesize that taking into account this duality is essential in closing the performance gap between human annotators and automated approaches. In an attempt to more closely model this process, we thus introduce a new solution for coastline detection that draws upon the advantages of both segmentation and edge detection approaches. Instead of focusing a predictor on just one of these tasks, our network is trained to jointly perform both tasks at the same time. Inspired by neural architectures for semantic segmentation and edge detection, the model uses an encoder-decoder architecture with skip connections in order to predict segmentation masks and edges at multiple resolutions.
+
+Another observation we make about coastline detection conducted by humans is the fact that not all areas of a given scene need the same amount of attention to detail. While it is of paramount importance that the coastal regions are precisely mapped, areas further away from the coastline do not receive much attention from a human annotator. By introducing a merging scheme based on hierarchical attention, our model can work in the same way. The intermediate multiresolution predictions are merged using this mechanism to obtain a final output that combines fine-grained low level outputs with coarser high level outputs in an efficient way.
+
+Overall, this work's contributions are threefold:
+
+- Coastline detection is recognized as a dual task. To solve this, a unified theory of segmentation and edge detection is presented. From this, an architecture that implements both semantic segmentation and edge detection is devised.  
+- Apart from the narrow coastal strip, there are large regions that require less detailed analysis. This is taken into account by allowing the model to output predictions at different resolution levels. Adding deep supervision for these side outputs improves the training efficiency and generalization performance of the model.  
+- In order to dynamically blend between coarse and high-resolution predictions, a hierarchical attention mechanism is used that takes into account the information available at all levels.
+
+The remainder of the paper is organized as follows. Section II gives a brief overview of current methods for coastline detection with a focus on polar regions, as well as existing approaches for combining segmentation and edge detection. Section III presents our proposed HED-UNet architecture. In Section IV, the used dataset is introduced. Further, the conducted experiments are explained. Finally, Section V presents numerical results comparing our model to other approaches and ablation studies that analyze the proposed model's elements in detail. Finally, it also includes a discussion of the observed model performance.
+
+# II. RELATED WORK
+
+This section will explore the state of the art for coastline detection with a focus on Antarctica. Compared to the general case, the detection of coastlines in the Antarctic requires additional care, as many methods are easily distracted by dynamic sea ice, like icebergs or ice melange. Locally, these confounding features can look almost identical to land ice, and can therefore only be excluded by the additional use of spatial context information.
+
+There are numerous existing approaches for detecting coastlines from satellite imagery. For the biggest part, they can be divided into the aforementioned two classes, differing in the output of interest.
+
+# A. Sea-Land Segmentation
+
+In the field of computer vision, semantic segmentation is a central topic. Each pixel is assigned a class which is to be predicted by the model. This technique is frequently used in remote sensing for various tasks. When the area of either sea or land is of importance, semantic segmentation models are used to distinguish between sea pixels and land pixels.
+
+1) Statistical Methods: In quite a few studies, this has been done by means of statistical analysis. For the Antarctic, the use of a bimodal Gaussian mixture model was proposed, for which parameters are estimated in order to derive an adaptive thresholding scheme. This approach can be applied to both SAR and optical imagery [1]. Similar dynamic thresholding schemes have been applied to different sensors [34]. While easy to implement and fast to evaluate, these methods completely discard the spatial relationships of the pixels, which renders them unfit to deal with the aforementioned issues.  
+Another localized way of segmenting images that has been applied to sea-land segmentation is given by the watershed algorithm [35]. It treats the pixel intensities as height values and then simulates the resulting surface being flooded with water. Finally, unsupervised clustering methods are helpful in the analysis of complex coastlines [36]. These methods have the benefit of being unsupervised, i.e. requiring no training prior to the evaluation, but the lack of supervision also means that the models cannot be taught to e.g. ignore icebergs.  
+2) Deep Learning Methods: With the rise of deep learning in remote sensing [37], convolutional neural networks (CNNs) have been shown to provide superior performance for many tasks, including the one of sea-land segmentation [38]–[40]. Deep convolutional architectures like SegNet [41] or UNet [42] leverage contextual information through their encoder-decoder architectures. So as they have more context to base their decisions on, they have the potential to produce more accurate results than pixelwise or shallow texture-based classifiers. This is of great interest to Antarctic coastline detection due to the aforementioned issues. Current developments in computer vision show a trend towards more complex models for semantic segmentation, which incorporate global information [43] or shape information [44].  
+Generally, these models require large amounts of labeled data, and take quite some time to train. However, they can outperform the previously mentioned methods.
+
+# B. Coastline Detection
+
+A closely related task is approached in coastline detection. Instead of segmenting a scene into sea and land, the coastline itself is of primary interest.
+
+1) Edge Tracing: One class of edge detection methods mark the boundaries in the image step by step. After some filtering to highlight the edges, which can be done e.g. using the Roberts operator [45] or the Sobel operator [46], pixels that are likely to lie on the edge are connected to form the entire boundary. Regarding coastline detection, this approach has been shown to work for SAR data, when applying preprocessing steps to account for the nature of the imagery [47]. They can also be connected using a shortest-path algorithm [29], or ridge tracing [48]. Yet another approach comes from exploiting detection duality. By the nature of the relation between sea, land and the coastline, the coastline can be derived from a sea-land segmentation by tracing the transitions between the sea and land class [49].
+
+While relatively simple, these methods often have some issues regarding robustness. When the tracing procedure takes a wrong turn, it is hard for the algorithm to return to the true boundary.
+
+2) Contour Methods: Active contours, sometimes also called Snakes [50], are quite similar to the edge tracing approach. Instead of the pixel-by-pixel approach, this class of methods uses an initial curve that is iteratively deformed to minimize an energy function. By choosing the right energy function, this framework can be used to delineate coastlines. For SAR imagery, active contours are able to find coastlines when given a good initialization [51], [52]. These models are sensitive to the provided initialization, meaning that they can converge to local minima that do not represent the desired edge.
+
+3) Level Set Methods: Instead of working with an explicit parametrization of the curve, these methods work with an implicit representation given by a scalar field in which the zero set represents the boundary [53], [54]. Adaptations of this method for SAR coastline detection use multiple level set iterations to go from coarse to fine delineations [55] or sophisticated preprocessing steps [56] to make the method work for this particular type of imagery.
+
+4) Deep Learning Methods: Only recently have approaches based on deep learning begun to outperform handcrafted edge detection algorithms. Specialized architectures leverage the framework of CNNs to derive features that predict the presence of edges [57]–[59]. Notably, the previously mentioned Roberts and Sobel operators can be viewed as a shallow CNNs with just one layer and a convolutional filter size of 2 and 3 respectively. Therefore, it is only natural that deeper CNNs with more layers are able to outperform these hardcoded edge detection operators.
+
+# C. Combining Semantic Segmentation and Edge Detection
+
+A common problem with semantic segmentation models is the blurriness near class boundaries. This likely stems from the fact that the edges make up a minority of the pixels, and are therefore not well enough represented by the standard
+
+pixelwise cross-entropy loss. Thus, the idea of augmenting semantic segmentation approaches with edge information is not a new one.
+
+One way of making a segmentation model aware of edges in the image is by adding an auxiliary loss term that encourages the prediction of crisp edges. This has been shown to work for sea-land segmentation [60].
+
+Surprisingly, simply adding the edge detection task as an auxiliary output for a segmentation model can improve the segmentation results quite a bit, even without further changes to the model [61]. This approach can also improve sea-land segmentation results in harbor areas [62].
+
+To further improve blurry segmentations, edge masks can be used as the basis for a spatial propagation of class labels. In [63], a segmentation map is initialized using a segmentation network and at the same time, edges are predicted. These edge masks are then used as the basis for a recursive multidirectional label propagation.
+
+For aerial scene classification, the use of an edge detection subnetwork before doing the segmentation has been shown to be beneficial. The detected edge masks are then used as additional input features for the segmentation model. This approach improves the shape accuracy of the resulting segmentation [64].
+
+Contrary to these approaches, we develop a unified theory of segmentation and edge detection. We then identify the components that successful neural networks use to solve either one of these tasks, and finally devise a model that incorporates the tools necessary to solve both tasks at the same time. The underlying assumption is that both segmentation and edge detection are of equivalent importance for detecting coastlines in satellite imagery.
+
+# III. PROPOSED METHOD
+
+Implementing the sea-land segmentation task via a UNet segmentation model [42] has become a popular approach for the automatic delineation of coastlines [38]-[40]. And also on our dataset, this method yields good results on the majority of the evaluated scenes [31]. But oftentimes the predictions become inaccurate and blurry in areas close to the coastline. As the precise location of the coastline is the central object of our study,
+
+On the other hand, edge detection models excel at delineating the edges in the given images. However, an edge delineation has no concept of "inside" and "outside" by itself, so this output alone is insufficient for labeling sea and land. Further, edge detection models are easily fooled by inland structures of similar appearance to the coastline, as well as icebergs near the coast. This implies the need for extensive post-processing and manual corrections.
+
+To put our aforementioned hypotheses into practice, we now introduce a hybrid model for simultaneous prediction of the sea-land segmentation and edge detection of the coastline. Following our observation that humans will usually take into account both the edge information as well as the textural shape information, we therefore propose a combined framework that draws upon the advantages of both these approaches. It takes
+
+![](images/0230218749879932be50561941cfde548bd33af5d394501fb2a9a7b26df6dee5.jpg)  
+Fig. 2. High-level structure of the proposed framework. First, the encoder and decoder calculate a pyramid of feature maps. Then, the task-specific merging heads combine this information using the hierarchical attention mechanism.
+
+inspiration from both UNet [42] and HED [57], as well as related architectures by combining key ideas in a very natural way. Therefore, we call our model HED-UNet.
+
+# A. Unifying Segmentation and Edge Detection
+
+Regarding the deep learning formulation of the tasks, both segmentation and edge detection are in their nature dense prediction tasks, i.e. for each input pixel, an output label needs to be predicted. In the case of segmentation, this is the class label, like "sea" or "land". For edge detection, it is a classification into the two classes "edge" and "no edge".
+
+This means that, in principle, a segmentation model can be trained to perform edge detection and vice versa. However, these models were designed for their respective tasks only, meaning the performance will be degraded when applying them to a different task. In order to construct a model that works well for both tasks, we will therefore identify the components of successful architectures for both tasks, and find a way to incorporate them into a single multitask model.
+
+1) Segmentation Building Blocks: Some successful semantic segmentation architectures employ the combination of an encoder and a decoder [41], [42]. The encoder conducts a series of downsampling steps to allow for the aggregation of contextual information at a lower resolution. In turn, the decoder then distributes this information to the individual pixels through a series of upsampling steps.
+
+In a more recent branch of semantic segmentation approaches, the network architecture is divided into a backbone network that calculates feature maps, and one or multiple prediction heads, which conduct the final classification based on these feature maps [43], [44], [65].
+
+The contextual aggregation capabilities of an encoder-decoder framework are needed for this task, as some regions can only be classified correctly by the use of contextual clues. At the same time, the backbone-head approach makes it easy to build models that tackle multiple tasks. These considerations lead to the idea of implementing backbone network that follows the encoder-decoder structure. This has been pioneered for the task of object detection in the framework of feature pyramid networks [66]. For our network, we will employ two task-specific prediction heads after calculating a feature pyramid through an encoder-decoder approach.
+
+2) Edge Detection Building Blocks: On the other hand, edge detection frameworks are optimized to provide sharp edge delineations while at the same time keeping down the amount of false positives. This means that they need to combine the crisp edges predicted at a high resolution with more robust, lower resolution features to reject false positives from the former. Edge detection methods therefore often try to strike a balance between predictions or feature maps at different resolutions, which can be done with an architecture that employs an encoder followed by a merging block [57]–[59]. The encoder part is similar to the encoders used in semantic segmentation models, it aggregates contextual information by downsampling. The merging part however is a new block that combines the information from different resolution levels after they have been upsampled to the full resolution.
+
+Looking back at the proposed feature pyramid backbone, such a merging part fulfills the function of a prediction head. This observation leads to the high level network architecture, as shown in Fig. 2. It is structured in such a way that it contains the components for both a segmentation and an edge detection network. After this general structure of the network has been fixed, the detailed layout for each one of these blocks will be outlined in Section III-B.
+
+3) Loss Function: In edge detection, the classes "edge" and "no edge" are highly imbalanced. Therefore, we use an adaptively balancing modification of the binary cross-entropy loss, as proposed in [57]. For a single image with a ground truth partition into positive pixels  $Y_{+}$  and negative pixels  $Y_{-}$  and a prediction  $\hat{p}$ , it is given as
+
+$$
+\mathcal {L} (\hat {p}) = - \frac {\left| Y _ {-} \right| \sum_ {j \in Y _ {+}} \log \hat {p} _ {j}}{\left| Y _ {+} \cup Y _ {-} \right|} - \frac {\left| Y _ {+} \right| \sum_ {j \in Y _ {-}} \log \left(1 - \hat {p} _ {j}\right)}{\left| Y _ {+} \cup Y _ {-} \right|}. \tag {1}
+$$
+
+This loss function gives equal weight to the positive and negative classes, no matter the ratio between the two class sizes. Thanks to this property, it is fit not only for edge detection, but for semantic segmentation as well. Therefore, it is used as the loss function for both tasks.
+
+# B. Architecture Details
+
+Regarding the model details, we start with the encoder-decoder backbone. Conjecturing that the model needs a large spatial context window to base its decisions on, we use a feature pyramid with 6 resolution levels, corresponding to 5 down- and upsampling steps. In this pyramid, the finest feature map is at the full image resolution, and the coarsest one is at  $1/32$  the resolution. The number 6 was chosen to cover a large enough receptive field needed for the task. Deepening the network even further would lead to receptive fields that exceed the image tiles' extents, and did not bring further improvements in our experiments. In the decoder part, the data flows are merged by element-wise addition.
+
+Inspired by the hierarchical nature of the HED architecture [57], we adopt the scheme of predicting coarse representations of the output from within deeper layers. A side output for both segmentation and edge detection is added for each
+
+![](images/476dade6f6e681c38a1592536668aff9cef405cd9dcdafbf2e4e9640a2eb62a6.jpg)  
+Fig. 3. Architectural details of the proposed network. The full model contains two task-specific merging heads, for clarity, only the segmentation head is shown here. The edge detection head follows the same structure.
+
+feature map, for a total of 6 outputs. These multiscale outputs are used in two different ways.
+
+1) Deep Supervision: When building a deep feature pyramid like here, there might not be much motivation for the model to encode meaningful and informative features to the deep, lowest resolution feature maps. In order to explicitly provide this motivation, we train the model to be able to predict the ground truth from each single feature map in the pyramid.
+
+This so-called deep supervision [67] is known to improve the learning effectiveness of a neural network, as well as its generalization capabilities. This is achieved by training intermediate network outputs on the ground truth data to provide additional and more direct training feedback to the earlier layers. In our case, an accordingly downsampled version of the ground truth segmentation is created for each one of the multiresolution predictions, and the corresponding edges are calculated. Then, these multiscale ground truths are compared with the predictions to provide additional loss terms. The resulting deep supervision encourages the network to better capture larger structures and make use of the available receptive field by encoding meaningful features in the deep layers.
+
+2) Multiscale Fusion: In the next step, these side outputs become part of the merging heads that combine the intermediate outputs into one full-resolution prediction. This is a central point in the original HED architecture [57], so we also implement it in the combined HED-UNet model. In this way, the model has a way of combining fine-grained delineations near the edges with the more robust high-level predictions further away from the edge. The way of merging used in HED is to combine the intermediate predictions using learned weights. But to further improve the merging performance, we propose the following attention-based merging mechanism.
+
+# C. Hierarchical Attention Merging Heads
+
+The final element of the network architecture are the merging heads. In the edge detection frameworks introduced earlier [57]-[59], this is done by feature-wise concatenation, followed by a  $1 \times 1$  convolution to merge the information from different levels. But in different areas, different fusion
+
+behavior might be needed. In coastal areas, the model might want to use predictions of the highest possible resolution in order to accurately delineate the coastline. However, farther away from the coast the lower resolution levels can provide a more general assessment of the scene, and thus lead to better classifications in these areas.
+
+To allow for this adaptive fusion of the multiscale predictions that takes into account the confidence at the different granularities, we therefore introduce a new fusion procedure based on attention. This technique was initially explored in natural language processing as sequential attention among words and tokens [68], and later also applied in computer vision as spatial attention within an image [69].
+
+Inspired by these works, we apply attention for merging multiscale predictions. Here, this mechanism allows the network to focus on the features that it deems most useful for each pixel of the current scene, instead of having fixed weights for feature fusion. So instead of sequential or spatial attention, our attention block allows the model to attend to different resolution levels. It works like this:
+
+For each prediction level, a weight map is created. The weight maps are then upsampled to match the output resolution, and turned into a categorical probability map by applying the softmax function over the concatenated resolution levels. To obtain the final prediction, the dot product between the predictions and the attention mask is calculated. This process is visualized in Fig. 3.
+
+For a pyramid of feature maps  $F_{k}$ , the final prediction  $\hat{p}$  is thus calculated as:
+
+$$
+\hat {p} = \sum_ {k} \mathrm {u} \left(f _ {k} \left(F _ {k}\right)\right) \cdot \operatorname {s o f t m a x} _ {k} \left(\mathrm {u} \left(g _ {k} \left(F _ {k}\right)\right)\right), \tag {2}
+$$
+
+where  $\mathfrak{u}(\cdot)$  denotes bilinear upsampling to the full output resolution. The functions  $f_{k}, g_{k}$  denote the multilevel prediction layers and the attention layers respectively, both are implemented as simple  $1 \times 1$  convolutional layers.
+
+This approach can be interpreted probabilistically as follows. The intermediate predictions  $f_{k}(F_{k})$  can be considered to be maps of Bernoulli probabilities for the output classification at different resolutions. Through the prediction process, these probabilities are conditioned on the input imagery. The original merging procedure with fixed weights corresponds to
+
+![](images/d68162fb00b6cc3cce54f093c8293b40333481e4631b89bbf52ec4c733f140dc.jpg)  
+Fig. 4. Spatial distribution of the scenes in the dataset. Scenes marked in green were used for model training, scenes marked in red were used for validation purposes. The red area in the top left is the "Antarctic Peninsula" validation site, while the bottom right red area is the "Wilkes Land" validation site. For most locations, data from 2 or 3 different sensing dates was used to allow for an assessment of each model's temporal stability. Marked in yellow is the footprint of the visualization tile in Fig. 7.
+
+a mixture model of these Bernoulli maps where the mixture coefficients  $w_{k}$  are learned and fixed. For an input scene  $X$ , the predicted probabilities  $Y$  are thus approximated as
+
+$$
+P \left(Y _ {i j} \mid X\right) \approx \sum_ {k} w _ {k} P \left(Y _ {i j} \mid X, \text {r e s o l u t i o n} = k\right). \tag {3}
+$$
+
+Contrary to that, the attention merging corresponds to a mixture model where the mixture coefficients  $w_{kij}$  are learned to dynamically depend on the input as well, resulting in the slightly different approximation
+
+$$
+P \left(Y _ {i j} \mid X\right) \approx \sum_ {k} w _ {k i j} (X) P \left(Y _ {i j} \mid X, \text {r e s o l u t i o n} = k\right). \tag {4}
+$$
+
+Notation-wise, this might seem like a small change. However, it leads to more flexibility in the resulting probabilistic model, which implies the potential for better classifications.
+
+From the probabilistic perspective, the model training corresponds to a simultaneous maximization of both the side outputs' likelihood as well as the likelihood of the full mixture under the observed data.
+
+# IV. DATASET AND EXPERIMENTAL SETUP
+
+In order to validate the effectiveness of the suggested improvements, we trained and validated several competing methods as well as the proposed model on a dataset of the Antarctic coast.
+
+# A. Dataset
+
+Our dataset consists of 16 cropped Sentinel-1 GRD scenes of Antarctica's coastline taken between June 2017 and December 2018 in the sensor's Extra Wide Swath acquisition mode.
+
+The spatial distribution of these tiles can be seen in Fig. 4. The data has a resolution of  $40\mathrm{m}$  and dual polarization with HH and HV channels. The cropped scenes have an average size of  $7870\times 6572$  pixels  $(315\mathrm{km}\times 263\mathrm{km})$ , and a combined area of around  $730000\mathrm{km}^2$ . All imagery is processed in the Antarctic Polar Stereographic projection (EPSG:3031) and converted to decibel. On these scenes, the coastline was manually annotated by experts in order to provide a ground truth sea-land segmentation and coastline delineation.
+
+The scenes within the dataset are clustered in 4 areas, out of which 2 were selected as validation areas and completely left them out of the training procedure. This leads to a split of 11 training scenes and 5 validation scenes. The scenes were all tiled into sections of  $768 \times 768$  pixels with  $50\%$  overlap between adjacent tiles to form the training and validation dataset, respectively. In order to improve generalization performance, we employed 8-fold data augmentation on the training set. This augmentation technique processes a single tile into the 8 different versions that can be obtained by horizontal or vertical mirroring, as well as rotating by multiples of  $90^{\circ}$ .
+
+# B. Evaluated Models
+
+As competitors to our model we evaluate the following models to provide a baseline.
+
+# 1) Traditional Methods:
+
+Gaussian Mixture The sea-land segmentation method presented in [1], which applies dynamic thresholding based on a bimodal mixture of gaussians.
+
+K-Medians Clustering An unsupervised sea-land segmentation method presented in [36] that employs k-midians clustering of the pixels in a scene on multiple scales.
+
+Sobel Edges The coastline detection method presented in [47], which applies the Sobel filter, then a spatial dilution process, and then a Roberts edge filter.
+
+Active Contours An active contours approach for coastline detection based on the Chan-Vese model [54].
+
+# 2) Deep Learning:
+
+HED The edge detection model from [57].
+
+UNet The segmentation model presented in [42], which is known to work well for coastline detection [31].
+
+DeepUNet A modification of the previous method that was developed for sea-land segmentation as proposed in [39].
+
+RDUNet Another modification of UNet developed for sealand segmentation, which was proposed in [38].
+
+HRNet + OCR One of the current state-of-the-art models for semantic segmentation in general computer vision [43].
+
+Gated-SCNN Another recent model for semantic segmentation in general computer vision [44]. This one is particularly interesting, as it also combines segmentation with edge detection.
+
+# C. Training Details
+
+The deep learning models were trained on the training dataset of Antarctic coastline scenes for 15 epochs on a Nvidia V100 card with 32GB of video memory. The model weights were optimized by an Adam optimizer using the hyperparameters suggested in [70], namely a learning rate of
+
+![](images/473f94388c2d710ba091a119181d7f95901908a43ee4a4369634e662c2dfde81.jpg)  
+Segmentation
+
+![](images/19a88ca2cc04ef1e1a603b83b0b3bd7ee29ca1c18680c1b5f3c844fe6150a974.jpg)  
+Edge Detection  
+Fig. 5. Qualitative results comparing the evaluated models on unseen validation tiles. In order to provide an informative visualization, the visualized tiles were selected to represent the full spectrum of easy (top) to hard (bottom) scenes within the validation set.
+
+TABLEI NUMERICAL RESULTS FOR THE EVALUATED MODELS  
+
+<table><tr><td rowspan="2">SiteMetric</td><td colspan="6">Wilkes Land</td><td colspan="5">Antarctic Peninsula</td></tr><tr><td>Accuracy</td><td>mIoU</td><td>Deviation</td><td>F1 ODS</td><td>F1 OIS</td><td>Accuracy</td><td>mIoU</td><td>Deviation</td><td>F1 ODS</td><td>F1 OIS</td><td></td></tr><tr><td>Gaussian Mixture [1]</td><td>77.4</td><td>63.0</td><td>773</td><td></td><td></td><td>74.7</td><td>58.8</td><td>765</td><td></td><td></td><td></td></tr><tr><td>K-Medians Clustering [36]</td><td>55.9</td><td>28.0</td><td>637</td><td></td><td></td><td>60.5</td><td>40.1</td><td>560</td><td></td><td></td><td></td></tr><tr><td>Sobel Edges [47]</td><td></td><td></td><td>507</td><td>29.0</td><td>31.8</td><td></td><td></td><td>644</td><td>21.1</td><td>20.8</td><td></td></tr><tr><td>Active Contours [54]</td><td></td><td></td><td>672</td><td>21.9</td><td>23.5</td><td></td><td></td><td>698</td><td>14.6</td><td>15.1</td><td></td></tr><tr><td>HED [57]</td><td></td><td></td><td>341 ± 22</td><td>38.4 ± 1.7</td><td>41.0 ± 1.0</td><td></td><td></td><td>398 ± 27</td><td>28.5 ± 0.8</td><td>29.6 ± 0.7</td><td></td></tr><tr><td>UNet [42]</td><td>89.2 ± 3.0</td><td>80.6 ± 4.7</td><td>271 ± 14</td><td></td><td></td><td>79.3 ± 2.8</td><td>65.0 ± 4.4</td><td>483 ± 40</td><td></td><td></td><td></td></tr><tr><td>DeepUNet [39]</td><td>87.3 ± 6.4</td><td>77.6 ± 9.9</td><td>287 ± 32</td><td></td><td></td><td>76.9 ± 4.8</td><td>61.8 ± 7.5</td><td>525 ± 118</td><td></td><td></td><td></td></tr><tr><td>RDUNet [38]</td><td>89.2 ± 1.4</td><td>80.1 ± 2.2</td><td>271 ± 26</td><td></td><td></td><td>78.3 ± 1.2</td><td>63.9 ± 2.0</td><td>460 ± 73</td><td></td><td></td><td></td></tr><tr><td>HRNet + OCR [43]</td><td>89.2 ± 2.5</td><td>80.2 ± 4.3</td><td>262 ± 35</td><td></td><td></td><td>78.6 ± 1.9</td><td>64.6 ± 2.5</td><td>467 ± 61</td><td></td><td></td><td></td></tr><tr><td>Gated-SCNN [44]</td><td>87.1 ± 0.2</td><td>76.8 ± 0.1</td><td>297 ± 2</td><td>31.6 ± 0.4</td><td>34.1 ± 0.1</td><td>77.7 ± 1.5</td><td>63.0 ± 2.2</td><td>471 ± 33</td><td>23.0 ± 1.7</td><td>25.4 ± 1.7</td><td></td></tr><tr><td>HED-UNet</td><td>92.0 ± 0.8</td><td>84.9 ± 1.4</td><td>222 ± 23</td><td>39.7 ± 1.2</td><td>41.6 ± 0.9</td><td>80.5 ± 1.6</td><td>67.2 ± 2.2</td><td>345 ± 24</td><td>27.1 ± 1.9</td><td>29.4 ± 1.8</td><td></td></tr></table>
+
+0.001,  $\beta_{1} = 0.9$ ,  $\beta_{2} = 0.999$  and  $\varepsilon = 10^{-8}$ . Due to the large size of the used tiles, the batch size was set to the low number of 4 samples per batch.
+
+# V. RESULTS AND DISCUSSION
+
+The improved performance from our method is quantified using the withheld validation dataset. To get informative insights on the actual coastline detection performance, the metrics are calculated only for pixels within  $2\mathrm{km}$  of the true coastline. This way, a distortion of the metrics from non-coastal areas can be avoided.
+
+The two validation areas (Antarctic Peninsula and Wilkes Land, see Fig. 4) are evaluated separately. While the Wilkes Land area can be considered of average difficulty, the Antarctic Peninsula seems to be a very tough location for all of the evaluated models.
+
+For the segmentation approaches, we evaluate the pixelwise accuracy as well as the mean intersection-over-union metric for the classes of water and land. For edge detection, we calculate the edge  $F_{1}$  scores at optimal image scale (OIS) and optimal dataset scale (ODS). Finally, we calculate an approximate deviation by averaging the distance to the ground truth coastline over all predicted coastline pixels ("Deviation"). Table I shows the numerical results obtained. The average distance metric can be considered the most important one for this task, as it estimates the overall error between the actual coastline and the predicted coastline. Regarding segmentation performance, the mIoU metric can be considered the primary metric. In order to get a visual impression of some of the models' performance, Fig. 5 shows predictions for a selection of validation tiles. The shown examples are ordered from what we consider easy to hard samples for the models, and showcase some of the difficulties with the dataset, like sea ice and confounding backscatter on the higher ice sheet.
+
+# A. Model Comparison
+
+First, it is easy to see that the traditional models are not really competitive on this dataset. We ascribe this to the repeatedly stated phenomena of icebergs and ice sheet regions with difficult backscatter characteristics. As these models are unsupervised, they simply do not have a way of learning how to deal with such impediments.
+
+Overall, the heterogeneity of the Antarctic coastline is astounding. While the coastline is found pretty well by most models in Wilkes Land, all models have trouble with the scenes from the Antarctic Peninsula.
+
+Among the deep learning based models, UNet [42] imposes a respectable baseline, and even outperforms the more recent models like HRNet+OCR [43] and Gated-SCNN [44] in some of the evaluated metrics. Even though the latter also has a side output for edge detection, we find that its edge detection results fall short in comparison to HED [57] and HED-UNet. A reason for this might be the lack of a pretrained backbone network for Sentinel-1 data, which forced us to randomly initialize the backbone and train it alongside the rest of the network. Further, this model was optimized for segmentation of scenes with many different classes and small objects, which is needed for tasks like autonomous driving. In our usecase however, there are only two classes which are nearly equal in area, imposing a very different data distribution.
+
+The ultimate goal of this study is to delineate the coastline as accurately as possible. In the corresponding average deviation metric, the proposed HED-UNet model outshines the alternative approaches, especially in the Antarctic Peninsula validation area. This confirms our assumptions that for this specific task, our considerations lead to increased performance.
+
+# B. Network Depth and Deep Supervision
+
+As a means of quantifying the improvements made to the architecture, we evaluate versions of our model with only some of the improvements applied. The results of this ablation study are displayed in Table II.
+
+For a fair comparison with UNet-based models, we evaluate the performance when only 5 resolution levels are used instead of 6, corresponding to 4 down- and upsampling steps instead of 5. While this setup performs slightly worse than the full HED-UNet, it still outperforms the baseline methods.
+
+Regarding deep supervision, we can see that it is of paramount importance for edge detection performance. Without it, the model is barely able to predict the presence of edges. What is more, the coastline is often missed completely due to this poor edge detection performance. On the other hand, deep supervision does not seem to alter the performance on the semantic segmentation task much. This is in line with the original models that we took inspiration from. While
+
+TABLE II NUMERICAL RESULTS FOR THE ABLATIONS  
+
+<table><tr><td rowspan="2">Data</td><td rowspan="2">Deep Sup.</td><td rowspan="2">Levels</td><td rowspan="2">Merging</td><td colspan="4">Wilkes Land</td><td colspan="6">Antarctic Peninsula</td></tr><tr><td>Accuracy</td><td>mIoU</td><td>Deviation</td><td>F1 ODS</td><td>F1 OIS</td><td>Accuracy</td><td>mIoU</td><td>Deviation</td><td>F1 ODS</td><td>F1 OIS</td></tr><tr><td>SAR</td><td>Yes</td><td>5</td><td>Attention</td><td>90.3 ± 1.3</td><td>82.2 ± 2.1</td><td>239 ± 16</td><td>37.2 ± 0.7</td><td>38.7 ± 0.9</td><td>77.0 ± 1.0</td><td>62.5 ± 1.3</td><td>379 ± 45</td><td>25.4 ± 1.2</td><td>27.0 ± 1.0</td></tr><tr><td>SAR</td><td>No</td><td>6</td><td>Attention</td><td>88.5 ± 1.4</td><td>79.2 ± 2.3</td><td>954 ± 7</td><td>7.1 ± 0.5</td><td>7.1 ± 0.5</td><td>80.3 ± 1.6</td><td>66.8 ± 2.1</td><td>895 ± 7</td><td>7.4 ± 0.2</td><td>7.5 ± 0.2</td></tr><tr><td>SAR</td><td>Yes</td><td>6</td><td>None</td><td>89.7 ± 1.2</td><td>81.1 ± 1.9</td><td>284 ± 37</td><td>37.5 ± 1.2</td><td>39.7 ± 1.3</td><td>81.8 ± 2.0</td><td>69.0 ± 2.9</td><td>378 ± 35</td><td>28.0 ± 1.8</td><td>30.2 ± 1.8</td></tr><tr><td>SAR</td><td>Yes</td><td>6</td><td>Learned</td><td>89.9 ± 2.5</td><td>81.6 ± 3.9</td><td>236 ± 14</td><td>37.0 ± 2.2</td><td>38.6 ± 2.2</td><td>81.4 ± 1.1</td><td>68.3 ± 1.6</td><td>391 ± 12</td><td>26.6 ± 1.4</td><td>29.1 ± 1.4</td></tr><tr><td>SAR</td><td>Yes</td><td>6</td><td>Attention</td><td>92.0 ± 0.8</td><td>84.9 ± 1.4</td><td>222 ± 23</td><td>39.7 ± 1.2</td><td>41.6 ± 0.9</td><td>80.5 ± 1.6</td><td>67.2 ± 2.2</td><td>345 ± 24</td><td>27.1 ± 1.9</td><td>29.4 ± 1.8</td></tr><tr><td>SAR+DEM</td><td>Yes</td><td>6</td><td>Attention</td><td>92.9 ± 1.4</td><td>86.7 ± 2.4</td><td>226 ± 47</td><td>35.1 ± 3.4</td><td>36.0 ± 3.5</td><td>91.6 ± 1.6</td><td>84.6 ± 2.7</td><td>210 ± 9</td><td>30.7 ± 2.1</td><td>31.4 ± 2.7</td></tr></table>
+
+the segmentation model UNet [42] does not employ deep supervision, the edge detection model HED [57] makes heavy use of it.
+
+# C. Merging Strategies
+
+After adding the deep supervision, we evaluate different merging strategies:
+
+a) None: First, we evaluate a configuration where just the last layer of the decoder is used for the predictions (denoted "None"). This corresponds to the workings of a UNet [42] model with two final prediction layers, one for each task.  
+b) Learned: Secondly, we evaluate the performance of the learned merging strategy, as originally proposed in [57]. Here, a prediction is computed for each resolution level in the feature pyramid. These predictions are then upsampled to full resolution and concatenated. After this, a  $1 \times 1$  convolutional layer with learned weights computes the final prediction from the concatenated prediction stack.  
+c) Attention: The last strategy is the hierarchical attention merging introduced in Sect. III-C, which Jnewdoes not rely on fixed weights like the previous strategy, but computes the merging weights dynamically for each pixel within each scene.
+
+From our results, learned merging does not improve much over no merging for segmentation, and even performs a bit worse for edge detection. The average deviation improves quite a bit in Wilkes Land, but worsens a bit on the Antarctic Peninsula in return. We ascribe this to the large differences in the validation areas. As the merging coefficients are fixed for the "Learned" approach, this might hint at the fact that the model learns coefficients that work well for Wilkes Land, but less so for the Antarctic Peninsula.
+
+This issue is overcome by our newly proposed attention merging strategy, which can adapt to the different scenes. It can learn to find good sets of merging coefficients for both Wilkes Land and the Antarctic Peninsula, even though the optimal values for each one might be different.
+
+Fig. 6 shows that the model indeed directs its attention in an adaptive fashion as we conjectured. Overall, a mix of all resolution levels is used to compute the final output. On tiles that are completely covered by one of the two classes, the attention shifts a bit towards the lower resolution levels, as they tend to provide more robust predictions. For pixels on the edge, the model heavily focuses on the highest available resolution level, in order to arrive at accurate delineations in these regions.
+
+# D. DEM Experiments
+
+Further, we look into including digital elevation data from the TanDEM-X elevation model [71]. We conjecture that this secondary data source can help the model better detect misclassifications from icebergs or dry-snow facies of the higher ice sheet, which have confounding SAR backscatter.
+
+To discourage the model from directly reproducing the coastline implied by the elevation model, we decided to downsample the DEM's resolution to  $640\mathrm{m}$ . This resolution is coarse enough to not make a segmentation based on the DEM alone competitive to the non-DEM models, which have an average deviation of less than  $300\mathrm{m}$ . Further, it allows for easy feature fusion, as it corresponds to the resolution of the feature map at  $1/16$  of the full resolution. Therefore, it is simply concatenated to the feature map after the fourth downsampling step in the encoder.
+
+The results when including the DEM are displayed as the last ablation in Table II. On the very hard scenes of the Arctic Peninsula, this additional information helps the model by a large margin, boosting the average deviation from  $345\mathrm{m}$  to  $210\mathrm{m}$ . However, the story is different for Wilkes Land. Here, the deviation worsens slightly, and the edge detection metrics go down considerably.
+
+This is a strong indicator that the model is indeed overfitting on the DEM to some extent. For example, in some highly dynamic coastal regions the model will be confused when the DEM and SAR imagery are contradictory.
+
+So all in all the inclusion of DEM data can be beneficial, but needs to be done very carefully to prevent the model from overfitting to the DEM alone.
+
+# E. Limitations
+
+Even though the newly proposed model outperforms the baselines on nearly all validation scenes, there are still cases where the results are not perfect. Most misclassifications can be attributed to one of two failure modes, which we will now briefly discuss. Visual examples for these failure modes can be seen in Fig. 8.
+
+1) Sea Ice: The large receptive field and multitask training help alleviate the issue of wrongly classified sea ice. But very large icebergs and areas of ice melange can still throw off the proposed model. The first failure example displays such an area where large clusters of sea ice confuse the model.  
+2) Missing Context: For areas close to the border of a tile, the model sometimes does not have enough contextual information to correctly classify them. This can be observed
+
+![](images/b94d02bc2a3cf450333075152aed3de316d6aff4909b4352cbeee4f3d455fed7.jpg)  
+Fig. 6. Amount of attention spent on the different resolution levels. Each plot analyzes a specific class of pixels in the validation dataset – from left to right: Average over all pixels, average over pixels from edge-less tiles, average over all edge pixels.
+
+![](images/c3d93d48c864a4a405644de39c358f894726c70037bf54a59b5b26bf4ffe34dc.jpg)
+
+![](images/4a06a628e0048bd491413460156b98200123cd6fb03e7d2b25afc75729b70bee.jpg)
+
+![](images/29765d2a946b735d559eb0827284468608431b4dcfd45aa0caf9a8e1880a9440.jpg)  
+Fig. 7. A section of George V Coast with Cape Hudson in the bottom left, imagery mosaiced from Sentinel-1 takes in early 2019. This scene is both temporally and spatially separated from the training and validation sets used. Overlaid in red is the coastline predicted by the HED-UNet model.
+
+in the second failure visualization, where a patch of sea ice directly next to the tile border is wrongly classified as land.
+
+Overall, these failures do not occur often throughout the dataset and apply not only to the HED-UNet models, but to the other compared models as well. Especially the first one requires much human interpretation on a large spatial context, which is difficult for a neural network to achieve without general reasoning capabilities.
+
+# F. Effective Receptive Fields
+
+Deep CNNs like the ones used in our experiments have very large theoretical receptive fields. It is conjectured that while long-range connections are theoretically possible in these networks, networks will often ignore them in favor of short-range connections.
+
+To assess how much of the spatial context is actually used by a CNN, its so-called effective receptive field (ERF) can be estimated [72]. This is done by analyzing the expected gradient magnitude of each input pixel with respect to a central output pixel. For a CNN  $f$  and a sequence of input images  $I_{k}$ , one
+
+![](images/b898c89902727e0dc56e137c46e7d046ef2b3f6795638f30e75b32f7a84a1802.jpg)  
+Fig. 8. Failure modes of the proposed model. Top: Confusion from a very large cluster of sea ice. Bottom: Confusion due to missing context at the border of the tile
+
+![](images/afd5b71f8577a3a6b8e6611ab4bde84a3c4a159145107b6b3aa672b758f7c965.jpg)
+
+![](images/ac27f871aeb601589d9aa9095e7c2d7090d1be7d24a191fe54a552a8d5e3a928.jpg)
+
+![](images/d45d0f518c248902efc799229a3c7d2b3cc2946fe58fe649afd75437254f1a2c.jpg)  
+Fig. 9. Effective receptive fields of some tested models for the prediction of a central pixel, visualized in image space. Theoretical receptive fields outlined in green. Note that the theoretical receptive fields of Gated-SCNN and HRNet+OCR are larger than the used patch size of  $768 \times 768$ .
+
+![](images/abee7225b417fb735164fe055035c2d5a5556548c090b9b98cd69acc6cbc254e.jpg)
+
+therefore looks at the values of
+
+$$
+E = \frac {1}{n} \sum_ {k = 1} ^ {n} | \nabla_ {I _ {k}} f (I _ {k}) _ {i, j} | \tag {5}
+$$
+
+for a central output pixel  $(i,j)$ . If for an input pixel  $(x,y)$ , the value  $E_{x,y}$  is non-negligible, then this pixel will influence the output predictions at position  $(i,j)$ . The spatial distribution of these relevant pixels is then called the effective receptive field.
+
+As the gradient magnitude gives insight on how much the prediction changes in response to a change in the input, the ERF allows for a measurement of the spatial context used by the model. A model with a larger ERF bases its decisions on a larger spatial context than one with a small ERF.
+
+We conjectured that for the task of Antarctic coastline detection, a model needs to take a large context window into account. And indeed, there seems to be a correlation between a larger ERF and better validation scores for this task.
+
+It can be observed that the UNet model is limited by its theoretical receptive field. Its ERF is forced into an almost quadratic shape because of this. The ERF of the Gated-SCNN model is particularly interesting with it's fractal-like shape. We conjecture that this is due to the Atrous Spatial Pyramid Pooling block used in the network architecture, which makes heavy use of dilated convolutions.
+
+Finally, the HRNet+OCR and HED-UNet models employ a very large ERF, which once more supports our assumption that a large receptive field is needed for coastline detection in Antarctica.
+
+# VI. CONCLUSION
+
+In this paper, we introduced a model for simultaneous segmentation and edge detection. The proposed HED-UNet learns to exploit the synergies between the two tasks, and thereby manages to surpass both edge detection and semantic segmentation baselines. By the use of deep supervision, we encourage the model to encode meaningful features in its deep layers, which allow for more general predictions. Finally, the proposed attention merging heads allow for better learning performance and more robust classifications.
+
+Compared to approaching the task with a regular UNet, the presented network architecture only requires little additional computational cost. Most of the performance gains stem from the adapted training procedure and a few additional layers, which do not require many computational resources compared to the layers already present.
+
+While it is not a general purpose model, we show that our proposed improvements to the model are indeed beneficial for the task of coastline detection. Visual and numerical inspection of the results confirm our assumption that the combination of the two tasks helps the model better grasp the concept of a coastline.
+
+Our model can be applied to coastline detection tasks not only in polar regions, but to coastal regions worldwide. Further, we are convinced that the approach taken by HED-UNet will greatly benefit other tasks requiring an edge detection approach in combination with semantic segmentation. Possible applications include the mapping of building footprints, roads, and bodies of water like lakes or rivers.
+
+# ACKNOWLEDGMENT
+
+We thank the European Union Copernicus program for providing Sentinel-1. TanDEM-X elevation data courtesy of the German Aerospace Center (DLR).
+
+# REFERENCES
+
+[1] H. Liu and K. C. Jezek, “A complete high-resolution coastline of Antarctica extracted from orthorectified Radarsat SAR Imagery,” *Photogramm. Eng. Remote Sens.*, vol. 70, no. 5, pp. 605–616, May 2004.  
+[2] J. Geng, H. Wang, J. Fan, and X. Ma, "Deep supervised and contractive neural network for SAR image classification," IEEE Trans. Geosci. Remote Sens., vol. 55, no. 4, pp. 2442-2459, Apr. 2017.
+
+[3] C. Robinson, L. Hou, K. Malkin, R. Soobitsky, J. Czawlytko, B. Dilkina, and N. Jojic, “Large scale high-resolution land cover mapping with multi-resolution data,” Proc. 2019 IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 12726-12735, 2019.  
+[4] X.-Y. Tong, G.-S. Xia, Q. Lu, H. Shen, S. Li, S. You, and L. Zhang, "Land-cover classification with high-resolution remote sensing images using transferable deep models," Remote Sens. Environ., vol. 237, p. 111322, Feb. 2020.  
+[5] F. Eugenio, J. Marcello, and J. Martin, "High-resolution maps of bathymetry and benthic habitats in shallow-water environments using multispectral remote sensing imagery," IEEE Trans. Geosci. Remote Sens., vol. 53, no. 7, pp. 3539-3549, Jul. 2015.  
+[6] J. Liang, J. Zhang, Y. Ma, and C.-Y. Zhang, “Derivation of bathymetry from high-resolution optical satellite imagery and USV sounding data,” Mar. Geod., vol. 40, no. 6, pp. 466-479, Nov. 2017.  
+[7] M. Erena, J. A. Dominguez, J. F. Atenza, S. García-Galiano, J. Soria, and Á. Pérez-Ruzafa, “Bathymetry time series using high spatial resolution satellite images,” Water, vol. 12, no. 2, p. 531, Feb. 2020.  
+[8] Y. Long, Y. Gong, Z. Xiao, and Q. Liu, "Accurate object localization in remote sensing images based on convolutional neural networks," IEEE Trans. Geosci. Remote Sens., vol. 55, no. 5, pp. 2486-2498, May 2017.  
+[9] N. Audebert, B. Le Saux, and S. Lefèvre, “Beyond RGB: Very high resolution urban remote sensing with multimodal deep networks,” *ISPRS* J. Photogramm. Remote Sens.*, vol. 140, pp. 20–32, Jun. 2018.  
+[10] L. Mou and X. X. Zhu, "Vehicle instance segmentation from aerial image and video using a multitask learning residual fully convolutional network," IEEE Trans. Geosci. Remote Sens., vol. 56, no. 11, pp. 6699-6711, Nov. 2018.  
+[11] L. Mou, Y. Hua, and X. X. Zhu, "Relation matters: Relational context-aware fully convolutional network for semantic segmentation of high-resolution aerial images," IEEE Trans. Geosci. Remote Sens., pp. 1-13, 2020.  
+[12] Q. Li, Y. Shi, X. Huang, and X. X. Zhu, "Building footprint generation by integrating convolution neural network with feature pairwise conditional random field (FPCRF)," IEEE Trans. Geosci. Remote Sens., pp. 1-18, 2020.  
+[13] D. Wen, X. Huang, L. Zhang, and J. A. Benediktsson, “A novel automatic change detection method for urban high-resolution remotely sensed imagery based on multiindex scene representation,” IEEE Trans. Geosci. Remote Sens., vol. 54, no. 1, pp. 609–625, Jan. 2016.  
+[14] O. A. Ajadi, F. J. Meyer, and P. W. Webley, "Change detection in synthetic aperture radar images using a multiscale-driven approach," Remote Sens., vol. 8, no. 6, p. 482, Jun. 2016.  
+[15] Z. Y. Lv, T. F. Liu, P. Zhang, J. A. Benediktsson, T. Lei, and X. Zhang, "Novel adaptive histogram trend similarity approach for land cover change detection by using bitemporal very-high-resolution remote sensing images," IEEE Trans. Geosci. Remote Sens., vol. 57, no. 12, pp. 9554-9574, Dec. 2019.  
+[16] B. Du, L. Ru, C. Wu, and L. Zhang, "Unsupervised deep slow feature analysis for change detection in multi-temporal remote sensing images," IEEE Trans. Geosci. Remote Sens., vol. 57, no. 12, pp. 9976-9992, Dec. 2019.  
+[17] C. Zhang, S. Wei, S. Ji, and M. Lu, "Detecting large-scale urban land cover changes from very high resolution remote sensing images using cnn-based classification," ISPRS Int. J. Geo-Inf., vol. 8, no. 4, p. 189, Apr. 2019.  
+[18] M. Engram, C. D. Arp, B. M. Jones, O. A. Ajadi, and F. J. Meyer, "Analyzing floating and bedfast lake ice regimes across Arctic Alaska using 25 years of space-borne SAR imagery," Remote Sens. Environ., vol. 209, pp. 660-676, May 2018.  
+[19] I. Sasgen, H. Konrad, V. Helm, and K. Grosfeld, “High-resolution mass trends of the Antarctic ice sheet through a spectral combination of satellite gravimetry and radar altimetry observations,” Remote Sens., vol. 11, no. 2, p. 144, Jan. 2019.  
+[20] D. O. Dammann, L. E. B. Eriksson, A. R. Mahoney, H. Eicken, and F. J. Meyer, "Mapping pan-Arctic landfast sea ice stability using Sentinel-1 interferometry," The Cryosphere, vol. 13, no. 2, pp. 557-577, Feb. 2019.  
+[21] I. Nitze, G. Grosse, B. M. Jones, V. E. Romanovsky, and J. Boike, "Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic," Nat. Commun., vol. 9, no. 1, pp. 1-11, Dec. 2018.  
+[22] J. E. Anderson, T. A. Douglas, R. A. Barbato, S. Saari, J. D. Edwards, and R. M. Jones, “Linking vegetation cover and seasonal thaw depths in interior Alaska permafrost terrains using remote sensing,” Remote Sens. Environ., vol. 233, p. 111363, Nov. 2019.
+
+[23] C. A. Baumhoer, A. J. Dietz, S. Dech, and C. Kuenzer, “Remote sensing of Antarctic glacier and ice-shelf front dynamics—A review,” Remote Sens., vol. 10, no. 9, p. 1445, Sep. 2018.  
+[24] T. Strozzi, A. Luckman, T. Murray, U. Wegmuller, and C. Werner, "Glacier motion estimation using SAR offset-tracking procedures," IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11, pp. 2384-2391, Nov. 2002.  
+[25] G. Vasile, E. Trouve, I. Petillot, P. Bolon, J.-M. Nicolas, M. Gay, J. Chanussot, T. Landes, P. Grussenmeyer, V. Buzuloiu, I. Hajnsek, C. Andres, M. Keller, and R. Horn, "High-resolution SAR interferometry: Estimation of local frequencies in the context of Alpine glaciers," IEEE Trans. Geosci. Remote Sens., vol. 46, no. 4, pp. 1079-1090, Apr. 2008.  
+[26] E. Erten, "Glacier velocity estimation by means of a polarimetric similarity measure," IEEE Trans. Geosci. Remote Sens., vol. 51, no. 6, pp. 3319-3327, Jun. 2013.  
+[27] V. Akbari, A. P. Doulgeris, and T. Eltoft, "Monitoring glacier changes using multitemporal multipolarization SAR images," IEEE Trans. Geosci. Remote Sens., vol. 52, no. 6, pp. 3729-3741, Jun. 2014.  
+[28] S. Lang, X. Liu, B. Zhao, X. Chen, and G. Fang, "Focused synthetic aperture radar processing of ice-sounding data collected over the east antarctic ice sheet via the modified range migration algorithm using curvelets," IEEE Trans. Geosci. Remote Sens., vol. 53, no. 8, pp. 4496-4509, Aug. 2015.  
+[29] L. Krieger and D. Floriciou, "Automatic calving front delineation on TerraSAR-X and Sentinel-1 SAR imagery," in Proc. 2017 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), Jul. 2017, pp. 2817-2820.  
+[30] V. Akbari and C. Brekke, "Iceberg detection in open and ice-infested waters using C-band polarimetric synthetic aperture radar," IEEE Trans. Geosci. Remote Sens., vol. 56, no. 1, pp. 407-421, Jan. 2018.  
+[31] C. A. Baumhoer, A. J. Dietz, C. Kneisel, and C. Kuenzer, "Automated extraction of antarctic glacier and ice shelf fronts from sentinel-1 imagery using deep learning," Remote Sens., vol. 11, no. 21, p. 2529, Jan. 2019.  
+[32] E. Zhang, L. Liu, and L. Huang, "Automatically delineating the calving front of Jakobshavn Isbrae from multitemporal TerraSAR-X images: A deep learning approach," The Cryosphere, vol. 13, no. 6, pp. 1729-1741, Jun. 2019.  
+[33] Y. Mohajerani, M. Wood, I. Velicogna, and E. Rignot, "Detection of glacier calving margins with convolutional neural networks: A case study," Remote Sens., vol. 11, no. 1, p. 74, Jan. 2019.  
+[34] B. W. J. Miles, C. R. Stokes, and S. S. R. Jamieson, "Simultaneous disintegration of outlet glaciers in Porpoise Bay (Wilkes Land), East Antarctica, driven by sea ice break-up," The Cryosphere, vol. 11, no. 1, pp. 427-442, Feb. 2017.  
+[35] Y. Liu, J. C. Moore, X. Cheng, R. M. Gladstone, J. N. Bassis, H. Liu, J. Wen, and F. Hui, "Ocean-driven thinning enhances iceberg calving and retreat of Antarctic ice shelves," Proc. Natl. Acad. Sci., vol. 112, no. 11, pp. 3263-3268, Mar. 2015.  
+[36] M. Schmitt, G. Baier, and X. X. Zhu, "Potential of nonlocally filtered pursuit monostatic TanDEM-X data for coastline detection," ISPRS J. Photogramm. Remote Sens., vol. 148, pp. 130-141, Feb. 2019.  
+[37] X. X. Zhu, D. Tuia, L. Mou, G. Xia, L. Zhang, F. Xu, and F. Fraundorfer, "Deep learning in remote sensing: A comprehensive review and list of resources," IEEE Geosci. Remote Sens. Mag., vol. 5, no. 4, pp. 8-36, 2017.  
+[38] P. Shamsolmoali, M. Zareapoor, R. Wang, H. Zhou, and J. Yang, "A novel deep structure U-Net for sea-land segmentation in remote sensing images," IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 12, no. 9, pp. 3219-3232, Sep. 2019.  
+[39] R. Li, W. Liu, L. Yang, S. Sun, W. Hu, F. Zhang, and W. Li, "DeepUNet: A deep fully convolutional network for pixel-level sea-land segmentation," IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 11, no. 11, pp. 3954–3962, Nov. 2018.  
+[40] Z. Chu, T. Tian, R. Feng, and L. Wang, "Sea-land segmentation with Res-UNet and fully connected CRF," in Proc. 2019 IEEE Int. Geosci. Remote Sens. Symp. (IGARSS), Jul. 2019, pp. 3840-3843.  
+[41] V. Badrinarayanan, A. Kendall, and R. Cipolla, "SegNet: A deep convolutional encoder-decoder architecture for image segmentation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 39, no. 12, pp. 2481-2495, Dec. 2017.  
+[42] O. Ronneberger, P. Fischer, and T. Brox, "U-Net: Convolutional networks for biomedical image segmentation," in Proc. Int. Conf. Med. Image Comput. Comput.-Assist. Intervention. (MICCAI), N. Navab, J. Hornegger, W. M. Wells, and A. F. Frangi, Eds., Oct. 2015, pp. 234-241.  
+[43] Y. Yuan, X. Chen, and J. Wang, "Object-contextual representations for semantic segmentation," in Computer Vision - ECCV 2020, A. Vedaldi,
+
+H. Bischof, T. Brox, and J.-M. Frahm, Eds. Cham: Springer International Publishing, 2020, pp. 173-190.  
+[44] T. Takikawa, D. Acuna, V. Jampani, and S. Fidler, "Gated-scnn: Gated shape CNNs for semantic segmentation," Proc. IEEE CVF Int. Conf. Comput. Vis. ICCV, Oct. 2019.  
+[45] L. G. Roberts, "Machine perception of three-dimensional solids," Ph.D. dissertation, Massachusetts Institute of Technology, 1963.  
+[46] W. K. Pratt, "Edge detection," in Digital Image Processing. John Wiley & Sons, Ltd, 2006, pp. 465-533.  
+[47] J.-S. Lee and I. Jurkevich, "Coastline detection and tracing In SAR images," IEEE Trans. Geosci. Remote Sens., vol. 28, no. 4, pp. 662-668, Jul. 1990.  
+[48] D. Wang and X. Liu, "Coastline extraction from SAR images using robust ridge tracing," Marine Geodesy, vol. 42, no. 3, pp. 286-315, May 2019.  
+[49] M. Modava, G. Akbarizadeh, and M. Soroosh, "Integration of spectral histogram and level set for coastline detection in SAR images," IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 2, pp. 810-819, Apr. 2019.  
+[50] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active contour models,” Int. J. Comput. Vis., vol. 1, no. 4, pp. 321–331, Jan. 1988.  
+[51] T. Klinger, M. Ziems, C. Heipke, H. W. Schenke, and N. Ott, “Antarctic Coastline Detection using Snakes,” *Photogramm. - Fernerkund. - Geoinformation*, vol. 2011, no. 6, pp. 421–434, Dec. 2011.  
+[52] C. Liu, Y. Xiao, and J. Yang, "A coastline detection method in polarimetric SAR images mixing the region-based and edge-based active contour models," IEEE Trans. Geosci. Remote Sens., vol. 55, no. 7, pp. 3735-3747, Jul. 2017.  
+[53] S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations," Journal of Computational Physics, vol. 79, no. 1, pp. 12-49, Nov. 1988.  
+[54] T. Chan and L. Vese, "An active contour model without edges," in Scale-Space Theories in Computer Vision. Springer, Berlin, Heidelberg, Sep. 1999, pp. 141-151.  
+[55] C. Liu, J. Yang, J. Yin, and W. An, "Coastline detection in SAR images using a hierarchical level set segmentation," IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 9, no. 11, pp. 4908-4920, Nov. 2016.  
+[56] M. Modava and G. Akbarizadeh, "A level set based method for coastline detection of SAR images," in 3rd International Conference on Pattern Recognition and Image Analysis (IPRIA). Shahrekord, Iran: IEEE, Apr. 2017, pp. 253-257.  
+[57] S. Xie and Z. Tu, “Holistically-nested edge detection,” in IEEE Int. Conf. Comput. Vis. (ICCV), Dec. 2015, pp. 1395–1403.  
+[58] Y. Liu, M.-M. Cheng, X. Hu, K. Wang, and X. Bai, "Richer convolutional features for edge detection," Proc. 2017 IEEE Conf. Comput. Vis. Pattern Recognit. CVPR, Jul. 2017.  
+[59] X. S. Poma, E. Riba, and A. Sappa, “Dense extreme inception network: Towards a robust CNN model for edge detection,” Proc. IEEE CVF Winter Conf. Appl. Comput. Vis. WACV, Mar. 2020.
+
+[60] D. Cheng, G. Meng, G. Cheng, and C. Pan, “SeNet: Structured edge network for sea-land segmentation,” IEEE Geosci. Remote Sens. Lett., vol. 14, no. 2, p. 5, 2017.  
+[61] Z. Jiang, Z. Chen, K. Ji, and J. Yang, "Semantic segmentation network combined with edge detection for building extraction in remote sensing images," in Int. Symp. Multispect. Image Processing Pattern Recognit. (MIPPR), vol. 11430. International Society for Optics and Photonics, Feb. 2020, p. 114300D.  
+[62] D. Cheng, G. Meng, S. Xiang, and C. Pan, "FusionNet: Edge aware deep convolutional networks for semantic segmentation of remote sensing harbor images," IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 10, no. 12, pp. 5769-5783, Dec. 2017.  
+[63] L.-C. Chen, J. T. Barron, G. Papandreou, K. Murphy, and A. L. Yuille, "Semantic image segmentation with task-specific edge detection using cnns and a discriminatively trained domain transform," Proc. 2016 IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 4545-4554, Jun. 2016.  
+[64] D. Marmanis, K. Schindler, J. D. Wegner, S. Galliani, M. Datcu, and U. Stilla, "Classification with an edge: Improving semantic image segmentation with boundary detection," ISPRS J. Photogramm. Remote Sens., vol. 135, pp. 158-172, Jan. 2018.  
+[65] L.-C. Chen, G. Papandreou, F. Schroff, and H. Adam, “Rethinking atrous convolution for semantic image segmentation,” ArXiv170605587Cs, Dec. 2017.  
+[66] T. Lin, P. Dollar, R. Girshick, K. He, B. Hariharan, and S. Belongie, “Feature pyramid networks for object detection,” Proc. 2017 IEEE Conf. Comput. Vis. Pattern Recognit. CVPR, pp. 936–944, 2017.  
+[67] C.-Y. Lee, S. Xie, P. Gallagher, Z. Zhang, and Z. Tu, “Deeply-supervised nets,” in Int. Conf. Artif. Intell. Stat. (AISTATS), G. Lebanon and S. V. N. Vishwanathan, Eds., vol. 38, May 2015, pp. 562-570.  
+[68] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, "Attention is all you need," Adv. Neural Inf. Process. Syst., vol. 30, p. 11, 2017.  
+[69] X. Wang, R. Girshick, A. Gupta, and K. He, “Non-local neural networks,” Proc. 2018 IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 7794–7803, 2018.  
+[70] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 3rd Int. Conf. Learn. Represent. ICLR, 2015.  
+[71] P. Rizzoli, M. Martone, C. Gonzalez, C. Wecklich, D. Borla Tridon, B. Brautigam, M. Bachmann, D. Schulze, T. Fritz, M. Huber, B. Wessel, G. Krieger, M. Zink, and A. Moreira, "Generation and performance assessment of the global TanDEM-X digital elevation model," ISPRS J. Photogramm. Remote Sens., vol. 132, pp. 119-139, Oct. 2017.  
+[72] W. Luo, Y. Li, R. Urtasun, and R. Zemel, "Understanding the effective receptive field in deep convolutional neural networks," in Int. Conf. Neural Inf. Process. Syst. (NIPS), Dec. 2016, pp. 4905-4913.

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+        "text": "Spatial-Phase Shallow Learning: Rethinking Face Forgery Detection in Frequency Domain",
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+        "text": "Honggu Liu $^{1*}$  Xiaodan Li $^{2}$  Wenbo Zhou $^{1\\dagger}$  Yuefeng Chen $^{2}$",
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+        "text": "Yuan He² Hui Xue² Weiming Zhang† Nenghai Yu¹",
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+        "text": "<sup>1</sup>University of Science and Technology of China <sup>2</sup>Alibaba Group",
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+        "text": "lhg9754@mail.ustc.edu.cn, {welbeckz,zhangwm，ynh}@ustc.edu.cn",
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+        "text": "{fiona.lxd, yuefeng.chenyf, heyuan.hy, hui.xueh}@alibaba-inc.com",
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+        "text": "Abstract",
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+        "text": "The remarkable success in face forgery techniques has received considerable attention in computer vision due to security concerns. We observe that up-sampling is a necessary step of most face forgery techniques, and cumulative up-sampling will result in obvious changes in the frequency domain, especially in the phase spectrum. According to the property of natural images, the phase spectrum preserves abundant frequency components that provide extra information and complement the loss of the amplitude spectrum. To this end, we present a novel Spatial-Phase Shallow Learning (SPSL) method, which combines spatial image and phase spectrum to capture the up-sampling artifacts of face forgery to improve the transferability, for face forgery detection. And we also theoretically analyze the validity of utilizing the phase spectrum. Moreover, we notice that local texture information is more crucial than high-level semantic information for the face forgery detection task. So we reduce the receptive fields by shallowing the network to suppress high-level features and focus on the local region. Extensive experiments show that SPSL can achieve the state-of-the-art performance on cross-datasets evaluation as well as multi-class classification and obtain comparable results on single dataset evaluation.",
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Benefiting from the tremendous success of generative techniques, such as Variational Autoencoders (VAE) [34] and Generative Adversarial Networks (GANs) [15], face forgery has become an emerging hot research topic in very recent years. The face forgery techniques are able to synthesize realistic faces that are indistinguishable for human",
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+        "image_caption": [
+            "Figure 1: The variation analysis in the frequency domain. The curve shows the average value of pixel difference (mean and variance) of the phase spectrum between 1000 origin and up-sampling samples increase dramatically with the increase of the number of up-sampling."
+        ],
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+    {
+        "type": "text",
+        "text": "eyes. However, these forgery techniques are likely to be abused for malicious purposes, causing serious security and ethical issues (e.g. celebrity pornography and political persecution). Therefore, it is of paramount importance to develop more general and practical methods for face forgery detection.",
+        "bbox": [
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+        "type": "text",
+        "text": "To alleviate the risks brought by malicious usage of face forgery, various methods [49, 25, 1, 48, 2, 38, 37, 12, 22, 35, 28, 8, 23] have been proposed. Most of these methods detect face forgery in a supervised fashion with prior knowledge of face manipulation methods [1, 6, 23]. Under this setting, these approaches achieve excellent performance on some public datasets [48, 20, 37, 26, 45]. However, these detection methods tend to suffer from overfitting thus their effectiveness is limited to the datasets which they are specifically trained on. Moreover, in real-world detection, it is inevitable to face a source/target mismatch",
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+        "text": "arXiv:2103.01856v3 [cs.CV] 10 Mar 2021",
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+        "text": "* Work done during the internship of Honggu Liu at Alibaba Group.",
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+        "text": "† Corresponding Author.",
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+        "img_path": "images/54fcf2b0f6ba416e75a2bcff1e35c2060488c2b26707c9a63a700feaf867e97a.jpg",
+        "image_caption": [
+            "Figure 2: The frequency domain analysis of the origin and up-sampling face. The residual images show that the differences of phase spectrum between origin and upsampling are bigger than the amplitude spectrum with the up-sampling. Best viewed in color. (Darker color indicates smaller pixel values)."
+        ],
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+        "type": "text",
+        "text": "problem when handling unseen samples, which is extremely challenging for deepfake detection task. Therefore, it is necessary to enhance the generalization and transferability of forgery detection techniques. Recently, some approaches [10, 22, 28, 46] have made attempts to improve the transferability, there are still deficiencies. For example, two-branch [28] achieves the state-of-the-art performance of cross-dataset detection at the expense of frame-level detection accuracy. Face X-ray [22] starts from a novel perspective that aims at detecting the blending boundary artifacts and obtains perfect performances in detecting unseen forgery method for raw videos, which significantly improves transferability of different manipulation methods [9, 43, 13, 42]. However, since only focus on the information extracted from the spatial domain, it is easily to be influenced by video compression. Thus, we need to concern about the more common artifacts in the generation of forgery images from various domains.",
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+        "text": "We obverse that up-sampling is a non-negligible step in generative models (e.g. VAE [34], GANs [15]), from which the generated part are then used to synthesize fake faces. This operation usually leaves a trace in the frequency domain, which provides cues for separating synthesized faces from real ones. Though [11] also tried to detect these artifacts with the amplitude spectrum, the performance is limited due to the information loss.",
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+        "text": "To this end, we propose Spatial-Phase Shallow Learning (SPSL) for face forgery detection, which leverages the phase spectrum for detecting the common artifacts. The pivotal thought is that the phase spectrum is more hypersensitive to up-sampling than the amplitude spectrum. As shown in Figure 1, with more times of up-sampling oper",
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+    {
+        "type": "text",
+        "text": "ations are performed, the average pixel differences of the phase spectrum get much greater than that of the amplitude spectrum. A visualization comparison can also be found in Figure 2.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Moreover, [5] used the patch-based classification to generalize the image forensics. Thus, we hold the opinion that local texture information is more important than high-level semantic information even high-level semantic information should be suppressed to a certain extent in the specific task of forged face detection. For this purpose, SPSL drops many convolutional layers to reduce the receptive field [3] and forces CNNs to pay more attention to local regions which are abundant in textures and lack high-level semantic information.",
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+        "type": "text",
+        "text": "As a result, SPSL focuses on the common step in the forged faces generation and pays more attention to textures leading to a performance improvement of the cross-datasets evaluation. At the same time, the performance on multiclass classification also improves due to the specific traces of different categories manipulation are left in the phase spectrum.",
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+        "text": "Extensive experiments demonstrate that SPSL significantly improved the transferability and achieved the state-of-the-art over cross-dataset evaluation.",
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+        "type": "text",
+        "text": "The major contributions in this paper are summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We firstly leverage the phase spectrum to detect forged face images and demonstrate that CNNs can capture extra implicit features of the phase spectrum which are beneficial to face forgery detection with precise mathematical derivation.",
+            "- Aiming at the specific problem of forged face detection, we assume that high-level semantic information should be appropriately suppressed. And we experimentally validate the hypothesis by decreasing the receptive field of CNNs with shallow network learning.",
+            "- We verify that our approach achieves the state-of-the-art performance of forged face detection over cross-dataset evaluation."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since face manipulation is a classical research topic [43, 33, 32, 21, 17, 42] in computer vision, verifying its authenticity is not a new problem. However, recent remarkable successes of deep learning make face manipulation easier and more realistic which poses a significant challenge of forged face detection. In this section, we briefly review the current face forgery detection methods that are representative and related to our work.",
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+        "text": "2",
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+    {
+        "type": "text",
+        "text": "2.1. Spatial-based Face forgery Detection",
+        "text_level": 1,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "With the development of face forgery, a wide variety of methods have been proposed to detect forged face. The majority of them exploit artifacts based on the spatial domain, especially in RGB. Some methods for deepfake detection focus on hand-crafted facial features from the video, such as eye blinking [24], inconsistent head poses [48], facial expression change [2]. Recent methods [1, 31, 37] capture high-level features from the spatial domain by using deep neural networks and show impressive performance. Nguyen et al. proposed a method [31] which leveraging capsule network [39] to detect face manipulation. Rossler et al. [37] show the best performance on many kinds of forgery algorithms with the efficient XceptionNet [6] at that time. Face X-ray [22] mainly focuses on the blending step which exists in most face forgery and thus achieved state-of-the-art performance on transferability in raw videos. However, it still has some limitations that the performance of Face X-ray will sharply drop when encounter low-resolution images, and it may not work with entirely synthesized images. Almost all of these CNN-based methods only use spatial domain information and therefore the performance is quite sensitive to the quality or data distribution of datasets. In our work, we combine the spatial domain with the frequency domain to take advantage of both.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Frequency-based Face forgery Detection",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Besides focusing on the spatial domain, some methods pay attention to the frequency domain for capturing artifacts of the forgery. In fact, frequency analysis is a common and important way in digital image processing and has been widely applied to various tasks in computer vision [44, 47, 41, 18]. Most of them use either Discrete Fourier Transform (DFT) or Wavelet Transform (WT), or Discrete Cosine Transform (DCT) to convert the spatial image to the frequency domain. Durall et al. [12] first proposed that averaging the amplitude of each frequency band with DFT can mine abnormal information of forgery in face manipulation detection.  $\\mathrm{F}^3$ -Net [35] extracted frequency-domain information using DCT and analyzed the statistic features for face forgery detection.  $\\mathrm{F}^3$ -Net achieved state-of-the-art performance on highly compressed videos, but the performance on cross-dataset evaluation drops greatly. Masi et al. [28] leverage a Laplacian of Gaussian (LoG) to make frequency enhancement for purpose of suppressing the image content present in the low-level feature maps. However, most of these related works mainly depend on low-level statistical features rather than high-level features extracted by CNNs, and therefore the frequency information was inadequately utilized. In our work, given the powerful capabilities of feature extraction of CNNs, we make use of the phase spectrum in DFT and explicitly prove the validity with theory analysis while we integrate it into the",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7a1a0058c513297622d390c098559e6d29e9a2ba888190d47cd83d2627641e3a.jpg",
+        "image_caption": [
+            "Figure 3: Overview of typical face manipulation pipeline. Most of the previous works only focus on forged faces, while we focus on both up-sampling and forged faces."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "whole learning process of CNNs.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. SPSL for Face Forgery Detection",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "In this section, we start by introducing the key observation of face forgery generation. Then we propose spatial-phase shallow learning to detect the observed common artifacts for face forgery detection. Finally, Making the network shallow can focus on the local region to further boost the improvement of transferability.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.1. Motivation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 3, a typical facial manipulation method consists of three stages [9]: 1) encoding source face; 2) swapping face in latent space; 3) decoding target face.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Up-sampling is a vital step for decoding the target face, based on either AutoEncoders [34] or GANs [15]. Thus, we leverage the phase information to detect up-sampling artifacts. For applying phase information to CNNs, we reconstruct the spatial domain representation of the phase spectrum from the frequency domain (i.e. IDFT with the frequency spectrum without amplitude). Finally, we concatenate the spatial domain representation of the phase spectrum with the RGB image in the channel, which results in an RGBP 4-channel image.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Capturing up-sampling artifacts via phase spectrum in face forgery",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To detect the observed common artifacts, namely upsampling, we analyze it in the frequency domain.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Up-sampling will lead to the emergence of new frequency components. And we make a claim as follows",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Claim 1. Phase spectrum is more sensitive to up-sampling artifacts and therefore helps face forgery detection.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To simplify the calculation, we make all the mathematical derivation based on the 1D signal. We first set up the basic notations used in this paper:  $x(n)$  and  $\\mathbf{X}(u)$  denote a 1D discrete signal and its Discrete Fourier Transform(DFT), where  $n$  is the spatial location of the signal and  $u$  represents the frequency.  $\\mathbf{A}(u)$  is the amplitude spectrum and  $\\mathbf{P}(u)$  is the phase spectrum. And we use  $c(n)$  and  $\\mathbf{C}(n)$  to denote the convolution kernel and its DFT representation. And we use  $*$  to denote convolutional operation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proof. The increase of spatial resolution in 2D corresponds to the extension of the time domain in 1D. Assume that the input  $x(n)$  is up-sampled by factor 2, then",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {x} (n) = \\left\\{ \\begin{array}{l l} x (\\frac {1}{2} n), & n = 2 k \\\\ 0, & n = 2 k + 1 \\end{array} \\right. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $k = 0,1,2,\\dots ,N - 1$  , and",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {X}} (u) = \\frac {1}{2 N} \\sum_ {n = 0} ^ {2 N - 1} \\hat {x} (n) e ^ {- j \\frac {2 \\pi u n}{2 N}} \\\\ = \\frac {1}{2 N} \\sum_ {n = 0} ^ {N - 1} \\hat {x} (2 n) e ^ {- j \\frac {2 \\pi u 2 n}{2 N}} \\tag {2} \\\\ = \\frac {1}{2 N} \\sum_ {n = 0} ^ {N - 1} x (n) e ^ {- j \\frac {2 \\pi 2 u n}{N}} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The we have  $\\hat{x}(n) = x\\left(\\frac{1}{2} n\\right) \\Leftrightarrow \\hat{\\mathbf{X}}(u) = \\mathbf{X}(2u)$  with the Eq. 2, which leads to the conclusion that the increase of spatial resolution will result in the compression in the frequency domain which is consistent with the property of Fourier Transform (FT). In fact, the essence of DFT is the principle value interval of Discrete Fourier Series (DFS) and thus new frequency components are the duplicate of origin frequency components.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Base on our inference that phase spectrum will keep more frequency components that tend to zero in amplitude spectrum, which is dually proved in the Appendix 1.1. We first assume the amplitude spectrum  $\\mathbf{X}_{\\mathbf{A}}(u)$  and the phase spectrum  $\\mathbf{X}_{\\mathbf{P}}(u)$  of original images  $x(n)$ . It is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {X} _ {A} (u) = \\underbrace {a _ {0} + a _ {1} e ^ {j \\theta_ {1}} + \\cdots + a _ {k} e ^ {j \\theta_ {k}}} _ {\\substack {(k + 1) \\text {items}}} \\tag{3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {X} _ {P} (u) = \\underbrace {p _ {0} + p _ {1} e ^ {j \\theta_ {1}} + \\cdots + p _ {N - 1} e ^ {j \\theta_ {N - 1}}} _ {N \\text {i t e m s}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and the corresponding up-sampling is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {X} _ {A} ^ {u p} (u) = \\underbrace {a _ {0} + \\cdots + a _ {k} e ^ {j \\theta_ {k}}} _ {(k + 1) \\text {i t e m s}} + \\underbrace {a _ {N} e ^ {j \\theta_ {N}} + \\cdots + a _ {N + k} e ^ {j \\theta_ {N + k}}} _ {(k + 1) \\text {i t e m s}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {X} _ {P} ^ {u p} (u) = \\underbrace {p _ {0} + p _ {1} e ^ {j \\theta_ {1}} + \\cdots + p _ {2 N - 1} e ^ {j \\theta_ {2 N - 1}}} _ {2 N \\text {i t e m s}} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We define that  $y_A(n)$  is the output of a convolution layer with an input  $x(n)$  and its frequency domain form is  $\\mathbf{Y}_{\\mathbf{A}}(u)$ . And we get",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} y _ {A} (n) = x (n) * c (n) \\\\ \\Updownarrow \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Y} _ {A} (u) = \\mathbf {X} _ {\\mathbf {A}} (u) \\cdot \\mathbf {C} (u)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "According to the deduction that the phase spectrum helps CNNs acquire and learn more abundant frequency components which are ignored with convolution calculations of amplitude spectrum proved in Appendix 1.2, we can deduce the frequency domain form is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Y} _ {A} (u) = \\underbrace {f _ {0} + f _ {1} e ^ {j \\theta_ {1}} + \\cdots + f _ {k + N - 1} e ^ {j \\theta_ {k + N - 1}}} _ {k + N \\text {i t e m s}} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Y} _ {A} ^ {u p} (u) = \\underbrace {f _ {0} + f _ {1} e ^ {j \\theta_ {1}} + \\cdots + f _ {2 N + k - 1} e ^ {j \\theta_ {2 N + k - 1}}} _ {2 N \\text {i t e m s}} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our work, we first take Inverse Discrete Fourier Transform (IDFT) to phase spectrum and acquire the spatial domain form  $p(n)$  of phase. And we state a theorem named the distributive law as follow,",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Theorem 1.  $(f(\\cdot) + g(\\cdot)) * h(\\cdot) = f(\\cdot) * h(\\cdot) + g(\\cdot) * h(\\cdot)$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Then we consider that we directly concatenate  $x(n)$  and  $p(n)$  in channel dimension based on theorem 1 and the output  $\\mathbf{Y}_{A + P}(u)$  is",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Y} _ {A + P} (u) = \\underbrace {f _ {0} + f _ {1} e ^ {j \\theta_ {1}} + \\cdots + f _ {2 N - 2} e ^ {j \\theta_ {2 N - 2}}} _ {2 N - 1 \\text {i t e m s}} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Y} _ {A + P} ^ {u p} (u) = \\underbrace {f _ {0} + f _ {1} e ^ {j \\theta_ {1}} + \\cdots + f _ {3 N - 2} e ^ {j \\theta_ {3 N - 2}}} _ {3 N - 1 \\text {i t e m s}} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, the number of learnable frequency components is  $N$  when we leverage the original image and its phase together, but the number just is  $N - k$  with the utilization of the original image alone. Therefore, it is clear that the difference between  $\\mathbf{Y}_{A + P}(u)$  and  $\\mathbf{Y}_{A + P}^{up}(u)$  is bigger than  $\\mathbf{Y}_A(u)$  and  $\\mathbf{Y}_A^{up}(u)$ . In particular, the value of  $k$  is usually small in nature images and thus our method observably improves the performance on the detection of face forgery. Thus, we conclude that the introduction of the phase spectrum helps capture more frequency artifacts caused by cumulative up-sampling in deepfake video generation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Suppressing the semantic information and focusing on local region",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We consider that the pivotal distinction between pristine face and forged face is local low-level features(e.g. textures, colors) instead of global high-level semantic features(e.g.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/cf5e566dd90665d936831f4e654ef68034a9773f8e70de219b616a2f90bd35c9.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Quantitative results (ACC  $(\\%)$  and AUC  $(\\%)$ ) on FaceForensics++ dataset with high-quality (light compression) and low quality (heavy compression) settings. The bold results are the best."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">HQ</td><td colspan=\"2\">LQ</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>Steg. Features [14]</td><td>70.97</td><td>-</td><td>55.98</td><td>-</td></tr><tr><td>Cozzolino et al. [7]</td><td>78.45</td><td>-</td><td>58.69</td><td>-</td></tr><tr><td>Bayer &amp; Stamm [4]</td><td>82.97</td><td>-</td><td>66.84</td><td>-</td></tr><tr><td>Rahmouni et al. [36]</td><td>79.08</td><td>-</td><td>61.18</td><td>-</td></tr><tr><td>MesoNet [1]</td><td>83.10</td><td>-</td><td>70.47</td><td>-</td></tr><tr><td>Face X-ray [22]</td><td>-</td><td>87.35</td><td>-</td><td>61.60</td></tr><tr><td>Xception [6]</td><td>92.39</td><td>94.86</td><td>80.32</td><td>81.76</td></tr><tr><td>Ours(Xception)</td><td>91.50</td><td>95.32</td><td>81.57</td><td>82.82</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "face, human). Because most of these semantic features are shared in both pristine and forged faces, extensive high-level semantic information more or less has a negative effect on forged face detection as it contains many common characteristics of pristine and forged face images. For the purpose of suppressing high-level semantic features and extracting more texture features, we straightforwardly shallow the neural network by throwing away many convolutional layers or blocks. Then we demonstrate that shallow networks are more transferable and efficient simultaneously.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce the overall experimental settings and then present extensive experimental results to demonstrate the superiority of our approach.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental settings",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Following recent related works [35, 28, 22, 23] of face forgery detection, we conduct our experiments on the two benchmark public deepfake datasets: FaceForensics++(FF++) [37] and Celeb-DF [26]. Both of them are large-scale and contain pristine and manipulated videos of human faces. FF++ consists of four kinds of common face manipulation methods [9, 43, 13, 42]. Celeb-DF is in general the most challenging to the current detection methods, and their overall performance on Celeb-DF is lowest across all datasets.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. In our experiments, we mainly utilize the Accuracy rate (ACC) and the Area Under Receiver Operating Characteristic Curve (AUC) as our evaluation metrics. (1) ACC. Accuracy rate is the most intuitive metric in face forgery detection. It is also applied to  $\\mathrm{FF} + +$  [37] and thus we use ACC as the major evaluation metric in the experiment. (2) AUC. Following the Celeb-DF [26] and Two-branch [28], we use AUC as another evaluation metric to evaluate the performance on cross-dataset. Besides, we",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "use the recall rate as our multi-class classification evaluation metric.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation and Hyper-Parameters. In our experiments, we use Xception [6] as the backbone of our approach. For the purpose of reducing receptive fields, we just retain the Xception Block 1-3 and Xception Block 12. The final spatial form of our phase spectrum is the IDFT of the absolute value of the pristine phase spectrum. We optimize the networks by Adam optimizer [19]. The initial learning rate  $lr = 2 \\times 10^{-3}$  and it drops to half of itself every time the validation loss does not decrease after 5 full epochs.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison with previous methods",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our method with previous deepfake detection methods. We train all models on only FF++ [37] and respectively evaluate them on FF++ in Section 4.2.1 and Celeb-DF in Section 4.2.2.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2.1 Comparable results on  $\\mathbf{FF} + +$",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our method with previous deepfake detection methods on FF++ [37]. Although our primary purpose is to improve the generalization and transferability, we also obtain comparable results in FF++ [37]. We first evaluate our methods on different video compression settings including high quality (HQ (c23)) and low quality (LQ (c40)). As the results shown in Table 1, the proposed method outperforms or is on par with baseline in both ACC and AUC with LQ settings. Low-quality videos have been highly compressed and many frequency components are weakened. The improvement of performance mainly benefits from the extra phase information captured by CNNs, which keeps more frequency components than plain RGB-based images. At the same time, we also obtain comparable results with HQ settings.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we also evaluate our approach on different face manipulation methods in  $\\mathrm{FF}++$  [37]. The results are demonstrated in Table 2. We train and test our models exactly on low-quality videos for each manipulation methods. We also reproduced the results of MesoNet [1] and Xception [6], and other results are directly cited from [37]. In general, basic experiments also show comparable results with previous methods though the transferability is the main purpose of SPSL.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.2 Cross-dataset evaluation on Celeb-DF",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we evaluate the transferability of our method given that it is trained on  $\\mathrm{FF}++$  with multiple manipulations but tested on Celeb-DF. We first verify that most of the previous methods show a drastic performance drop on the cross-dataset evaluation. Table 3 shows the AUC comparison with some recent methods for face forgery detection. Our method obtains the state-of-the-art AUC on Celeb-DF",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/84581e6f2a7cf5f06955c045dae5496532e12f50119764626a3a44518907033b.jpg",
+        "image_caption": [
+            "Figure 4: Visualization of various manipulation methods and our spatial domain representations of the phase spectrum in  $\\mathrm{FF}++$  [37]. Each image and phase spectrum is the average of all frames of a video. Every manipulation method tends to be a specific pattern in the phase spectrum while it is not obvious in the RGB domain. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            112,
+            87,
+            859,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/c1645057dbe18b82ff6deac8160b0499e58c6d7a97ab38d2021cdf68d0b23fe5.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">DF [9]</td><td colspan=\"2\">F2F [43]</td><td colspan=\"2\">FS [13]</td><td colspan=\"2\">NT [42]</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>Steg. Features [14]</td><td>73.64</td><td>-</td><td>73.72</td><td>-</td><td>68.93</td><td>-</td><td>63.33</td><td>-</td></tr><tr><td>Cozzolino et al. [7]</td><td>85.45</td><td>-</td><td>67.88</td><td>-</td><td>73.79</td><td>-</td><td>78.00</td><td>-</td></tr><tr><td>Rahmouni et al. [36]</td><td>85.45</td><td>-</td><td>64.23</td><td>-</td><td>56.31</td><td>-</td><td>60.07</td><td>-</td></tr><tr><td>Bayar and Stamm [4]</td><td>84.55</td><td>-</td><td>73.72</td><td>-</td><td>82.52</td><td>-</td><td>70.67</td><td>-</td></tr><tr><td>MesoNet [1]</td><td>87.27</td><td>-</td><td>56.20</td><td>-</td><td>61.17</td><td>-</td><td>40.67</td><td>-</td></tr><tr><td>XceptionNet [6]</td><td>95.15</td><td>99.08</td><td>83.48</td><td>93.77</td><td>92.09</td><td>97.42</td><td>77.89</td><td>84.23</td></tr><tr><td>Ours(Xception)</td><td>93.48</td><td>98.50</td><td>86.02</td><td>94.62</td><td>92.26</td><td>98.10</td><td>76.78</td><td>80.49</td></tr></table>",
+        "bbox": [
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+            683
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Quantitative results (ACC (%) and AUC (%)) on FaceForensics++ dataset with four different manipulation methods, i.e. DeepFakes(DF) [9], Face2Face(F2F) [43], FaceSwap(FS) [13], NeuralTextures(NT) [42]. The bold results are best.",
+        "bbox": [
+            75,
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+            726
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "while still having a good performance on  $\\mathrm{FF}++$  compared with all the other methods. The performance gains mainly benefit from the extra appreciable frequency components of the phase spectrum, which are enhanced many times in the cumulative up-sampling, and thus the differences of frequency components perceptible by convolutional kernel between pristine images and forgery become more striking. Therefore, the proposed SPSL is capable of detecting common artifacts.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Multi-class classification evaluation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We furthermore evaluate the proposed SPSL on multiclass classification with different face manipulation methods list in  $\\mathrm{FF} + +$  [37] in this section. The models are trained and tested on  $\\mathrm{FF} + +$  with five types of labels, and multiclass classification is more challenging and significant than binary classification. The results are shown in Table 4 by the way of recall rate. With all three kinds of compression setting, the proposed SPSL completely surpasses the orig-",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/04149349fe44f39199ab747861e8824d2c51628b1abc8276df8e3621701e31b6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>FF++ [37]</td><td>Celeb-DF [26]</td></tr><tr><td>Two-stream [49]</td><td>70.10</td><td>53.80</td></tr><tr><td>Meso4 [1]</td><td>84.70</td><td>54.80</td></tr><tr><td>MesoInception4 [1]</td><td>83.00</td><td>53.60</td></tr><tr><td>HeadPose [48]</td><td>47.30</td><td>54.60</td></tr><tr><td>FWA [25]</td><td>80.10</td><td>56.90</td></tr><tr><td>VA-MLP [29]</td><td>66.40</td><td>55.00</td></tr><tr><td>VA-LogReg</td><td>78.00</td><td>55.10</td></tr><tr><td>Xception-c40 [37]</td><td>95.50</td><td>65.50</td></tr><tr><td>Multi-task [30]</td><td>76.30</td><td>54.30</td></tr><tr><td>Capsule [31]</td><td>96.60</td><td>57.50</td></tr><tr><td>DSP-FWA [25]</td><td>93.00</td><td>64.60</td></tr><tr><td>SMIL [23]</td><td>96.80</td><td>56.30</td></tr><tr><td>Two-branch [28]</td><td>93.20</td><td>73.40</td></tr><tr><td>F3-Net [35]</td><td>97.97</td><td>65.17</td></tr><tr><td>SPSL(Xception)</td><td>96.91</td><td>76.88</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "inal XceptionNet method. Furthermore, we also show the t-SNE [27] feature spaces of data in FF++ high quality with the multi-class classification task, by the Xception and our SPSL, as shown in Figure 5. Xception is more likely to confuse pristine faces with NeuralTextures-based fake faces because this manipulation method modifies very limited pixels in the spatial domain, as shown in Figure 5(a). Conversely, the proposed SPSL can split up all classes in the embedding feature spaces, as shown in Figure 5(b). These improvements may benefit from the salient difference of phase spectrum among various manipulation methods and we show the average phase spectrum in the spatial domain of every frame of a video in Figure 4. For all four kinds of manipulation methods in FF++ [37], the spatial images of the phase spectrum show distinguishing results for each method. In particular, NeuralTextures-based images, which just slightly tampered with lip, are very similar to pristine images causing almost indistinguishable in the RGB domain but the spatial images of the phase spectrum are still separable.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1. Effectiveness of Phase spectrum and Shallow network",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the effectiveness of both Phase spectrum and Shallow network, we first respectively evaluate one of",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/f05819acbd24f00696e0d99f73e6da009a3d3046d1dd4f0f9e068c9e6780e1e7.jpg",
+        "table_caption": [
+            "Table 3: Cross-dataset evaluation (AUC (\\%)) on Celeb-DF. Best competing methods on Celeb-DF are reported. Our method obtains the state-of-the-art performance on cross-dataset evaluation. At the same time, our method still performs well when tested on just deepfake class(96.91%) AUC on  $\\mathrm{FF}++$ . Results for some other methods are from [26], and the bold results are the best."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>DF</td><td>F2F</td><td>FS</td><td>NT</td><td>ORG</td></tr><tr><td>MesoIncep4 [1]</td><td>94.81</td><td>43.32</td><td>73.24</td><td>40.39</td><td>85.16</td></tr><tr><td>Xception-c0 [6]</td><td>97.84</td><td>96.68</td><td>96.84</td><td>87.67</td><td>98.03</td></tr><tr><td>SPSL (Xception-c0)</td><td>99.05</td><td>97.20</td><td>97.63</td><td>91.40</td><td>98.25</td></tr><tr><td>Xception-c23 [6]</td><td>88.00</td><td>88.61</td><td>87.07</td><td>74.83</td><td>75.52</td></tr><tr><td>SPSL (Xception-c23)</td><td>94.18</td><td>93.59</td><td>95.62</td><td>81.72</td><td>88.72</td></tr><tr><td>Xception-c40 [6]</td><td>86.61</td><td>78.88</td><td>83.16</td><td>52.94</td><td>75.55</td></tr><tr><td>SPSL (Xception-c40)</td><td>91.16</td><td>78.31</td><td>88.75</td><td>58.97</td><td>77.49</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4: The recall rate (\\%) of origin and each manipulation method with Raw (c0), HQ (c23) and LQ (c40) settings in our multi-class classification.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0af2e2153f67d78a188af9d4f751d5f98485e69c47e2ebbafcb309af873623d7.jpg",
+        "image_caption": [
+            "(a) Baseline",
+            "Figure 5: The t-SNE feature spaces visualization of the basic Xception (a) and SPSL (b) on FaceForensics++ [37] high quality (HQ) in the multi-class classification task. Red color dots represent pristine images, and rest colors respectively indicate the different manipulation methods. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0c0539663d7d643f6ed0628478b97e1147cbb927bef845e47a3f4d216e626e99.jpg",
+        "image_caption": [
+            "(b) SPSL"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            699,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "them with baseline and combine them finally. All models are trained on  $\\mathrm{FF} + +$  [37] and tested on Celeb-DF [26]. The results are listed in Table 5. Compared with model 1(baseline Xception), model 2(Xception with phase spectrum) and model 3 (shallow Xception) improve the AUC scores of Celeb-DF. The transferability has a great improvement with both of them. When combining phase spectrum and shallow network, SPSL gets the best performance and the AUC score increase by about  $13\\%$ . Furthermore, to demonstrate the effectiveness of the proposed SPSL better, we respectively visualize the Gradient-weighted Class Activation Mapping(Grad-CAM) [40] of the baseline and SPSL,",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6382da54e4edf0a2ac9443702d0e5e3451ec66ac331e0df66fa5f922ad8dd084.jpg",
+        "image_caption": [
+            "Real"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            157
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/42615e4a4ec39e5a804cad9166b0be58a2c845b6a4ee51bb7e9401693098c7e6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/8cfaff0f2a74ea8a66018965b2ea9b4b8234e5574210fdd3ec4dad46d28e19b6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a6919b981adaed6b58a9471cefc66917418462a01711965455e9b99e20d6025.jpg",
+        "image_caption": [
+            "Fake",
+            "DF",
+            "Figure 6: The Grad-CAM of the baseline Xception and the proposed SPSL, including two different manipulation methods in FF++ [37] and another Celeb-DF [26] datasets. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
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+        "img_path": "images/c8a093422922128dac2765b911d31c571e81353dd1b30bf9e0a0f59aa436f43c.jpg",
+        "image_caption": [
+            "Baseline"
+        ],
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+    {
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+        "img_path": "images/c8324fcefe48c8231621fc347cdd9212545c406645a0131741d8744b8567236a.jpg",
+        "image_caption": [
+            "FS"
+        ],
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+        "img_path": "images/44292f043a799dcd0d226384615b71ffd305b5e930083e4fd4caf1929333b033.jpg",
+        "image_caption": [
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+        "image_caption": [
+            "SPSL"
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+    {
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+    {
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+        "img_path": "images/abc6d002506aa72dd75b2f6a46ccab95068977870c224567a78cf54c9f7b8a66.jpg",
+        "image_caption": [
+            "Celeb-DF"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "image",
+        "img_path": "images/d5c7b491700cb7143520a95e6334fcb52b1dc0e13956aa82e3f7b3b509b62106.jpg",
+        "image_caption": [
+            "Baseline"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b22d73de76d9d7b8a00500c12e8b4b725572b91e85d1b362ce25e508954ee1d7.jpg",
+        "image_caption": [
+            "SPSL"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "as shown in Figure 6. The Grad-CAM indicates that the proposed SPSL prefers to focus on more microcosmic regions while the baseline model pays more attention to global information, and this phenomenon also accords with our motivation. Furthermore, we demonstrate the correlation analysis between the performance and the number of convolution layers of various backbone networks in Appendix 2.",
+        "bbox": [
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ID</td><td>Phase</td><td>Shallow</td><td>Celeb-DF [26]</td></tr><tr><td>1</td><td>-</td><td>-</td><td>59.98</td></tr><tr><td>2</td><td>√</td><td>-</td><td>69.01</td></tr><tr><td>3</td><td>-</td><td>√</td><td>66.74</td></tr><tr><td>4</td><td>√</td><td>√</td><td>72.39</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Ablation study of the proposed SPSL. These models are trained on  $\\mathrm{FF}++$  with high quality(HQ) settings and tested on Celeb-DF (AUC  $(\\%)$ ). We compare SPSL and its variants by removing phase spectrum and shallow operation step by step.",
+        "bbox": [
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+            513,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2. Universality of SPSL with Various Backbones",
+        "text_level": 1,
+        "bbox": [
+            76,
+            608,
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+        ],
+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "All the above-mentioned experiments are based on XceptionNet [6], and thus we also evaluate the universality of SPSL with two types of ResNet [16]. For both ResNet34 and ResNet50, we directly halve the residual block to shallow networks. The results listed in Table 6 demonstrate that the proposed SPSL is a general framework for various backbones.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Limitations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Even if we have demonstrated the effectiveness of the proposed SPSL and achieved satisfactory performance on cross-dataset evaluation and multi-class classification, we are aware that there exist some limitations of our work.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our method depends on the existence of up-sampling in forged face generation. Thus, the performance may drop if the forgery face is not produced by methods based on generative models. Besides, our method also suffers from a",
+        "bbox": [
+            75,
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/feef038b097dc053f47054fba2dd5769e9ef570ef391f0b48deacd516e8623f3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"2\">FF++ [37]</td><td colspan=\"2\">Celeb-DF [26]</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>ResNet-34</td><td>71.55</td><td>81.58</td><td>65.19</td><td>66.90</td></tr><tr><td>SPSL (ResNet-34)</td><td>83.24</td><td>89.26</td><td>66.79</td><td>71.78</td></tr><tr><td>ResNet-50</td><td>81.83</td><td>83.51</td><td>69.40</td><td>70.05</td></tr><tr><td>SPSL (ResNet-50)</td><td>86.64</td><td>91.04</td><td>68.28</td><td>73.09</td></tr></table>",
+        "bbox": [
+            532,
+            296,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6: The results (ACC (\\%) and AUC (\\%)) on FF++ [37] and cross-dataset evaluation on Celeb-DF [26] of two different backbones with the proposed SPSL.",
+        "bbox": [
+            498,
+            469,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "transferability drop when encountering an entirely different type of face forgery manipulation. For instance, the model trained on identity swap datasets may fail to detect forgery faces whose expressions are swapped. This is expected since manipulations from different categories can leave a specific trace in the phase spectrum as shown in Figure 4, this is also the reason why our method makes a remarkable improvement of multi-class classification.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            664,
+            617,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel face forgery detection method, SPSL, which takes advantage of both spatial and frequency information. The core competence of SPSL is that phase spectrum contains more abundant appreciable frequency components and these components will be duplicated in the process of up-sampling which is the necessary step of forged face generation. Besides, SPSL forces the network to focus on the local microcosmic region and suppress global semantic information for more robustness. We perform a meticulous mathematical derivation to prove the rationality of the proposed SPSL, and extensive experiments demonstrate that the SPSL has an excellent performance on the face forgery detection, especially in the challenging cross-dataset evaluation task.",
+        "bbox": [
+            496,
+            689,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
+            478,
+            924,
+            488,
+            935
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. In 2018 IEEE International Workshop on Information Forensics and Security (WIFS), pages 1-7. IEEE, 2018. 1, 3, 5, 6, 7",
+            "[2] Shruti Agarwal, Hany Farid, Yuming Gu, Mingming He, Koki Nagano, and Hao Li. Protecting world leaders against deep fakes. In CVPR Workshops, pages 38-45, 2019. 1, 3",
+            "[3] André Araujo, Wade Norris, and Jack Sim. Computing receptive fields of convolutional neural networks. Distill, 2019. https://distill.pub/2019/computing-receptive-fields. 2",
+            "[4] Belhassen Bayar and Matthew C Stamm. A deep learning approach to universal image manipulation detection using a new convolutional layer. In Proceedings of the 4th ACM Workshop on Information Hiding and Multimedia Security, pages 5-10, 2016. 5, 6",
+            "[5] Lucy Chai, David Bau, Ser-Nam Lim, and Phillip Isola. What makes fake images detectable? understanding properties that generalize. arXiv preprint arXiv:2008.10588, 2020. 2",
+            "[6] Francois Chollet. Xception: Deep learning with depthwise separable convolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017. 1, 3, 5, 6, 7, 8",
+            "[7] Davide Cozzolino, Giovanni Poggi, and Luisa Verdoliva. Recasting residual-based local descriptors as convolutional neural networks: an application to image forgery detection. In Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, pages 159-164, 2017. 5, 6",
+            "[8] Hao Dang, Feng Liu, Joel Stehouwer, Xiaoming Liu, and Anil K Jain. On the detection of digital face manipulation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5781-5790, 2020. 1",
+            "[9] DeepFakes. Deepfakes github. http://github.com/deepfakes/faceswap, 2017. Accessed 2020-08-18. 2, 3, 5, 6",
+            "[10] Mengnan Du, Shiva Pentyala, Yuening Li, and Xia Hu. Towards generalizable forgery detection with locality-aware autoencoder. arXiv preprint arXiv:1909.05999, 2019. 2",
+            "[11] Ricard Durall, Margret Keuper, and Janis Keuper. Watch your up-convolution: Cnn based generative deep neural networks are failing to reproduce spectral distributions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7890–7899, 2020. 2",
+            "[12] Ricard Durall, Margret Keuper, Franz-Josef Pfreundt, and Janis Keuper. Unmasking deepfakes with simple features. arXiv preprint arXiv:1911.00686, 2019. 1, 3",
+            "[13] FaceSwap. Faceswap github. https://github.com/MarekKowalski/FaceSwap, 2016. Accessed 2020-08-18. 2,5,6",
+            "[14] Jessica Fridrich and Jan Kodovsky. Rich models for steganalysis of digital images. IEEE Transactions on Information Forensics and Security, 7(3):868-882, 2012. 5, 6",
+            "[15] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and"
+        ],
+        "bbox": [
+            78,
+            114,
+            470,
+            901
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pages 2672-2680, 2014. 1, 2, 3",
+            "[16] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 8",
+            "[17] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4401-4410, 2019. 2",
+            "[18] Gahyun Kim, Sungmin Eum, Jae Kyu Suhr, Dong Ik Kim, Kang Ryoung Park, and Jaihie Kim. Face liveness detection based on texture and frequency analyses. In 2012 5th IAPR international conference on biometrics (ICB), pages 67-72. IEEE, 2012. 3",
+            "[19] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.5",
+            "[20] Pavel Korshunov and Sébastien Marcel. Deepfakes: a new threat to face recognition? assessment and detection. arXiv preprint arXiv:1812.08685, 2018. 1",
+            "[21] Iryna Korshunova, Wenzhe Shi, Joni Dambre, and Lucas Theis. Fast face-swap using convolutional neural networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 3677-3685, 2017. 2",
+            "[22] Lingzhi Li, Jianmin Bao, Ting Zhang, Hao Yang, Dong Chen, Fang Wen, and Baining Guo. Face x-ray for more general face forgery detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5001-5010, 2020. 1, 2, 3, 5",
+            "[23] Xiaodan Li, Yining Lang, Yuefeng Chen, Xiaofeng Mao, Yuan He, Shuhui Wang, Hui Xue, and Quan Lu. Sharp multiple instance learning for deepfake video detection. In Proceedings of the 28th ACM International Conference on Multimedia, pages 1864-1872, 2020. 1, 5, 7",
+            "[24] Yuezun Li, Ming-Ching Chang, and Siwei Lyu. In ictu oculi: Exposing ai created fake videos by detecting eye blinking. In 2018 IEEE International Workshop on Information Forensics and Security (WIFS), pages 1-7. IEEE, 2018. 3",
+            "[25] Yuezun Li and Siwei Lyu. Exposing deepfake videos by detecting face warping artifacts. arXiv preprint arXiv:1811.00656, 2018. 1, 7",
+            "[26] Yuezun Li, Xin Yang, Pu Sun, Honggang Qi, and Siwei Lyu. Celeb-df: A large-scale challenging dataset for deepfake forensics. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3207-3216, 2020. 1, 5, 7, 8",
+            "[27] Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579-2605, 2008. 7",
+            "[28] Iacopo Masi, Aditya Killekar, Royston Marian Mascarenhas, Shenoy Pratik Gurudatt, and Wael AbdAlmageed. Two-branch recurrent network for isolating deepfakes in videos. arXiv preprint arXiv:2008.03412, 2020. 1, 2, 3, 5, 7",
+            "[29] Falko Matern, Christian Riess, and Marc Stamminger. Exploiting visual artifacts to expose deepfakes and face manip-"
+        ],
+        "bbox": [
+            503,
+            92,
+            890,
+            902
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            478,
+            924,
+            491,
+            936
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "ulations. In 2019 IEEE Winter Applications of Computer Vision Workshops (WACvw), pages 83-92. IEEE, 2019. 7",
+            "[30] Huy H Nguyen, Fuming Fang, Junichi Yamagishi, and Isao Echizen. Multi-task learning for detecting and segmenting manipulated facial images and videos. arXiv preprint arXiv:1906.06876, 2019. 7",
+            "[31] Huy H Nguyen, Junichi Yamagishi, and Isao Echizen. Capsule-forensics: Using capsule networks to detect forged images and videos. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2307-2311. IEEE, 2019. 3, 7",
+            "[32] Yuval Nirkin, Yosi Keller, and Tal Hassner. Fsgan: Subject agnostic face swapping and reenactment. In Proceedings of the IEEE international conference on computer vision, pages 7184-7193, 2019. 2",
+            "[33] Ivan Petrov, Daiheng Gao, Nikolay Chervoniy, Kunlin Liu, Sugasa Marangonda, Chris Ume, Jian Jiang, Luis RP, Sheng Zhang, Pingyu Wu, et al. Deepfacelab: A simple, flexible and extensible face swapping framework. arXiv preprint arXiv:2005.05535, 2020. 2",
+            "[34] Yunchen Pu, Zhe Gan, Ricardo Henao, Xin Yuan, Chunyuan Li, Andrew Stevens, and Lawrence Carin. Variational autoencoder for deep learning of images, labels and captions. In Advances in neural information processing systems, pages 2352-2360, 2016. 1, 2, 3",
+            "[35] Yuyang Qian, Guojun Yin, Lu Sheng, Zixuan Chen, and Jing Shao. Thinking in frequency: Face forgery detection by mining frequency-aware clues. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision – ECCV 2020, pages 86–103, Cham, 2020. Springer International Publishing. 1, 3, 5, 7",
+            "[36] Nicolas Rahmouni, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Distinguishing computer graphics from natural images using convolution neural networks. In 2017 IEEE Workshop on Information Forensics and Security (WIFS), pages 1-6. IEEE, 2017. 5, 6",
+            "[37] Andreas Rossler, Davide Cozzolino, Luisa Verdoliva, Christian Riess, Justus Thies, and Matthias Nießner. Faceforensics: Learning to detect manipulated facial images. In Proceedings of the IEEE International Conference on Computer Vision, pages 1-11, 2019. 1, 3, 5, 6, 7, 8",
+            "[38] Ekraam Sabir, Jiaxin Cheng, Ayush Jaiswal, Wael AbdAlmageed, Iacopo Masi, and Prem Natarajan. Recurrent convolutional strategies for face manipulation detection in videos. Interfaces (GUI), 3(1), 2019. 1",
+            "[39] Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton. Dynamic routing between capsules. In Advances in neural information processing systems, pages 3856-3866, 2017. 3",
+            "[40] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via gradient-based localization. In Proceedings of the IEEE international conference on computer vision, pages 618-626, 2017. 7",
+            "[41] José A Stuchi, Marcus A Angeloni, Rodrigo F Pereira, Levy Boccato, Guilherme Folego, Paulo VS Prado, and Romis RF Attux. Improving image classification with frequency do"
+        ],
+        "bbox": [
+            78,
+            92,
+            470,
+            900
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "main layers for feature extraction. In 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP), pages 1-6. IEEE, 2017. 3",
+            "[42] Justus Thies, Michael Zollhöfer, and Matthias Nießner. Deferred neural rendering: Image synthesis using neural textures. ACM Transactions on Graphics (TOG), 38(4):1-12, 2019. 2, 5, 6",
+            "[43] Justus Thies, Michael Zollhofer, Marc Stamminger, Christian Theobalt, and Matthias Nießner. Face2face: Real-time face capture and reenactment of rgb videos. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2387-2395, 2016. 2, 5, 6",
+            "[44] Haohan Wang, Xindi Wu, Zeyi Huang, and Eric P Xing. High-frequency component helps explain the generalization of convolutional neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8684-8694, 2020. 3",
+            "[45] Sheng-Yu Wang, Oliver Wang, Richard Zhang, Andrew Owens, and Alexei A Efros. Cnn-generated images are surprisingly easy to spot... for now. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8695-8704, 2020. 1",
+            "[46] Xinsheng Xuan, Bo Peng, Wei Wang, and Jing Dong. On the generalization of gan image forensics. In Chinese Conference on Biometric Recognition, pages 134-141. Springer, 2019. 2",
+            "[47] Shengke Xue, Wenyuan Qiu, Fan Liu, and Xinyu Jin. Faster image super-resolution by improved frequency-domain neural networks. Signal, Image and Video Processing, 14(2):257-265, 2020. 3",
+            "[48] Xin Yang, Yuezun Li, and Siwei Lyu. Exposing deep fakes using inconsistent head poses. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 8261-8265. IEEE, 2019. 1, 3, 7",
+            "[49] Peng Zhou, Xintong Han, Vlad I Morariu, and Larry S Davis. Two-stream neural networks for tampered face detection. In 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 1831-1839. IEEE, 2017. 1, 7"
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            640
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
+            477,
+            924,
+            495,
+            936
+        ],
+        "page_idx": 9
+    }
+]

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+# Spatial-Phase Shallow Learning: Rethinking Face Forgery Detection in Frequency Domain
+
+Honggu Liu $^{1*}$  Xiaodan Li $^{2}$  Wenbo Zhou $^{1\dagger}$  Yuefeng Chen $^{2}$
+
+Yuan He² Hui Xue² Weiming Zhang† Nenghai Yu¹
+
+<sup>1</sup>University of Science and Technology of China <sup>2</sup>Alibaba Group
+
+lhg9754@mail.ustc.edu.cn, {welbeckz,zhangwm，ynh}@ustc.edu.cn
+
+{fiona.lxd, yuefeng.chenyf, heyuan.hy, hui.xueh}@alibaba-inc.com
+
+# Abstract
+
+The remarkable success in face forgery techniques has received considerable attention in computer vision due to security concerns. We observe that up-sampling is a necessary step of most face forgery techniques, and cumulative up-sampling will result in obvious changes in the frequency domain, especially in the phase spectrum. According to the property of natural images, the phase spectrum preserves abundant frequency components that provide extra information and complement the loss of the amplitude spectrum. To this end, we present a novel Spatial-Phase Shallow Learning (SPSL) method, which combines spatial image and phase spectrum to capture the up-sampling artifacts of face forgery to improve the transferability, for face forgery detection. And we also theoretically analyze the validity of utilizing the phase spectrum. Moreover, we notice that local texture information is more crucial than high-level semantic information for the face forgery detection task. So we reduce the receptive fields by shallowing the network to suppress high-level features and focus on the local region. Extensive experiments show that SPSL can achieve the state-of-the-art performance on cross-datasets evaluation as well as multi-class classification and obtain comparable results on single dataset evaluation.
+
+# 1. Introduction
+
+Benefiting from the tremendous success of generative techniques, such as Variational Autoencoders (VAE) [34] and Generative Adversarial Networks (GANs) [15], face forgery has become an emerging hot research topic in very recent years. The face forgery techniques are able to synthesize realistic faces that are indistinguishable for human
+
+![](images/1e27f428cdcce852c541d11645ec98b2bfd033727f76e6b8f977f692af787275.jpg)  
+Figure 1: The variation analysis in the frequency domain. The curve shows the average value of pixel difference (mean and variance) of the phase spectrum between 1000 origin and up-sampling samples increase dramatically with the increase of the number of up-sampling.
+
+eyes. However, these forgery techniques are likely to be abused for malicious purposes, causing serious security and ethical issues (e.g. celebrity pornography and political persecution). Therefore, it is of paramount importance to develop more general and practical methods for face forgery detection.
+
+To alleviate the risks brought by malicious usage of face forgery, various methods [49, 25, 1, 48, 2, 38, 37, 12, 22, 35, 28, 8, 23] have been proposed. Most of these methods detect face forgery in a supervised fashion with prior knowledge of face manipulation methods [1, 6, 23]. Under this setting, these approaches achieve excellent performance on some public datasets [48, 20, 37, 26, 45]. However, these detection methods tend to suffer from overfitting thus their effectiveness is limited to the datasets which they are specifically trained on. Moreover, in real-world detection, it is inevitable to face a source/target mismatch
+
+![](images/54fcf2b0f6ba416e75a2bcff1e35c2060488c2b26707c9a63a700feaf867e97a.jpg)  
+Figure 2: The frequency domain analysis of the origin and up-sampling face. The residual images show that the differences of phase spectrum between origin and upsampling are bigger than the amplitude spectrum with the up-sampling. Best viewed in color. (Darker color indicates smaller pixel values).
+
+problem when handling unseen samples, which is extremely challenging for deepfake detection task. Therefore, it is necessary to enhance the generalization and transferability of forgery detection techniques. Recently, some approaches [10, 22, 28, 46] have made attempts to improve the transferability, there are still deficiencies. For example, two-branch [28] achieves the state-of-the-art performance of cross-dataset detection at the expense of frame-level detection accuracy. Face X-ray [22] starts from a novel perspective that aims at detecting the blending boundary artifacts and obtains perfect performances in detecting unseen forgery method for raw videos, which significantly improves transferability of different manipulation methods [9, 43, 13, 42]. However, since only focus on the information extracted from the spatial domain, it is easily to be influenced by video compression. Thus, we need to concern about the more common artifacts in the generation of forgery images from various domains.
+
+We obverse that up-sampling is a non-negligible step in generative models (e.g. VAE [34], GANs [15]), from which the generated part are then used to synthesize fake faces. This operation usually leaves a trace in the frequency domain, which provides cues for separating synthesized faces from real ones. Though [11] also tried to detect these artifacts with the amplitude spectrum, the performance is limited due to the information loss.
+
+To this end, we propose Spatial-Phase Shallow Learning (SPSL) for face forgery detection, which leverages the phase spectrum for detecting the common artifacts. The pivotal thought is that the phase spectrum is more hypersensitive to up-sampling than the amplitude spectrum. As shown in Figure 1, with more times of up-sampling oper
+
+ations are performed, the average pixel differences of the phase spectrum get much greater than that of the amplitude spectrum. A visualization comparison can also be found in Figure 2.
+
+Moreover, [5] used the patch-based classification to generalize the image forensics. Thus, we hold the opinion that local texture information is more important than high-level semantic information even high-level semantic information should be suppressed to a certain extent in the specific task of forged face detection. For this purpose, SPSL drops many convolutional layers to reduce the receptive field [3] and forces CNNs to pay more attention to local regions which are abundant in textures and lack high-level semantic information.
+
+As a result, SPSL focuses on the common step in the forged faces generation and pays more attention to textures leading to a performance improvement of the cross-datasets evaluation. At the same time, the performance on multiclass classification also improves due to the specific traces of different categories manipulation are left in the phase spectrum.
+
+Extensive experiments demonstrate that SPSL significantly improved the transferability and achieved the state-of-the-art over cross-dataset evaluation.
+
+The major contributions in this paper are summarized as follows:
+
+- We firstly leverage the phase spectrum to detect forged face images and demonstrate that CNNs can capture extra implicit features of the phase spectrum which are beneficial to face forgery detection with precise mathematical derivation.  
+- Aiming at the specific problem of forged face detection, we assume that high-level semantic information should be appropriately suppressed. And we experimentally validate the hypothesis by decreasing the receptive field of CNNs with shallow network learning.  
+- We verify that our approach achieves the state-of-the-art performance of forged face detection over cross-dataset evaluation.
+
+# 2. Related work
+
+Since face manipulation is a classical research topic [43, 33, 32, 21, 17, 42] in computer vision, verifying its authenticity is not a new problem. However, recent remarkable successes of deep learning make face manipulation easier and more realistic which poses a significant challenge of forged face detection. In this section, we briefly review the current face forgery detection methods that are representative and related to our work.
+
+# 2.1. Spatial-based Face forgery Detection
+
+With the development of face forgery, a wide variety of methods have been proposed to detect forged face. The majority of them exploit artifacts based on the spatial domain, especially in RGB. Some methods for deepfake detection focus on hand-crafted facial features from the video, such as eye blinking [24], inconsistent head poses [48], facial expression change [2]. Recent methods [1, 31, 37] capture high-level features from the spatial domain by using deep neural networks and show impressive performance. Nguyen et al. proposed a method [31] which leveraging capsule network [39] to detect face manipulation. Rossler et al. [37] show the best performance on many kinds of forgery algorithms with the efficient XceptionNet [6] at that time. Face X-ray [22] mainly focuses on the blending step which exists in most face forgery and thus achieved state-of-the-art performance on transferability in raw videos. However, it still has some limitations that the performance of Face X-ray will sharply drop when encounter low-resolution images, and it may not work with entirely synthesized images. Almost all of these CNN-based methods only use spatial domain information and therefore the performance is quite sensitive to the quality or data distribution of datasets. In our work, we combine the spatial domain with the frequency domain to take advantage of both.
+
+# 2.2. Frequency-based Face forgery Detection
+
+Besides focusing on the spatial domain, some methods pay attention to the frequency domain for capturing artifacts of the forgery. In fact, frequency analysis is a common and important way in digital image processing and has been widely applied to various tasks in computer vision [44, 47, 41, 18]. Most of them use either Discrete Fourier Transform (DFT) or Wavelet Transform (WT), or Discrete Cosine Transform (DCT) to convert the spatial image to the frequency domain. Durall et al. [12] first proposed that averaging the amplitude of each frequency band with DFT can mine abnormal information of forgery in face manipulation detection.  $\mathrm{F}^3$ -Net [35] extracted frequency-domain information using DCT and analyzed the statistic features for face forgery detection.  $\mathrm{F}^3$ -Net achieved state-of-the-art performance on highly compressed videos, but the performance on cross-dataset evaluation drops greatly. Masi et al. [28] leverage a Laplacian of Gaussian (LoG) to make frequency enhancement for purpose of suppressing the image content present in the low-level feature maps. However, most of these related works mainly depend on low-level statistical features rather than high-level features extracted by CNNs, and therefore the frequency information was inadequately utilized. In our work, given the powerful capabilities of feature extraction of CNNs, we make use of the phase spectrum in DFT and explicitly prove the validity with theory analysis while we integrate it into the
+
+![](images/7a1a0058c513297622d390c098559e6d29e9a2ba888190d47cd83d2627641e3a.jpg)  
+Figure 3: Overview of typical face manipulation pipeline. Most of the previous works only focus on forged faces, while we focus on both up-sampling and forged faces.
+
+whole learning process of CNNs.
+
+# 3. SPSL for Face Forgery Detection
+
+In this section, we start by introducing the key observation of face forgery generation. Then we propose spatial-phase shallow learning to detect the observed common artifacts for face forgery detection. Finally, Making the network shallow can focus on the local region to further boost the improvement of transferability.
+
+# 3.1. Motivation
+
+As shown in Figure 3, a typical facial manipulation method consists of three stages [9]: 1) encoding source face; 2) swapping face in latent space; 3) decoding target face.
+
+Up-sampling is a vital step for decoding the target face, based on either AutoEncoders [34] or GANs [15]. Thus, we leverage the phase information to detect up-sampling artifacts. For applying phase information to CNNs, we reconstruct the spatial domain representation of the phase spectrum from the frequency domain (i.e. IDFT with the frequency spectrum without amplitude). Finally, we concatenate the spatial domain representation of the phase spectrum with the RGB image in the channel, which results in an RGBP 4-channel image.
+
+# 3.2. Capturing up-sampling artifacts via phase spectrum in face forgery
+
+To detect the observed common artifacts, namely upsampling, we analyze it in the frequency domain.
+
+Up-sampling will lead to the emergence of new frequency components. And we make a claim as follows
+
+Claim 1. Phase spectrum is more sensitive to up-sampling artifacts and therefore helps face forgery detection.
+
+To simplify the calculation, we make all the mathematical derivation based on the 1D signal. We first set up the basic notations used in this paper:  $x(n)$  and  $\mathbf{X}(u)$  denote a 1D discrete signal and its Discrete Fourier Transform(DFT), where  $n$  is the spatial location of the signal and  $u$  represents the frequency.  $\mathbf{A}(u)$  is the amplitude spectrum and  $\mathbf{P}(u)$  is the phase spectrum. And we use  $c(n)$  and  $\mathbf{C}(n)$  to denote the convolution kernel and its DFT representation. And we use  $*$  to denote convolutional operation.
+
+Proof. The increase of spatial resolution in 2D corresponds to the extension of the time domain in 1D. Assume that the input  $x(n)$  is up-sampled by factor 2, then
+
+$$
+\hat {x} (n) = \left\{ \begin{array}{l l} x (\frac {1}{2} n), & n = 2 k \\ 0, & n = 2 k + 1 \end{array} \right. \tag {1}
+$$
+
+where  $k = 0,1,2,\dots ,N - 1$  , and
+
+$$
+\begin{array}{l} \hat {\mathbf {X}} (u) = \frac {1}{2 N} \sum_ {n = 0} ^ {2 N - 1} \hat {x} (n) e ^ {- j \frac {2 \pi u n}{2 N}} \\ = \frac {1}{2 N} \sum_ {n = 0} ^ {N - 1} \hat {x} (2 n) e ^ {- j \frac {2 \pi u 2 n}{2 N}} \tag {2} \\ = \frac {1}{2 N} \sum_ {n = 0} ^ {N - 1} x (n) e ^ {- j \frac {2 \pi 2 u n}{N}} \\ \end{array}
+$$
+
+The we have  $\hat{x}(n) = x\left(\frac{1}{2} n\right) \Leftrightarrow \hat{\mathbf{X}}(u) = \mathbf{X}(2u)$  with the Eq. 2, which leads to the conclusion that the increase of spatial resolution will result in the compression in the frequency domain which is consistent with the property of Fourier Transform (FT). In fact, the essence of DFT is the principle value interval of Discrete Fourier Series (DFS) and thus new frequency components are the duplicate of origin frequency components.
+
+Base on our inference that phase spectrum will keep more frequency components that tend to zero in amplitude spectrum, which is dually proved in the Appendix 1.1. We first assume the amplitude spectrum  $\mathbf{X}_{\mathbf{A}}(u)$  and the phase spectrum  $\mathbf{X}_{\mathbf{P}}(u)$  of original images  $x(n)$ . It is
+
+$$
+\mathbf {X} _ {A} (u) = \underbrace {a _ {0} + a _ {1} e ^ {j \theta_ {1}} + \cdots + a _ {k} e ^ {j \theta_ {k}}} _ {\substack {(k + 1) \text {items}}} \tag{3}
+$$
+
+$$
+\mathbf {X} _ {P} (u) = \underbrace {p _ {0} + p _ {1} e ^ {j \theta_ {1}} + \cdots + p _ {N - 1} e ^ {j \theta_ {N - 1}}} _ {N \text {i t e m s}}
+$$
+
+and the corresponding up-sampling is
+
+$$
+\mathbf {X} _ {A} ^ {u p} (u) = \underbrace {a _ {0} + \cdots + a _ {k} e ^ {j \theta_ {k}}} _ {(k + 1) \text {i t e m s}} + \underbrace {a _ {N} e ^ {j \theta_ {N}} + \cdots + a _ {N + k} e ^ {j \theta_ {N + k}}} _ {(k + 1) \text {i t e m s}}
+$$
+
+$$
+\mathbf {X} _ {P} ^ {u p} (u) = \underbrace {p _ {0} + p _ {1} e ^ {j \theta_ {1}} + \cdots + p _ {2 N - 1} e ^ {j \theta_ {2 N - 1}}} _ {2 N \text {i t e m s}} \tag {4}
+$$
+
+We define that  $y_A(n)$  is the output of a convolution layer with an input  $x(n)$  and its frequency domain form is  $\mathbf{Y}_{\mathbf{A}}(u)$ . And we get
+
+$$
+\begin{array}{l} y _ {A} (n) = x (n) * c (n) \\ \Updownarrow \tag {5} \\ \end{array}
+$$
+
+$$
+\mathbf {Y} _ {A} (u) = \mathbf {X} _ {\mathbf {A}} (u) \cdot \mathbf {C} (u)
+$$
+
+According to the deduction that the phase spectrum helps CNNs acquire and learn more abundant frequency components which are ignored with convolution calculations of amplitude spectrum proved in Appendix 1.2, we can deduce the frequency domain form is
+
+$$
+\mathbf {Y} _ {A} (u) = \underbrace {f _ {0} + f _ {1} e ^ {j \theta_ {1}} + \cdots + f _ {k + N - 1} e ^ {j \theta_ {k + N - 1}}} _ {k + N \text {i t e m s}} \tag {6}
+$$
+
+$$
+\mathbf {Y} _ {A} ^ {u p} (u) = \underbrace {f _ {0} + f _ {1} e ^ {j \theta_ {1}} + \cdots + f _ {2 N + k - 1} e ^ {j \theta_ {2 N + k - 1}}} _ {2 N \text {i t e m s}} \tag {7}
+$$
+
+In our work, we first take Inverse Discrete Fourier Transform (IDFT) to phase spectrum and acquire the spatial domain form  $p(n)$  of phase. And we state a theorem named the distributive law as follow,
+
+Theorem 1.  $(f(\cdot) + g(\cdot)) * h(\cdot) = f(\cdot) * h(\cdot) + g(\cdot) * h(\cdot)$
+
+Then we consider that we directly concatenate  $x(n)$  and  $p(n)$  in channel dimension based on theorem 1 and the output  $\mathbf{Y}_{A + P}(u)$  is
+
+$$
+\mathbf {Y} _ {A + P} (u) = \underbrace {f _ {0} + f _ {1} e ^ {j \theta_ {1}} + \cdots + f _ {2 N - 2} e ^ {j \theta_ {2 N - 2}}} _ {2 N - 1 \text {i t e m s}} \tag {8}
+$$
+
+$$
+\mathbf {Y} _ {A + P} ^ {u p} (u) = \underbrace {f _ {0} + f _ {1} e ^ {j \theta_ {1}} + \cdots + f _ {3 N - 2} e ^ {j \theta_ {3 N - 2}}} _ {3 N - 1 \text {i t e m s}} \tag {9}
+$$
+
+Intuitively, the number of learnable frequency components is  $N$  when we leverage the original image and its phase together, but the number just is  $N - k$  with the utilization of the original image alone. Therefore, it is clear that the difference between  $\mathbf{Y}_{A + P}(u)$  and  $\mathbf{Y}_{A + P}^{up}(u)$  is bigger than  $\mathbf{Y}_A(u)$  and  $\mathbf{Y}_A^{up}(u)$ . In particular, the value of  $k$  is usually small in nature images and thus our method observably improves the performance on the detection of face forgery. Thus, we conclude that the introduction of the phase spectrum helps capture more frequency artifacts caused by cumulative up-sampling in deepfake video generation.
+
+# 3.3. Suppressing the semantic information and focusing on local region
+
+We consider that the pivotal distinction between pristine face and forged face is local low-level features(e.g. textures, colors) instead of global high-level semantic features(e.g.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">HQ</td><td colspan="2">LQ</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>Steg. Features [14]</td><td>70.97</td><td>-</td><td>55.98</td><td>-</td></tr><tr><td>Cozzolino et al. [7]</td><td>78.45</td><td>-</td><td>58.69</td><td>-</td></tr><tr><td>Bayer &amp; Stamm [4]</td><td>82.97</td><td>-</td><td>66.84</td><td>-</td></tr><tr><td>Rahmouni et al. [36]</td><td>79.08</td><td>-</td><td>61.18</td><td>-</td></tr><tr><td>MesoNet [1]</td><td>83.10</td><td>-</td><td>70.47</td><td>-</td></tr><tr><td>Face X-ray [22]</td><td>-</td><td>87.35</td><td>-</td><td>61.60</td></tr><tr><td>Xception [6]</td><td>92.39</td><td>94.86</td><td>80.32</td><td>81.76</td></tr><tr><td>Ours(Xception)</td><td>91.50</td><td>95.32</td><td>81.57</td><td>82.82</td></tr></table>
+
+Table 1: Quantitative results (ACC  $(\%)$  and AUC  $(\%)$ ) on FaceForensics++ dataset with high-quality (light compression) and low quality (heavy compression) settings. The bold results are the best.
+
+face, human). Because most of these semantic features are shared in both pristine and forged faces, extensive high-level semantic information more or less has a negative effect on forged face detection as it contains many common characteristics of pristine and forged face images. For the purpose of suppressing high-level semantic features and extracting more texture features, we straightforwardly shallow the neural network by throwing away many convolutional layers or blocks. Then we demonstrate that shallow networks are more transferable and efficient simultaneously.
+
+# 4. Experiments
+
+In this section, we first introduce the overall experimental settings and then present extensive experimental results to demonstrate the superiority of our approach.
+
+# 4.1. Experimental settings
+
+Datasets. Following recent related works [35, 28, 22, 23] of face forgery detection, we conduct our experiments on the two benchmark public deepfake datasets: FaceForensics++(FF++) [37] and Celeb-DF [26]. Both of them are large-scale and contain pristine and manipulated videos of human faces. FF++ consists of four kinds of common face manipulation methods [9, 43, 13, 42]. Celeb-DF is in general the most challenging to the current detection methods, and their overall performance on Celeb-DF is lowest across all datasets.
+
+Evaluation metrics. In our experiments, we mainly utilize the Accuracy rate (ACC) and the Area Under Receiver Operating Characteristic Curve (AUC) as our evaluation metrics. (1) ACC. Accuracy rate is the most intuitive metric in face forgery detection. It is also applied to  $\mathrm{FF} + +$  [37] and thus we use ACC as the major evaluation metric in the experiment. (2) AUC. Following the Celeb-DF [26] and Two-branch [28], we use AUC as another evaluation metric to evaluate the performance on cross-dataset. Besides, we
+
+use the recall rate as our multi-class classification evaluation metric.
+
+Implementation and Hyper-Parameters. In our experiments, we use Xception [6] as the backbone of our approach. For the purpose of reducing receptive fields, we just retain the Xception Block 1-3 and Xception Block 12. The final spatial form of our phase spectrum is the IDFT of the absolute value of the pristine phase spectrum. We optimize the networks by Adam optimizer [19]. The initial learning rate  $lr = 2 \times 10^{-3}$  and it drops to half of itself every time the validation loss does not decrease after 5 full epochs.
+
+# 4.2. Comparison with previous methods
+
+In this section, we compare our method with previous deepfake detection methods. We train all models on only FF++ [37] and respectively evaluate them on FF++ in Section 4.2.1 and Celeb-DF in Section 4.2.2.
+
+# 4.2.1 Comparable results on  $\mathbf{FF} + +$
+
+In this section, we compare our method with previous deepfake detection methods on FF++ [37]. Although our primary purpose is to improve the generalization and transferability, we also obtain comparable results in FF++ [37]. We first evaluate our methods on different video compression settings including high quality (HQ (c23)) and low quality (LQ (c40)). As the results shown in Table 1, the proposed method outperforms or is on par with baseline in both ACC and AUC with LQ settings. Low-quality videos have been highly compressed and many frequency components are weakened. The improvement of performance mainly benefits from the extra phase information captured by CNNs, which keeps more frequency components than plain RGB-based images. At the same time, we also obtain comparable results with HQ settings.
+
+Furthermore, we also evaluate our approach on different face manipulation methods in  $\mathrm{FF}++$  [37]. The results are demonstrated in Table 2. We train and test our models exactly on low-quality videos for each manipulation methods. We also reproduced the results of MesoNet [1] and Xception [6], and other results are directly cited from [37]. In general, basic experiments also show comparable results with previous methods though the transferability is the main purpose of SPSL.
+
+# 4.2.2 Cross-dataset evaluation on Celeb-DF
+
+In this section, we evaluate the transferability of our method given that it is trained on  $\mathrm{FF}++$  with multiple manipulations but tested on Celeb-DF. We first verify that most of the previous methods show a drastic performance drop on the cross-dataset evaluation. Table 3 shows the AUC comparison with some recent methods for face forgery detection. Our method obtains the state-of-the-art AUC on Celeb-DF
+
+![](images/84581e6f2a7cf5f06955c045dae5496532e12f50119764626a3a44518907033b.jpg)  
+Figure 4: Visualization of various manipulation methods and our spatial domain representations of the phase spectrum in  $\mathrm{FF}++$  [37]. Each image and phase spectrum is the average of all frames of a video. Every manipulation method tends to be a specific pattern in the phase spectrum while it is not obvious in the RGB domain. Best viewed in color.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">DF [9]</td><td colspan="2">F2F [43]</td><td colspan="2">FS [13]</td><td colspan="2">NT [42]</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>Steg. Features [14]</td><td>73.64</td><td>-</td><td>73.72</td><td>-</td><td>68.93</td><td>-</td><td>63.33</td><td>-</td></tr><tr><td>Cozzolino et al. [7]</td><td>85.45</td><td>-</td><td>67.88</td><td>-</td><td>73.79</td><td>-</td><td>78.00</td><td>-</td></tr><tr><td>Rahmouni et al. [36]</td><td>85.45</td><td>-</td><td>64.23</td><td>-</td><td>56.31</td><td>-</td><td>60.07</td><td>-</td></tr><tr><td>Bayar and Stamm [4]</td><td>84.55</td><td>-</td><td>73.72</td><td>-</td><td>82.52</td><td>-</td><td>70.67</td><td>-</td></tr><tr><td>MesoNet [1]</td><td>87.27</td><td>-</td><td>56.20</td><td>-</td><td>61.17</td><td>-</td><td>40.67</td><td>-</td></tr><tr><td>XceptionNet [6]</td><td>95.15</td><td>99.08</td><td>83.48</td><td>93.77</td><td>92.09</td><td>97.42</td><td>77.89</td><td>84.23</td></tr><tr><td>Ours(Xception)</td><td>93.48</td><td>98.50</td><td>86.02</td><td>94.62</td><td>92.26</td><td>98.10</td><td>76.78</td><td>80.49</td></tr></table>
+
+Table 2: Quantitative results (ACC (%) and AUC (%)) on FaceForensics++ dataset with four different manipulation methods, i.e. DeepFakes(DF) [9], Face2Face(F2F) [43], FaceSwap(FS) [13], NeuralTextures(NT) [42]. The bold results are best.
+
+while still having a good performance on  $\mathrm{FF}++$  compared with all the other methods. The performance gains mainly benefit from the extra appreciable frequency components of the phase spectrum, which are enhanced many times in the cumulative up-sampling, and thus the differences of frequency components perceptible by convolutional kernel between pristine images and forgery become more striking. Therefore, the proposed SPSL is capable of detecting common artifacts.
+
+# 4.3. Multi-class classification evaluation
+
+We furthermore evaluate the proposed SPSL on multiclass classification with different face manipulation methods list in  $\mathrm{FF} + +$  [37] in this section. The models are trained and tested on  $\mathrm{FF} + +$  with five types of labels, and multiclass classification is more challenging and significant than binary classification. The results are shown in Table 4 by the way of recall rate. With all three kinds of compression setting, the proposed SPSL completely surpasses the orig-
+
+<table><tr><td>Method</td><td>FF++ [37]</td><td>Celeb-DF [26]</td></tr><tr><td>Two-stream [49]</td><td>70.10</td><td>53.80</td></tr><tr><td>Meso4 [1]</td><td>84.70</td><td>54.80</td></tr><tr><td>MesoInception4 [1]</td><td>83.00</td><td>53.60</td></tr><tr><td>HeadPose [48]</td><td>47.30</td><td>54.60</td></tr><tr><td>FWA [25]</td><td>80.10</td><td>56.90</td></tr><tr><td>VA-MLP [29]</td><td>66.40</td><td>55.00</td></tr><tr><td>VA-LogReg</td><td>78.00</td><td>55.10</td></tr><tr><td>Xception-c40 [37]</td><td>95.50</td><td>65.50</td></tr><tr><td>Multi-task [30]</td><td>76.30</td><td>54.30</td></tr><tr><td>Capsule [31]</td><td>96.60</td><td>57.50</td></tr><tr><td>DSP-FWA [25]</td><td>93.00</td><td>64.60</td></tr><tr><td>SMIL [23]</td><td>96.80</td><td>56.30</td></tr><tr><td>Two-branch [28]</td><td>93.20</td><td>73.40</td></tr><tr><td>F3-Net [35]</td><td>97.97</td><td>65.17</td></tr><tr><td>SPSL(Xception)</td><td>96.91</td><td>76.88</td></tr></table>
+
+inal XceptionNet method. Furthermore, we also show the t-SNE [27] feature spaces of data in FF++ high quality with the multi-class classification task, by the Xception and our SPSL, as shown in Figure 5. Xception is more likely to confuse pristine faces with NeuralTextures-based fake faces because this manipulation method modifies very limited pixels in the spatial domain, as shown in Figure 5(a). Conversely, the proposed SPSL can split up all classes in the embedding feature spaces, as shown in Figure 5(b). These improvements may benefit from the salient difference of phase spectrum among various manipulation methods and we show the average phase spectrum in the spatial domain of every frame of a video in Figure 4. For all four kinds of manipulation methods in FF++ [37], the spatial images of the phase spectrum show distinguishing results for each method. In particular, NeuralTextures-based images, which just slightly tampered with lip, are very similar to pristine images causing almost indistinguishable in the RGB domain but the spatial images of the phase spectrum are still separable.
+
+# 5. Ablation Study
+
+# 5.1. Effectiveness of Phase spectrum and Shallow network
+
+To evaluate the effectiveness of both Phase spectrum and Shallow network, we first respectively evaluate one of
+
+Table 3: Cross-dataset evaluation (AUC (\%)) on Celeb-DF. Best competing methods on Celeb-DF are reported. Our method obtains the state-of-the-art performance on cross-dataset evaluation. At the same time, our method still performs well when tested on just deepfake class(96.91%) AUC on  $\mathrm{FF}++$ . Results for some other methods are from [26], and the bold results are the best.  
+
+<table><tr><td>Methods</td><td>DF</td><td>F2F</td><td>FS</td><td>NT</td><td>ORG</td></tr><tr><td>MesoIncep4 [1]</td><td>94.81</td><td>43.32</td><td>73.24</td><td>40.39</td><td>85.16</td></tr><tr><td>Xception-c0 [6]</td><td>97.84</td><td>96.68</td><td>96.84</td><td>87.67</td><td>98.03</td></tr><tr><td>SPSL (Xception-c0)</td><td>99.05</td><td>97.20</td><td>97.63</td><td>91.40</td><td>98.25</td></tr><tr><td>Xception-c23 [6]</td><td>88.00</td><td>88.61</td><td>87.07</td><td>74.83</td><td>75.52</td></tr><tr><td>SPSL (Xception-c23)</td><td>94.18</td><td>93.59</td><td>95.62</td><td>81.72</td><td>88.72</td></tr><tr><td>Xception-c40 [6]</td><td>86.61</td><td>78.88</td><td>83.16</td><td>52.94</td><td>75.55</td></tr><tr><td>SPSL (Xception-c40)</td><td>91.16</td><td>78.31</td><td>88.75</td><td>58.97</td><td>77.49</td></tr></table>
+
+Table 4: The recall rate (\%) of origin and each manipulation method with Raw (c0), HQ (c23) and LQ (c40) settings in our multi-class classification.
+
+![](images/0af2e2153f67d78a188af9d4f751d5f98485e69c47e2ebbafcb309af873623d7.jpg)  
+(a) Baseline  
+Figure 5: The t-SNE feature spaces visualization of the basic Xception (a) and SPSL (b) on FaceForensics++ [37] high quality (HQ) in the multi-class classification task. Red color dots represent pristine images, and rest colors respectively indicate the different manipulation methods. Best viewed in color.
+
+![](images/0c0539663d7d643f6ed0628478b97e1147cbb927bef845e47a3f4d216e626e99.jpg)  
+(b) SPSL
+
+them with baseline and combine them finally. All models are trained on  $\mathrm{FF} + +$  [37] and tested on Celeb-DF [26]. The results are listed in Table 5. Compared with model 1(baseline Xception), model 2(Xception with phase spectrum) and model 3 (shallow Xception) improve the AUC scores of Celeb-DF. The transferability has a great improvement with both of them. When combining phase spectrum and shallow network, SPSL gets the best performance and the AUC score increase by about  $13\%$ . Furthermore, to demonstrate the effectiveness of the proposed SPSL better, we respectively visualize the Gradient-weighted Class Activation Mapping(Grad-CAM) [40] of the baseline and SPSL,
+
+![](images/6382da54e4edf0a2ac9443702d0e5e3451ec66ac331e0df66fa5f922ad8dd084.jpg)  
+Real
+
+![](images/42615e4a4ec39e5a804cad9166b0be58a2c845b6a4ee51bb7e9401693098c7e6.jpg)
+
+![](images/8cfaff0f2a74ea8a66018965b2ea9b4b8234e5574210fdd3ec4dad46d28e19b6.jpg)
+
+![](images/2a6919b981adaed6b58a9471cefc66917418462a01711965455e9b99e20d6025.jpg)  
+Fake  
+DF  
+Figure 6: The Grad-CAM of the baseline Xception and the proposed SPSL, including two different manipulation methods in FF++ [37] and another Celeb-DF [26] datasets. Best viewed in color.
+
+![](images/c8a093422922128dac2765b911d31c571e81353dd1b30bf9e0a0f59aa436f43c.jpg)  
+Baseline
+
+![](images/75652029af64a4696fc80fe3bb8714d899cebee1da22e462333c1cda8ea2872f.jpg)  
+SPSL
+
+![](images/e50f9d438274752e0c26da7121ac28fe1d0a133320fa5221eb1d27610f64825b.jpg)
+
+![](images/e107ed86a28a2445e08e635b1aee9d50cb4ac2f0d15c632de218952f2325c692.jpg)
+
+![](images/445dbcbd6fc294ce8db28c4696f0c598befc4e07cd4c8dd527b4fca3b053a196.jpg)
+
+![](images/c8324fcefe48c8231621fc347cdd9212545c406645a0131741d8744b8567236a.jpg)  
+FS
+
+![](images/44292f043a799dcd0d226384615b71ffd305b5e930083e4fd4caf1929333b033.jpg)  
+Baseline
+
+![](images/6fc3267f90172df216ce83e50ba3fdb9763a8adbba9e6fd8fef22b1c6f8b66dd.jpg)  
+SPSL
+
+![](images/82f7520fcb04eb98384b901e8cdc4729ad3345831ef327a269000d1857d3e779.jpg)
+
+![](images/2fd399ab024c581ecc6df52e8c7bf24d953bda81a676aedab6d3ed7a98dbc1a4.jpg)
+
+![](images/d949905f899757d507d0094f3b3e5812811467e7f4128f2728c72c41e54cad2f.jpg)
+
+![](images/abc6d002506aa72dd75b2f6a46ccab95068977870c224567a78cf54c9f7b8a66.jpg)  
+Celeb-DF
+
+![](images/d5c7b491700cb7143520a95e6334fcb52b1dc0e13956aa82e3f7b3b509b62106.jpg)  
+Baseline
+
+![](images/b22d73de76d9d7b8a00500c12e8b4b725572b91e85d1b362ce25e508954ee1d7.jpg)  
+SPSL
+
+as shown in Figure 6. The Grad-CAM indicates that the proposed SPSL prefers to focus on more microcosmic regions while the baseline model pays more attention to global information, and this phenomenon also accords with our motivation. Furthermore, we demonstrate the correlation analysis between the performance and the number of convolution layers of various backbone networks in Appendix 2.
+
+<table><tr><td>ID</td><td>Phase</td><td>Shallow</td><td>Celeb-DF [26]</td></tr><tr><td>1</td><td>-</td><td>-</td><td>59.98</td></tr><tr><td>2</td><td>√</td><td>-</td><td>69.01</td></tr><tr><td>3</td><td>-</td><td>√</td><td>66.74</td></tr><tr><td>4</td><td>√</td><td>√</td><td>72.39</td></tr></table>
+
+Table 5: Ablation study of the proposed SPSL. These models are trained on  $\mathrm{FF}++$  with high quality(HQ) settings and tested on Celeb-DF (AUC  $(\%)$ ). We compare SPSL and its variants by removing phase spectrum and shallow operation step by step.
+
+# 5.2. Universality of SPSL with Various Backbones
+
+All the above-mentioned experiments are based on XceptionNet [6], and thus we also evaluate the universality of SPSL with two types of ResNet [16]. For both ResNet34 and ResNet50, we directly halve the residual block to shallow networks. The results listed in Table 6 demonstrate that the proposed SPSL is a general framework for various backbones.
+
+# 6. Limitations
+
+Even if we have demonstrated the effectiveness of the proposed SPSL and achieved satisfactory performance on cross-dataset evaluation and multi-class classification, we are aware that there exist some limitations of our work.
+
+Our method depends on the existence of up-sampling in forged face generation. Thus, the performance may drop if the forgery face is not produced by methods based on generative models. Besides, our method also suffers from a
+
+<table><tr><td rowspan="2">Backbone</td><td colspan="2">FF++ [37]</td><td colspan="2">Celeb-DF [26]</td></tr><tr><td>ACC</td><td>AUC</td><td>ACC</td><td>AUC</td></tr><tr><td>ResNet-34</td><td>71.55</td><td>81.58</td><td>65.19</td><td>66.90</td></tr><tr><td>SPSL (ResNet-34)</td><td>83.24</td><td>89.26</td><td>66.79</td><td>71.78</td></tr><tr><td>ResNet-50</td><td>81.83</td><td>83.51</td><td>69.40</td><td>70.05</td></tr><tr><td>SPSL (ResNet-50)</td><td>86.64</td><td>91.04</td><td>68.28</td><td>73.09</td></tr></table>
+
+Table 6: The results (ACC (\%) and AUC (\%)) on FF++ [37] and cross-dataset evaluation on Celeb-DF [26] of two different backbones with the proposed SPSL.
+
+transferability drop when encountering an entirely different type of face forgery manipulation. For instance, the model trained on identity swap datasets may fail to detect forgery faces whose expressions are swapped. This is expected since manipulations from different categories can leave a specific trace in the phase spectrum as shown in Figure 4, this is also the reason why our method makes a remarkable improvement of multi-class classification.
+
+# 7. Conclusion
+
+In this work, we propose a novel face forgery detection method, SPSL, which takes advantage of both spatial and frequency information. The core competence of SPSL is that phase spectrum contains more abundant appreciable frequency components and these components will be duplicated in the process of up-sampling which is the necessary step of forged face generation. Besides, SPSL forces the network to focus on the local microcosmic region and suppress global semantic information for more robustness. We perform a meticulous mathematical derivation to prove the rationality of the proposed SPSL, and extensive experiments demonstrate that the SPSL has an excellent performance on the face forgery detection, especially in the challenging cross-dataset evaluation task.
+
+# References
+
+[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. In 2018 IEEE International Workshop on Information Forensics and Security (WIFS), pages 1-7. IEEE, 2018. 1, 3, 5, 6, 7  
+[2] Shruti Agarwal, Hany Farid, Yuming Gu, Mingming He, Koki Nagano, and Hao Li. Protecting world leaders against deep fakes. In CVPR Workshops, pages 38-45, 2019. 1, 3  
+[3] André Araujo, Wade Norris, and Jack Sim. Computing receptive fields of convolutional neural networks. Distill, 2019. https://distill.pub/2019/computing-receptive-fields. 2  
+[4] Belhassen Bayar and Matthew C Stamm. A deep learning approach to universal image manipulation detection using a new convolutional layer. In Proceedings of the 4th ACM Workshop on Information Hiding and Multimedia Security, pages 5-10, 2016. 5, 6  
+[5] Lucy Chai, David Bau, Ser-Nam Lim, and Phillip Isola. What makes fake images detectable? understanding properties that generalize. arXiv preprint arXiv:2008.10588, 2020. 2  
+[6] Francois Chollet. Xception: Deep learning with depthwise separable convolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017. 1, 3, 5, 6, 7, 8  
+[7] Davide Cozzolino, Giovanni Poggi, and Luisa Verdoliva. Recasting residual-based local descriptors as convolutional neural networks: an application to image forgery detection. In Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, pages 159-164, 2017. 5, 6  
+[8] Hao Dang, Feng Liu, Joel Stehouwer, Xiaoming Liu, and Anil K Jain. On the detection of digital face manipulation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5781-5790, 2020. 1  
+[9] DeepFakes. Deepfakes github. http://github.com/deepfakes/faceswap, 2017. Accessed 2020-08-18. 2, 3, 5, 6  
+[10] Mengnan Du, Shiva Pentyala, Yuening Li, and Xia Hu. Towards generalizable forgery detection with locality-aware autoencoder. arXiv preprint arXiv:1909.05999, 2019. 2  
+[11] Ricard Durall, Margret Keuper, and Janis Keuper. Watch your up-convolution: Cnn based generative deep neural networks are failing to reproduce spectral distributions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7890–7899, 2020. 2  
+[12] Ricard Durall, Margret Keuper, Franz-Josef Pfreundt, and Janis Keuper. Unmasking deepfakes with simple features. arXiv preprint arXiv:1911.00686, 2019. 1, 3  
+[13] FaceSwap. Faceswap github. https://github.com/MarekKowalski/FaceSwap, 2016. Accessed 2020-08-18. 2,5,6  
+[14] Jessica Fridrich and Jan Kodovsky. Rich models for steganalysis of digital images. IEEE Transactions on Information Forensics and Security, 7(3):868-882, 2012. 5, 6  
+[15] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and
+
+Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pages 2672-2680, 2014. 1, 2, 3  
+[16] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 8  
+[17] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4401-4410, 2019. 2  
+[18] Gahyun Kim, Sungmin Eum, Jae Kyu Suhr, Dong Ik Kim, Kang Ryoung Park, and Jaihie Kim. Face liveness detection based on texture and frequency analyses. In 2012 5th IAPR international conference on biometrics (ICB), pages 67-72. IEEE, 2012. 3  
+[19] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.5  
+[20] Pavel Korshunov and Sébastien Marcel. Deepfakes: a new threat to face recognition? assessment and detection. arXiv preprint arXiv:1812.08685, 2018. 1  
+[21] Iryna Korshunova, Wenzhe Shi, Joni Dambre, and Lucas Theis. Fast face-swap using convolutional neural networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 3677-3685, 2017. 2  
+[22] Lingzhi Li, Jianmin Bao, Ting Zhang, Hao Yang, Dong Chen, Fang Wen, and Baining Guo. Face x-ray for more general face forgery detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5001-5010, 2020. 1, 2, 3, 5  
+[23] Xiaodan Li, Yining Lang, Yuefeng Chen, Xiaofeng Mao, Yuan He, Shuhui Wang, Hui Xue, and Quan Lu. Sharp multiple instance learning for deepfake video detection. In Proceedings of the 28th ACM International Conference on Multimedia, pages 1864-1872, 2020. 1, 5, 7  
+[24] Yuezun Li, Ming-Ching Chang, and Siwei Lyu. In ictu oculi: Exposing ai created fake videos by detecting eye blinking. In 2018 IEEE International Workshop on Information Forensics and Security (WIFS), pages 1-7. IEEE, 2018. 3  
+[25] Yuezun Li and Siwei Lyu. Exposing deepfake videos by detecting face warping artifacts. arXiv preprint arXiv:1811.00656, 2018. 1, 7  
+[26] Yuezun Li, Xin Yang, Pu Sun, Honggang Qi, and Siwei Lyu. Celeb-df: A large-scale challenging dataset for deepfake forensics. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3207-3216, 2020. 1, 5, 7, 8  
+[27] Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579-2605, 2008. 7  
+[28] Iacopo Masi, Aditya Killekar, Royston Marian Mascarenhas, Shenoy Pratik Gurudatt, and Wael AbdAlmageed. Two-branch recurrent network for isolating deepfakes in videos. arXiv preprint arXiv:2008.03412, 2020. 1, 2, 3, 5, 7  
+[29] Falko Matern, Christian Riess, and Marc Stamminger. Exploiting visual artifacts to expose deepfakes and face manip-
+
+ulations. In 2019 IEEE Winter Applications of Computer Vision Workshops (WACvw), pages 83-92. IEEE, 2019. 7  
+[30] Huy H Nguyen, Fuming Fang, Junichi Yamagishi, and Isao Echizen. Multi-task learning for detecting and segmenting manipulated facial images and videos. arXiv preprint arXiv:1906.06876, 2019. 7  
+[31] Huy H Nguyen, Junichi Yamagishi, and Isao Echizen. Capsule-forensics: Using capsule networks to detect forged images and videos. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2307-2311. IEEE, 2019. 3, 7  
+[32] Yuval Nirkin, Yosi Keller, and Tal Hassner. Fsgan: Subject agnostic face swapping and reenactment. In Proceedings of the IEEE international conference on computer vision, pages 7184-7193, 2019. 2  
+[33] Ivan Petrov, Daiheng Gao, Nikolay Chervoniy, Kunlin Liu, Sugasa Marangonda, Chris Ume, Jian Jiang, Luis RP, Sheng Zhang, Pingyu Wu, et al. Deepfacelab: A simple, flexible and extensible face swapping framework. arXiv preprint arXiv:2005.05535, 2020. 2  
+[34] Yunchen Pu, Zhe Gan, Ricardo Henao, Xin Yuan, Chunyuan Li, Andrew Stevens, and Lawrence Carin. Variational autoencoder for deep learning of images, labels and captions. In Advances in neural information processing systems, pages 2352-2360, 2016. 1, 2, 3  
+[35] Yuyang Qian, Guojun Yin, Lu Sheng, Zixuan Chen, and Jing Shao. Thinking in frequency: Face forgery detection by mining frequency-aware clues. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision – ECCV 2020, pages 86–103, Cham, 2020. Springer International Publishing. 1, 3, 5, 7  
+[36] Nicolas Rahmouni, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Distinguishing computer graphics from natural images using convolution neural networks. In 2017 IEEE Workshop on Information Forensics and Security (WIFS), pages 1-6. IEEE, 2017. 5, 6  
+[37] Andreas Rossler, Davide Cozzolino, Luisa Verdoliva, Christian Riess, Justus Thies, and Matthias Nießner. Faceforensics: Learning to detect manipulated facial images. In Proceedings of the IEEE International Conference on Computer Vision, pages 1-11, 2019. 1, 3, 5, 6, 7, 8  
+[38] Ekraam Sabir, Jiaxin Cheng, Ayush Jaiswal, Wael AbdAlmageed, Iacopo Masi, and Prem Natarajan. Recurrent convolutional strategies for face manipulation detection in videos. Interfaces (GUI), 3(1), 2019. 1  
+[39] Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton. Dynamic routing between capsules. In Advances in neural information processing systems, pages 3856-3866, 2017. 3  
+[40] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via gradient-based localization. In Proceedings of the IEEE international conference on computer vision, pages 618-626, 2017. 7  
+[41] José A Stuchi, Marcus A Angeloni, Rodrigo F Pereira, Levy Boccato, Guilherme Folego, Paulo VS Prado, and Romis RF Attux. Improving image classification with frequency do
+
+main layers for feature extraction. In 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP), pages 1-6. IEEE, 2017. 3  
+[42] Justus Thies, Michael Zollhöfer, and Matthias Nießner. Deferred neural rendering: Image synthesis using neural textures. ACM Transactions on Graphics (TOG), 38(4):1-12, 2019. 2, 5, 6  
+[43] Justus Thies, Michael Zollhofer, Marc Stamminger, Christian Theobalt, and Matthias Nießner. Face2face: Real-time face capture and reenactment of rgb videos. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2387-2395, 2016. 2, 5, 6  
+[44] Haohan Wang, Xindi Wu, Zeyi Huang, and Eric P Xing. High-frequency component helps explain the generalization of convolutional neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8684-8694, 2020. 3  
+[45] Sheng-Yu Wang, Oliver Wang, Richard Zhang, Andrew Owens, and Alexei A Efros. Cnn-generated images are surprisingly easy to spot... for now. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8695-8704, 2020. 1  
+[46] Xinsheng Xuan, Bo Peng, Wei Wang, and Jing Dong. On the generalization of gan image forensics. In Chinese Conference on Biometric Recognition, pages 134-141. Springer, 2019. 2  
+[47] Shengke Xue, Wenyuan Qiu, Fan Liu, and Xinyu Jin. Faster image super-resolution by improved frequency-domain neural networks. Signal, Image and Video Processing, 14(2):257-265, 2020. 3  
+[48] Xin Yang, Yuezun Li, and Siwei Lyu. Exposing deep fakes using inconsistent head poses. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 8261-8265. IEEE, 2019. 1, 3, 7  
+[49] Peng Zhou, Xintong Han, Vlad I Morariu, and Larry S Davis. Two-stream neural networks for tampered face detection. In 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pages 1831-1839. IEEE, 2017. 1, 7

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+# Have We Learned to Explain?: How Interpretability Methods Can Learn to Encode Predictions in their Interpretations.
+
+Neil Jethani
+
+NYU Grossman SOM, NYU
+
+nj594@nyu.edu
+
+Mukund Sudarshan
+
+NYU
+
+Yindalon Aphinyanaphongs
+
+NYU Langone
+
+Rajesh Ranganath
+
+NYU
+
+# Abstract
+
+While the need for interpretable machine learning has been established, many common approaches are slow, lack fidelity, or hard to evaluate. Amortized explanation methods reduce the cost of providing interpretations by learning a global selector model that returns feature importances for a single instance of data. The selector model is trained to optimize the fidelity of the interpretations, as evaluated by a predictor model for the target. Popular methods learn the selector and predictor model in concert, which we show allows predictions to be encoded within interpretations. We introduce EVAL-X as a method to quantitatively evaluate interpretations and REAL-X as an amortized explanation method, which learn a predictor model that approximates the true data generating distribution given any subset of the input. We show EVAL-X can detect when predictions are encoded in interpretations and show the advantages of REAL-X through quantitative and radiologist evaluation.
+
+# 1 INTRODUCTION
+
+The spread of machine learning models within many crucial aspects of society, has made interpretable machine learning increasingly consequential for trusting model decisions (Lipton, 2017), identifying model failure modes (Zech et al., 2018), and expanding knowledge (Silver et al., 2017). Interpretability in machine learning is a well-studied problem, and many methods have been introduced to offer an understanding of which features locally, in a given instance of data, are important for generating the target. This goal can be stated as instance-wise feature selection (IWFS). For example, IWFS produces saliency maps to explains images, where pixels are segmented based on their importance.
+
+Providing interpretable explanations is a difficult problem,
+
+and many popular approaches are either slow or lack fidelity and are hard to evaluate. Locally-linear methods (Lundberg and Lee, 2017; Ribeiro et al., 2016) and perturbation methods (Zeiler and Fergus, 2014) are slow — relying on evaluating numerous feature subsets or solving an optimization problem for each instance of data. While gradient-based methods (Simonyan et al., 2013; Springenberg et al., 2014) provide faster explanations, recent studies (Adebayo et al., 2018; Hooker et al., 2019) have shown that their explanations are inaccurate/lack fidelity.
+
+Recently, multiple works (Dabkowski and Gal, 2017; Chen et al., 2018; Yoon et al., 2019; Schwab and Karlen, 2019), which we refer to as amortized explanation methods (AEMs), amortize the cost of providing model-agnostic explanations by learning a single global selector model that efficiently identifies the subset of locally important features in an instance of data with a single forward pass. AEMs learn the global selector model by optimizing an objective that measures the fidelity of the explanations.
+
+AEMs assess feature subset selections, provided as masked inputs, using a predictor model for the target. Either the original predictor model trained on the full feature set is used or a new predictor model is trained. If the original predictor model is used and simple masking, such as with a default value, is employed, (Dabkowski and Gal, 2017; Schwab and Karlen, 2019) the masked inputs will come from a different distribution than that on which the model was trained, violating a key assumption in machine learning (Hooker et al., 2019). Instead, L2X and INVASE fit a new predictor model jointly with the selector model. We refer to such methods as joint amortized explanation methods (JAMs). JAMs have been used for a range of applications — providing image saliency maps, identifying important sentences in text, and identifying features involved in predicting mortality at the patient-level (Chen et al., 2018; Yoon et al., 2019).
+
+While JAMs seek to provide users with fast, high fidelity explanations, we show that they encode predictions within interpretations and omit features involved in control flow. Figure 1 illustrates this point; it plots explanations from L2X Chen et al. (2018) on MNIST (LeCun et al., 1998) trained with a selector model that outputs a single important
+
+![](images/61a1796e8bbc67ae7866db5524815a66829688238e8b8bcedd6428838d1812e4.jpg)  
+Figure 1: L2X classifies digits with  $96\%$  accuracy from a single feature selection.
+
+pixel and achieves  $96.0\%$  accuracy. Here, the selector model makes the classification decision and transmits it to the predictor model via the binary code of the selections, encoding the prediction. The issues with JAMs stem from the predictor model co-adapting to work with the selector model to fit the data, allowing the predictor model to map from selection masks to predictions. Had the selections in fig. 1 been evaluated under the true data generating distribution of the target given single feature subsets of the input, the digits could not have been accurately predicted. To identify such issues in practice, interpretations should be evaluated.
+
+We first develop EVAL-X $^1$  as a method to evaluate interpretations, which learns to approximate the true data generating distribution of the target given subsets of the input. Then, we introduce REAL-x $^1$  as a novel AEM, which learns to select minimal feature subsets that maximize the likelihood of the data under an estimate of the true data generating distribution of the target given subsets of the input. REAL-x provides fast, high fidelity/accuracy explanations without encoding predictions or relying on model predictions generated by out-of-distribution inputs. We compare REAL-x to existing JAMs on established synthetic, MNIST, and Chest X-Ray datasets. We show that REAL-x helps address the issues with JAMs through quantitative EVAL-X and expert clinical evaluation.
+
+# 1.1 Related Work
+
+Interpretability methods can be divided into four different approaches - gradient-based, perturbation-based, locally linear, and amortized explanation methods.
+
+Gradient-based methods, such as (Simonyan et al., 2013; Springenberg et al., 2014; Shrikumar et al., 2017), calculate the gradient of the target with respect to features in the input. Simonyan et al. (2013), for example, does so with
+
+imaging data, overlaying a "saliency map" of important pixels. Similarly, grad-CAM (Selvaraju et al., 2019) calculates the gradient of the target with respect to intermediate layers in a CNN. In addition to often requiring strong modeling assumptions (i.e. restricting the model class to CNNs), these methods do not optimize any objective to ensure the fidelity/accuracy of their explanations. Hooker et al. (2019) show that the estimates of feature importance derived from many gradient-based methods are often no better than a random assignment of feature importance. Adebayo et al. (2018) show that even random model parameters and targets provide seemingly acceptable explanations.
+
+Perturbation-based approaches, such as (Zeiler and Fergus, 2014; Zhou and Troyanskaya, 2015; Zintgraf et al., 2017), perturb the inputs and observe the effect on the target or neurons within a network in order to gauge feature importance. This process requires separate forward passes through the network for each perturbation, which is computationally inefficient and can underestimate the importance of features (Shrikumar et al., 2017).
+
+Locally linear methods, popularly LIME (Ribeiro et al., 2016) and SHAP (Lundberg and Lee, 2017), provide an explanation that is a linear function of simplified variables to explain the prediction of a single input. Locally linear methods assume model linearity in order to explain complex feature interactions and non-linear decision boundaries. These methods require selecting different feature subsets for each instance in order to assess the their impact on the prediction of the target, a computationally-intensive process. In order to assess model predictions given only a subset of features, the missing features are sampled independently, resulting in model inputs that can be out-of-distribution. This can lead to unexpected results because there is no expectation on what the model will return on out-of-distribution inputs. While these methods do optimize for the fidelity of their explanations, they are slow, require strong modeling assumptions, such as linearity, and rely on out-of-distribution estimates.
+
+Amortized explanation methods, (Dabkowski and Gal, 2017; Chen et al., 2018; Yoon et al., 2019; Schwab and Karlen, 2019), learn a global model to explain any sample of data. AEMs are the only class of methods that provide both an objective to measure explanation fidelity and fast explanations with a single forward pass. AEMs accomplish all this while only requiring that the predictor model is differentiable, demanding no strong modeling assumptions. However, current approaches either rely on out-of-distribution model inputs (Dabkowski and Gal, 2017; Schwab and Karlen, 2019) or, as we show, encode predictions (Chen et al., 2018; Yoon et al., 2019). We address these issues with REAL-x.
+
+Meanwhile, evaluating interpretations is less well studied. Given the interpretations, many approaches mask out the unimportant features in the inputs and assess their ability to predict the target. Most approaches (Samek et al.,
+
+2017; Chen et al., 2018) do so using a prediction model trained on the full feature set. In this case, the masked inputs come from a different distribution than those on which the model is trained. To address this issue, Hooker et al. (2019) introduced ROAR, which instead retransmits a prediction model on the masked-inputs. However, if the predictions are encoded within the interpretations, then ROAR can learn these encodings. We introduce EVAL-X to address these issues.
+
+# 2 AMORTIZED EXPLANATIONS
+
+We begin by introducing some preliminaries that we refer to throughout the paper. Let features  $\mathbf{x}$  be a random vector in  $\mathbb{R}^D$ , and the response  $\mathbf{y} \in \{1, \dots, K\}$ . For a given positive integer  $j \leq D$ , let  $\mathbf{x}_j$  be the  $j$ th component of  $\mathbf{x}$  and  $\mathbf{x}_S := \{\mathbf{x}_j\}_{j \in S}$  be a subset of features, where  $S \subseteq \{1, \dots, D\}$ .  $F$  is a distribution over  $(\mathbf{x}, \mathbf{y})$ .
+
+For every instance  $(\pmb{x}^{(i)},\pmb{y}^{(i)})\sim F(\mathbf{x},\mathbf{y})$  ,instance-wise feature selection (IWFS) identifies a minimal subset of features  $x_{S^{(i)}}^{(i)}$  that are relevant to the corresponding target  $\pmb{y}^{(i)}$  Formally, IWFS seeks  $\pmb{x}_{S^{(i)}}^{(i)}$  such that under the conditional distribution  $F(\mathbf{y}\mid \cdot)$  (Yoon et al., 2019)
+
+$$
+F (\mathbf {y} \mid \mathbf {x} _ {S ^ {(i)}} = \boldsymbol {x} _ {S ^ {(i)}} ^ {(i)}) = F (\mathbf {y} \mid \mathbf {x} = \boldsymbol {x} ^ {(i)}). \tag {1}
+$$
+
+Here,  $F(\mathbf{y} \mid \mathbf{x})$  can either be the population distribution from which the data is drawn or, to provide model interpretations, a trained model.
+
+# 2.1 Amortized Explanation Methods (AEMs)
+
+AEMs refer to a general class of interpretability methods that learn a global selector model to identify a subset of important features locally in any given instance of data  $(\boldsymbol{x}^{(i)},\boldsymbol{y}^{(i)})$ . The selector model is a distribution  $q_{\mathrm{sel}}(\mathbf{s}|\mathbf{x};\beta)$  over a selector variable  $\mathbf{s}$ , which indicates the important features for a given sample of  $\mathbf{x}$ . For images, the selector model returns the salient pixels. AEMs optimize  $q_{\mathrm{sel}}$  with an objective that measures the fidelity of the selections (i.e. the ability of the selections to predict the target).
+
+Joint amortized explanation methods (JAMs). Recent, popular AEMs, L2X (Chen et al., 2018) and INVASE (Yoon et al., 2019) learn  $q_{\mathrm{sel}}(\mathbf{s} \mid \mathbf{x}; \beta)$  in concert with a predictor model  $q_{\mathrm{pred}}(\mathbf{y} \mid m(\mathbf{x}, \mathbf{s}); \theta)$ . We refer to such methods as joint amortized explanation methods (JAMs). JAMs use a regularizer  $R(\mathbf{s})$  to control the number of selected features and a masking function  $m$  to hide the  $j$ th feature  $x_j$  with the selector variable  $s_j$ . For example, the masking function  $m$  can replace features with a mask token  $\text{mask}^2$  using binary indicators  $s$ :
+
+$$
+m \left(\boldsymbol {x} ^ {(i)}, \boldsymbol {s} ^ {(i)}\right) _ {j} = \left\{ \begin{array}{l l} \boldsymbol {x} _ {j} ^ {(i)} & \text {i f} \boldsymbol {s} _ {j} ^ {(i)} = 1 \\ [ \text {m a s k} ] & \text {i f} \boldsymbol {s} _ {j} ^ {(i)} = 0 \end{array} . \right. \tag {2}
+$$
+
+To learn the parameters of the selector model,  $\beta$ , and the predictor model,  $\theta$ , the JAM objective maximizes
+
+$$
+\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {s} \sim q _ {\text {s e l}} (\boldsymbol {s} \mid \boldsymbol {x}; \beta)} [ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) - \lambda R (\boldsymbol {s}) ] \tag {3}
+$$
+
+This objective seeks to measure the ability of the selections to predict the target. Equation (3) can be optimized with score function (Glynn, 1990; Williams, 1992) or reparameterization gradients (Kingma and Welling, 2014) and doesn't make any model-specific assumptions like linearity.
+
+INVASE is a JAM that models the selector variable  $\mathbf{s}$  using independent Bernoulli distributions denoted  $\mathcal{B}$  whose probabilities are given by a function  $f$  of the features. It sets  $R(\mathbf{s}) = \ell_0(\mathbf{s})$  to enforce sparse feature selections and uses the masking from eq. (2). INVASE also uses  $q_{\mathrm{control}}(\boldsymbol{y} \mid \boldsymbol{x}; \phi)$  as a control variate within the objective to reduce the variance of the score function gradients during optimization. The INVASE objective for learning  $\theta$  and  $\beta$  is
+
+$$
+\begin{array}{l} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {s} _ {j} \sim \mathcal {B} (f _ {\beta} (\boldsymbol {x}) _ {j})} [ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) \\ - \log q _ {\text {c o n t r o l}} (\boldsymbol {y} \mid \boldsymbol {x}; \phi) - \lambda \| \mathbf {s} \| _ {0} ] \\ \end{array}
+$$
+
+The use of  $q_{\mathrm{control}}$  does not alter INVASE's objective with respect to the selector or predictor model, so it fits into the form of eq. (3).
+
+L2X is a JAM that uses  $k$  independent samples from a Concrete distribution (Maddison et al., 2016; Jang et al., 2017) to define the selector model in order to make use of reparameterization gradients during optimization. In L2X,  $s$  is sampled from  $q_{\mathrm{sel}}(\mathbf{s} \mid \mathbf{x}; \beta)$  as
+
+$$
+\begin{array}{l} \boldsymbol {c} _ {j} \sim \operatorname {C o n c r e t e} (f _ {\beta} (\boldsymbol {x})), \quad C = [ \boldsymbol {c} _ {1}, \dots , \boldsymbol {c} _ {k} ] \in \mathbb {R} ^ {D \times k}, \\ \boldsymbol{s}_{i} = \max_{1\leq j\leq k}C_{ij} \\ \end{array}
+$$
+
+Selection with the mask function is accomplished with multiplication:  $m(\mathbf{x},\mathbf{s}) = \mathbf{x}\odot \mathbf{s}$ . Sparse selections are enforced by selecting a selection limit  $k$  that sets the number of samples taken from a Concrete distribution, assigning a hard bound on the number of features selected. L2X optimizes the following objective for learning  $\theta$  and  $\beta$ :
+
+$$
+\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {s \sim q _ {\text {s e l}} (\boldsymbol {s} \mid \boldsymbol {x}; \beta)} \left[ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid \boldsymbol {x} \odot \boldsymbol {s}; \theta) \right]. \tag {4}
+$$
+
+Equation (3) and eq. (4) represent the same constrained optimization problem, where in eq. (4) the constraint over the number of features selected is applied explicitly via the selection limit  $k$ .
+
+# 3 PROBLEMS WITH JAMs
+
+By maximizing an objective for providing high-fidelity selections, AEMs learn a selector model that makes it fast and simple to explain any new sample of data. In this section, however, we reveal a pair of problems with the JAM objective:
+
+1. Encoding predictions with the learned selector.  
+2. Failure to select features involved in control flow.
+
+# 3.1 Encoding Predictions
+
+JAMs use the selector variable,  $\mathbf{s}$ , to make selections that mask features in the input. For simplicity, we focus on the masking function from eq. (2) and on independent Bernoulli selector variables  $\mathbf{s}_j \sim \mathrm{Bernoulli}(f_\beta(\mathbf{x})_j)$  like in INVASE.
+
+For noise free classification, the following lemma states that the selector model can encode the target using the selection of at most a single feature in each sample of data. The intuition here is that the selector variable  $s$  is a binary code that can pass quite a bit of information to predict the target. A proof is available in appendix D.1.
+
+Lemma 1. Let  $\mathbf{x} \in \mathbb{R}^D$  and target  $\mathbf{y} \in \{1, \dots, K\}$ . If  $\mathbf{y}$  is a deterministic function of  $\mathbf{x}$  and  $K \leq D$ , then JAMs with monotone increasing regularizers  $R$  will select at most one feature at optimality.
+
+The proof for this lemma works by having the selector  $q_{\mathrm{sel}}$  make the classification based on its input  $x$ , encode the class into a binary code, and transmit this code via the selector variable to  $q_{\mathrm{pred}}$  while making use of as few bits as possible. In this setting, if  $K \leq D$ , selection of only a single feature can encode the target. Further, if the regularizer  $R$  is monotone increasing, then an encoding with a single feature will be the preferred maximizer of the JAM objective.
+
+This idea can be generalized to settings where  $\mathbf{y}$  is not a deterministic function of  $\mathbf{x}$ . In this case, levels of uncertainty can be encoded through the selected features. This is formally captured with lemma 3 in appendix C and proved in appendix D.2. Again, the intuition here is that selector variable produces many unique binary combinations. Each binary combination of the selector variable acts as an index that the predictor model uses to output a probability vector for the target classes. When the input dimensionality  $D$  is large, a massive number of indices are available. This allows the selector model to accurately encode uncertainties about the target, without requiring that the predictor model use the input feature values.
+
+# 3.2 Omitting Control Flow Features
+
+![](images/802640467784cf8cc2f882b79fafdd41a13457d03ed057ebafda158ea4fab34e.jpg)  
+Figure 2: Generative process where the  $F(\mathbf{y} \mid \mathbf{x})$  is a tree.
+
+Existing AEMs can learn to ignore features that only appear in the control flow of a generative process. We consider a simple example of such a process in fig. 2, where  $\mathbf{x}_i\sim \mathcal{N}(0,1)$ . Here,  $\mathbf{x}_{11}$  is involved in a branching decision, such that based on its value either the subset of features  $\mathbf{x}_{\mathcal{A}} = \{\mathbf{x}_i\}_{i = 1}^8$  or  $\mathbf{x}_{\mathcal{B}} = \{\mathbf{x}_i\}_{i = 4}^{10}$  is used to generate  $\mathbf{y}$ . We refer to features, like  $\mathbf{x}_{11}$ , that are involved only in the
+
+branching decisions/nodes of tree structured generative process as control flow features.
+
+Consider using a JAM to explain this process. In the first case, when  $\mathbf{x}_{11} \geq 0$ , the selector learns to select  $\mathbf{x}_A$ , while the predictor model approximates  $F_A$  to generate the target  $\mathbf{y}$ . Likewise, when  $\mathbf{x}_{11} < 0$  the selector can select  $\mathbf{x}_B$  and the predictor can generate  $\mathbf{y}$  by modeling  $F_B$ . In all cases, the predictor model can use  $F_A$  or  $F_B$  based on the unique subset of features selected. JAMs do not select  $\mathbf{x}_{11}$ , even though  $\mathbf{x}_{11}$  is important across all samples. Lemma 2 proved in appendix D.3 formalizes this phenomenon.
+
+Lemma 2. Assume that the true  $F(\mathbf{y} \mid \mathbf{x})$  is computed as a tree, where the leaves  $\ell_i$  are the conditional distributions  $F_i(\mathbf{y} \mid \mathbf{x}_{S_i})$  of  $\mathbf{y}$  given distinct subsets of features  $S_i$  in  $\mathbf{x}$ . Given a monotone increasing regularizer  $R$ , the preferred maximizer of the JAM objective excludes control flow features that are involved in branching decisions.
+
+The proof of this lemma works by having the selector select each distinct subset of features found at the leaves of the tree. Given that each distinct subset uniquely maps to an  $F_{i}$ , the predictor model can learn this mapping and generate the target as well as possible. Under monotone increasing regularization  $R$ , the solution that omits control flow features will be preferred over one that selects the full set of relevant features. While L2X does not employ monotone increasing regularization, the L2X objective still omits control flow features and encodes predictions when the selection limit  $k$  is set appropriately to maximize the likelihood of the target while selecting the minimal number of features. Both L2X and INVASE benchmark their methods on datasets that contain control flow features. We describe these datasets and empirically demonstrate that JAMs fail to select control flow features in section 6.3.
+
+Further, control flow features likely exist in many real-world datasets. Consider using electronic health record data to predict mortality in patients presenting with chest pain. Troponin lab values, a measure of heart injury, can function as a control flow feature. Abnormal Troponin values indicate that cardiac imagining should be used to assess disease severity and, therefore, mortality. Meanwhile, normal Troponin values indicate that the chest pain may be non-cardiac, and perhaps a chest X-Ray would better inform mortality prediction. In this case, using JAMs to interpret the prediction will not capture the roll that Troponin plays in determining a patient's mortality.
+
+# 4 EVAL-X: THE EVALUATOR
+
+From the prior sections it is clear that JAMs can learn to make selections that, instead of selecting the set of relevant features, simply encode their contribution. In order to trust the explanations provided by JAMs, selections need to be quantitatively evaluated.
+
+The goal of instance-wise feature selection (IWFS) is to find
+
+a minimal subset of features  $\pmb{x}_{\mathcal{S}^{(i)}}^{(i)}$  that are relevant to the corresponding target  $\pmb{y}^{(i)}$ , which was stated in eq. (1) as
+
+$$
+F (\mathbf {y} \mid \mathbf {x} _ {\mathcal {S} ^ {(i)}} = \boldsymbol {x} _ {\mathcal {S} ^ {(i)}} ^ {(i)}) = F (\mathbf {y} \mid \mathbf {x} = \boldsymbol {x} ^ {(i)}).
+$$
+
+The evaluation of IWFS should reflect the goal—the selections should be evaluated on the true conditional distribution  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{S}^{(i)}} = \boldsymbol{x}_{\mathcal{S}^{(i)}}^{(i)})$ . More generally, evaluating any potential selection of a subset of features  $\mathcal{R}$  requires access to  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$ . We propose a new method for evaluating AEMs, called EVAL-X, which trains an evaluator model  $q_{\mathrm{eval - x}}$  to estimate this distribution by maximizing
+
+$$
+\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {r} \sim \mathcal {B} (0. 5)} [ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \eta) ]. \tag {5}
+$$
+
+Here  $\mathbf{r}$  is sampled randomly, independent of  $\mathbf{x}$ , from a Bernoulli distribution, mimicking any potential selection of the input. At optimality, EVAL-X learns the true  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$ , which we show in appendix E. In practice, reaching optimality may be difficult. In appendix F.1 we compare the evaluations returned by EVAL-X against those returned by distinct models trained on each feature subset and show that EVAL-X performs similarly, where we consider the set of distinct models as ground truth. Algorithm 2 found in appendix B.1 summarizes the EVAL-X training procedure. In practice, predictive performance metrics returned by the EVAL-X should be used to quantitatively evaluate selections.
+
+Of note, this evaluation differs from the common approach of simply masking the uninformative features and seeing how performance degrades on a model trained on the full feature set. Chen et al. (2018) suggests evaluating using post-hoc accuracy following this approach. However, as mentioned by Hooker et al. (2019), samples where a subset of the features are masked are out of the distribution of the original input. Hooker et al. (2019) address these out of distribution issues with ROAR, where they suggest training and testing a model on samples from the same distribution of masked inputs,  $m(\mathbf{x},\mathbf{s})$ . However, this procedure allows the post-hoc evaluation model to learn the predictions encoded in the selector variable – precisely what should be avoided.
+
+Evaluating explanations using EVAL-X not only aligns with the goal of instance-wise feature selection (IWFS), but also addresses the out of distribution issues.
+
+# 5 REAL-X, LET US EXPLAIN!
+
+We now describe our method to ensure that the learned selections also respect the true data distribution given subsets of the input  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$ .
+
+JAMs learn to select features and make predictions in concert. This flexibility allows JAMs to learn to make predictions from information encoded in the choice of selections. If the predictor model is learned disjointly, however, this possibility is eliminated.
+
+Therefore, we propose learning the predictor model disjointly to approximate  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$  whilst learning to select the minimal subset of features to maximize the probability of the data. Given the insights of section 4, this procedure is expressed as learning  $q_{\mathrm{pred}}(\cdot ; \theta)$  to maximize
+
+$$
+\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {r} \sim \mathcal {B} (0. 5)} [ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \theta) ],
+$$
+
+while learning  $q_{\mathrm{sel}}(\cdot ;\beta)$  to maximize
+
+$$
+\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {s} \sim q _ {\text {s e l}} (\boldsymbol {s} | \boldsymbol {x}; \beta)} \left[ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) - \lambda R (\boldsymbol {s}) \right].
+$$
+
+This modification to the training procedure ensures that  $q_{\mathrm{pred}}$  respects the true data distribution and avoids encoding predictions within the learned selector variable.
+
+To make the method concrete,  $q_{\mathrm{sel}}$  and  $R$  need to be chosen. We introduce the following procedure as REAL-X:
+
+$$
+\max  _ {\beta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \mathbb {E} _ {\mathbf {s} _ {i} \sim \mathcal {B} (f _ {\beta} (\boldsymbol {x}) _ {i})} \left[ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) - \lambda \| \boldsymbol {s} \| _ {0} \right],
+$$
+
+$$
+\max  _ {\theta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \mathbb {E} _ {\boldsymbol {r} _ {i} \sim \mathcal {B} (0. 5)} [ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \theta) ]. \tag {6}
+$$
+
+REAL-x is a new AEM. REAL-x learns a global selector model to identify the subset of important features locally in any given instance of data. The selector model is trained on a global objective that measures selection fidelity. REAL-x uses discrete selections sampled independently from a Bernoulli distribution and penalizes the number of features selected.
+
+# 5.1 Implementation
+
+To optimize over discrete feature selections, REAL-x employs REBAR gradients (Tucker et al., 2017), a score function gradient estimator that uses relaxed continuous selections within a control variate to lower the variance of the gradient estimates. Algorithm 1 summarizes the training procedure (reference appendix A for eqs. (8) to (11)).
+
+# Algorithm 1 REAL-x Algorithm
+
+Input:  $\mathcal{D} := (\pmb{x},\pmb{y})$ , where  $\pmb{x} \in \mathbb{R}^{N\times D}$ , feature matrix;  $\pmb{y} \in \mathbb{R}^N$ , labels  
+Output:  $q_{\mathrm{sel}}(\cdot ;\beta)$ , function that returns feature selections given an instance of  $\mathbf{x}$  
+Select:  $\lambda$ , regularization constant;  $\alpha$ , learning rate;  $M$ , minibatch size,  $T$ , training-steps  
+for 1,...,  $T$  do
+
+Randomly sample mini-batch of size  $M$ $(\pmb{x}^{(i)},\pmb{y}^{(i)})_{i = 1}^{M}\sim \mathcal{D}$
+
+for  $i = 1,\dots,M$  do
+
+Sample Selections:
+
+$\pmb{r}^{(i)} \sim$  Bernoulli(0.5)
+
+Sample  $s^{(i)}, z^{(i)}$ , and  $\tilde{z}^{(i)}$  using  $q_{\mathrm{sel}}(\cdot ;\beta)$  as in
+
+eqs. (8) to (10)
+
+end
+
+Optimize Models:
+
+$\theta = \theta +\alpha \nabla_{\theta}\left[\frac{1}{M}\sum_{i = 1}^{M}\log q_{\mathrm{pred}}(\pmb{y}^{(i)}|m(\pmb{x}^{(i)},\pmb{r}^{(i)};\theta)\right]$  
+$\beta = \beta +\alpha \frac{1}{M}\sum_{i = 1}^{M}\hat{g}_{\beta}$ $(\hat{g}_{\beta}$  as in eq. (11))
+
+end
+
+Note that the user has the option to train  $q_{\mathrm{pred}}$  first, then optimize  $q_{\mathrm{sel}}$ . We show in appendix F.2 that this approach performs similarly. The algorithm makes clear that the predictor model is updated independently of REAL-x's learned selections and, therefore, cannot make accurate predictions from selections that directly encode the target or omit control flow features.
+
+# 6 EXPERIMENTS
+
+We have shown that existing AEMs can encode predictions within selections and fail to select features involved in control flow. We then introduced EVAL-X as a procedure for quantitatively evaluating explanations. Further, we proposed REAL-x as a simple method to address the issues with existing AEMs by mirroring our evaluation procedure.
+
+In order to properly evaluate REAL-x, we introduce BASE-x as a baseline to ensure that the results we obtain on REAL-x are not due to changes in the optimization procedure. BASE-x is a JAM that mimics the gradient optimization and regularization procedure of REAL-x. We evaluate all the JAMs - L2X $^3$ , INVASE $^4$ , and BASE-x - and our method, REAL-x, on a number of established Synthetic Datasets, MNIST, and on real-world Chest X-Rays.
+
+We show that REAL-x selects control flow features in synthetic data. On imaging data, we demonstrate that REAL-x obtains higher predictive performance on EVAL-X, while other method's seek to encode the classification. Further, we elicit expert radiologist feedback to rank the explanations of cardiomegaly returned by each method.
+
+# 6.1 Trading-Off Interpretability and Accuracy
+
+While the goal of IWFS (eq. (1)) assumes that a small human-interpretable subset of features generate the target, in practice there is a trade-off between interpretability and predictive accuracy. This trade-off has been discussed by many prior works (Selvaraju et al., 2019; Lakkaraju et al., 2017; Ishibuchi and Nojima, 2007).
+
+A simple explanation of the data, one with fewer features selected, allows for greater human interpretability. However, on real-word data this is likely to come at the cost of predictive accuracy. The AEMs considered optimize multiple objectives — an objective that measures the fidelity of the learned selections and an objective that measures the interpretability of the selections by limiting the number of features selected. By tuning the hyper-parameter balancing these objectives, different solutions along the multi-objective Pareto front can be reached to trade-off interpretability and predictive accuracy. For the real-world datasets, we, therefore, choose the hyper-parameter associated with the most interpretable solution such that the following condition is met: Accuracy (ACC) is within  $5\%$  of a model trained on
+
+the full feature set. We report the performance of the model trained on the full feature set, and refer to this model as FULL. For our synthetic datasets, we do not need to make this trade-off because we know that only a small number of interpretable features generate the target and instead chose the hyper-parameter that maximizes the accuracy.
+
+# 6.2 Evaluation
+
+We also evaluate the selections obtained by each method using the predictive performance measured by EVAL-X, which we denote as eAUROC and eACC. Together, we show that good predictive performance, as measured by AUROC and ACC, attained by L2X and INVASE does not imply good performance upon evaluation with EVAL-X. A phenomenon that we have described explicitly in section 3. Whereas, REAL-X is more robust to these issues.
+
+It is possible to use EVAL-X to select AEM models. However, for a JAM that at optimum encodes predictions or omits control flow features, the effectiveness of such a procedure would hinge on poor optimization of the JAM's objective.
+
+# 6.3 Synthetic Datasets
+
+Both L2X and INVASE evaluate their methods on a number of synthetic datasets<sup>2</sup>, where the data generation procedure is described as follows:
+
+$$
+\left\{\mathbf {x} _ {i} \right\} _ {i = 1} ^ {1 1} \sim \mathcal {N} (0, 1) \quad \mathbf {y} \sim \text {B e r n o u l l i} \left(\frac {1}{1 + f (\mathbf {x})}\right),
+$$
+
+The functions for  $f(\mathbf{x})$  vary as follows:
+
+$$
+\begin{array}{l} \bullet f _ {\mathbf {A}} (\mathbf {x}) = \exp (\mathbf {x} _ {1} \mathbf {x} _ {2}) \\ \cdot f _ {\mathbf {B}} (\mathbf {x}) = \exp \left(\sum_ {i = 3} ^ {6} \mathbf {x} _ {i} ^ {2} - 4\right) \\ \cdot f _ {\mathbf {C}} (\mathbf {x}) = \exp (- 1 0 \sin (0. 2 \mathbf {x} _ {7}) + | \mathbf {x} _ {8} | + \mathbf {x} _ {9} + e ^ {- \mathbf {x} _ {1 0}} - 2. 4), \\ \end{array}
+$$
+
+resulting in the following datasets
+
+$$
+\begin{array}{l} \bullet \mathbf {S 1}: I f x _ {1 1} <   0: f _ {\mathbf {A}} (\mathbf {x}); e l s e f _ {\mathbf {B}} (\mathbf {x}) \\ \bullet \mathrm {S 2}: \text {I f} \mathrm {x} _ {1 1} <   0: f _ {\mathbf {A}} (\mathbf {x}); \text {e l s e} f _ {\mathbf {C}} (\mathbf {x}) \\ \bullet \mathrm {S 3}: \text {I f} \mathrm {x} _ {1 1} <   0: f _ {\mathbf {B}} (\mathbf {x}); \text {e l s e} f _ {\mathbf {C}} (\mathbf {x}) \\ \end{array}
+$$
+
+This data generating process contains a control flow feature. Let  $\mathbf{x}_{\mathcal{A}} = \{\mathbf{x}_i\}_{i=1}^2$ ,  $\mathbf{x}_{\mathcal{B}} = \{\mathbf{x}_i\}_{i=3}^6$ ,  $\mathbf{x}_{\mathcal{C}} = \{\mathbf{x}_i\}_{i=7}^{10}$ , and  $F_J(\mathbf{y}|\mathbf{x}) := \text{Bernoulli}\left(\frac{1}{1 + f_J(\mathbf{x})}\right)$  for some function  $f_J$ .  $F(\mathbf{y}|\mathbf{x})$  in S1-3 is computed as a tree, where  $\mathbf{x}_{11}$  splits the data into the leaf conditional distributions  $F_A(\mathbf{y}|\mathbf{x}_{\mathcal{A}})$ ,  $F_B(\mathbf{y}|\mathbf{x}_{\mathcal{B}})$ , or  $F_C(\mathbf{y}|\mathbf{x}_{\mathcal{C}})$ . The feature sets  $\mathbf{x}_{\mathcal{A}}, \mathbf{x}_{\mathcal{B}}$ , and  $\mathbf{x}_{\mathcal{C}}$  are distinct and do not contain  $\mathbf{x}_{11}$ . Thus,  $\mathbf{x}_{11}$  is a control flow feature.
+
+Model training. The training and test sets both contained 10,000 samples of data. For all methods, we used neural networks with 3 hidden layers for the selector model and 2 hidden layers for the predictor model. The hidden layers were linear with dimension 200. All methods were trained for 1,000 epochs using Adam for optimization with a learning
+
+rate of  $10^{-4}$ . We tuned the hyper-parameters controlling the number of features to select across  $k = \{1,2,3,4,5,6,7\}$  for L2X and  $\lambda = \{0.05,0.075,.1,0.125,0.15,.2,.25\}$  for INVASE, REAL-x, and BASE-x. We select the configuration that yields the largest ACC.
+
+Table 1: REAL-x achieves superior CFSRs, TPRs, and post-hoc eAUROC on instance-wise tasks.  
+
+<table><tr><td>Metric</td><td>Method</td><td>S1</td><td>S2</td><td>S3</td></tr><tr><td rowspan="4">CFSR</td><td>REAL-x</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>L2x</td><td>24.3</td><td>31.2</td><td>61.5</td></tr><tr><td>INVASE</td><td>41.1</td><td>47.2</td><td>37.6</td></tr><tr><td>BASE-x</td><td>35.0</td><td>24.5</td><td>27.2</td></tr><tr><td rowspan="4">TPR</td><td>REAL-x</td><td>98.4</td><td>96.7</td><td>93.5</td></tr><tr><td>L2x</td><td>78.5</td><td>81.1</td><td>81.0</td></tr><tr><td>INVASE</td><td>80.6</td><td>80.4</td><td>86.3</td></tr><tr><td>BASE-x</td><td>84.7</td><td>75.6</td><td>83.5</td></tr><tr><td rowspan="4">FDR</td><td>REAL-x</td><td>10.7</td><td>6.3</td><td>2.6</td></tr><tr><td>L2x</td><td>22.0</td><td>20.2</td><td>19.0</td></tr><tr><td>INVASE</td><td>1.3</td><td>3.1</td><td>1.1</td></tr><tr><td>BASE-x</td><td>1.3</td><td>1.6</td><td>1.1</td></tr><tr><td rowspan="4">AUROC</td><td>REAL-x</td><td>0.782</td><td>0.805</td><td>0.875</td></tr><tr><td>L2x</td><td>0.752</td><td>0.790</td><td>0.852</td></tr><tr><td>INVASE</td><td>0.803</td><td>0.806</td><td>0.886</td></tr><tr><td>BASE-x</td><td>0.799</td><td>0.805</td><td>0.886</td></tr><tr><td rowspan="4">eAUROC</td><td>REAL-x</td><td>0.774</td><td>0.804</td><td>0.873</td></tr><tr><td>L2x</td><td>0.742</td><td>0.771</td><td>0.848</td></tr><tr><td>INVASE</td><td>0.740</td><td>0.783</td><td>0.868</td></tr><tr><td>BASE-x</td><td>0.762</td><td>0.773</td><td>0.867</td></tr><tr><td rowspan="4">ACC</td><td>REAL-x</td><td>70.1%</td><td>71.5%</td><td>79.6%</td></tr><tr><td>L2x</td><td>67.1%</td><td>70.5%</td><td>76.7%</td></tr><tr><td>INVASE</td><td>71.3%</td><td>71.4%</td><td>80.6%</td></tr><tr><td>BASE-x</td><td>71.0%</td><td>71.2%</td><td>80.6%</td></tr><tr><td rowspan="4">eACC</td><td>REAL-x</td><td>68.6%</td><td>71.2%</td><td>79.3%</td></tr><tr><td>L2x</td><td>68.4%</td><td>70.1%</td><td>76.9%</td></tr><tr><td>INVASE</td><td>66.8%</td><td>69.2%</td><td>78.8%</td></tr><tr><td>BASE-x</td><td>68.5%</td><td>68.8%</td><td>78.7%</td></tr><tr><td rowspan="4">k or λ</td><td>REAL-x</td><td>0.05</td><td>0.05</td><td>0.1</td></tr><tr><td>L2x</td><td>4</td><td>4</td><td>5</td></tr><tr><td>INVASE</td><td>0.2</td><td>0.15</td><td>0.2</td></tr><tr><td>BASE-x</td><td>0.15</td><td>0.125</td><td>0.2</td></tr></table>
+
+Results. We summarize our results for each dataset, paying special attention to the control flow feature selection rate (CFSR), defined by the proportion of control flow features selected. We also include the ACC, AUROC, the TPR, defined by the proportion of important features selected, the FDR, defined by the proportion of selected features that are not important, and the corresponding EVAL-X evaluation metrics (eAUROC, eACC). We summarize these results in Table 1, which show that only REAL-X consistently selects the control flow feature and attains a higher TPR, eAUROC, and
+
+eACC. From lemma 2 in section 3.2 we expect that JAMs should never select the control flow feature. However, the fact that JAMs occasionally do so is due to either incomplete optimization (INVASE) or no preference in selecting the control feature (L2X when  $k$  is large enough). Yet, requiring REAL-x to predict well from random selections results in a slightly greater FDR. By not selecting control flow features, L2X and INVASE achieve lesser TPRs. Though REAL-x often does not obtain the highest AUROC and ACC, it obtains greater eAUROC and eACC upon evaluation with EVAL-X due to the selection of the control flow feature. These results help highlight REAL-x's ability to address issues that prior methods have with selecting control flow features.
+
+# 6.4 MNIST
+
+The MNIST dataset (LeCun et al., 1998) is comprised of 70,000,  $28 \times 28$  images of handwritten digits in  $\{0, \dots, 9\}$ .
+
+Model training. The images were trained using 60,000 samples and evaluated on 10,000 samples. For all methods, we used neural networks with 3 hidden layers for the selector model and 2 hidden layers for the predictor model. The hidden layers were linear with dimension 200. All methods were trained for 500 epochs using Adam for optimization with a learning rate of  $10^{-4}$ . We tuned the hyper-parameters controlling the number of features to select across  $k = \{1,5,15,50,100,200\}$  for L2X and  $\lambda = \{0.1,1.0,5.0,10.0,25.0,50.0\}$  for INVASE, REAL-x, and BASE-x. We then selected the configuration that allowed for the smallest number of features to be selected while retaining an ACC within  $5\%$  of that obtained by a model trained on the full feature set.
+
+Table 2: Digit pixels selected by REAL-x yield superior results upon post-hoc evaluation.  
+
+<table><tr><td>Method</td><td>ACC</td><td>AUROC</td><td>eACC</td><td>eAUROC</td><td>k\λ</td></tr><tr><td>FULL</td><td>97.8%</td><td>0.999</td><td>—</td><td>—</td><td>—</td></tr><tr><td>REAL-x</td><td>93.8%</td><td>0.997</td><td>86.7%</td><td>0.989</td><td>5.0</td></tr><tr><td>L2X</td><td>96.0%</td><td>0.998</td><td>11.4%</td><td>0.561</td><td>1</td></tr><tr><td>INVASE</td><td>93.1%</td><td>0.996</td><td>50.3%</td><td>0.883</td><td>10.0</td></tr><tr><td>BASE-x</td><td>92.8%</td><td>0.996</td><td>56.9%</td><td>0.899</td><td>10.0</td></tr></table>
+
+Results. Table 2 shows that while L2X, INVASE, and BASE-x all make selections that allow for high predictive performance (ACC  $\geq 92.8\%$ ), when evaluated with EVAL-X the predictive performance is significantly worse. Looking at the selections made by each method on fig. 3 helps clarify this discrepancy. As we saw earlier, L2X can encode the prediction with a single feature. We also see evidence of encoding with BASE-x, where certain digits,  $\{1,7\}$ , are encoded by the selection of a few features or no features. INVASE, however, seems to optimize poorly in high-dimensions and instead selects a conserved set of features across dig-
+
+![](images/ae72cf4646476b5153a6de08f2ad99d943b31a0479bb35783bf641ec6211dbec.jpg)  
+Figure 3: REAL-x makes reasonable selections, with other methods encode predictions. Each column is labeled with the method used to learn selections. For each digit two random samples are provided and selections are presented in dark red.
+
+![](images/d4e7b834d156e9c645c82cba8b3aa459e9bd9f6f331a27d716107c6ac96071e7.jpg)  
+Figure 4: REAL-x makes reasonable selections around the margins of the heart without encoding the prediction. 5 random samples of Cardiomegaly and Normal Chest X-Rays are presented for each method. The selected inputs are places beside images with the selections overlaid in red.
+
+its. REAL-x, however, performs far better upon EVAL-X evaluation. Also, REAL-x's selections appear reasonable, selecting pixels along the entire digit or along regions that help distinguish digits.
+
+# 6.5 Chest X-Ray Images
+
+The NIH ChestX-ray8 Dataset<sup>5</sup> (Wang et al., 2017) contains 112, 120 chest X-ray images from 30, 805 patients, each labeled with the presence of 8 diseases. We selected a subset of 5,600 X-rays labeled either cardiomegaly or normal, including all 2,776 X-rays with cardiomegaly. Cardiomegaly is characterized by an enlarged heart, and can be diagnosed by measuring the maximal horizontal diameter of the heart relative to that of the chest cavity and assessing the contour
+
+of the heart. Given this, we expect to see selections that establish the margins of the heart and chest cavity.
+
+Model training. We used 5,000, 300, and 300 images for training, validation, and testing respectively. UNet and DenseNet121 architectures were used for the selector and predictor models respectively. All methods were trained for 50 epochs using a learning rate of  $10^{-4}$ . We choose to learn  $16 \times 16$  super-pixel selections. We tuned the hyper-parameters controlling the number of features to select across  $k = \{1,5,15,50,100\}$  for L2X and  $\lambda = \{0.1,1.0,2.5,5.0,50.0\}$  for INVASE, REAL-x, and BASE-X. We then selected the configuration that allowed for the smallest number of features to be selected while retaining an ACC within  $5\%$  of that obtained by a model trained on the full feature set.
+
+Table 3: REAL-x yields superior post-hoc evaluation.  
+
+<table><tr><td>Method</td><td>ACC</td><td>AUROC</td><td>eACC</td><td>eAUROC</td><td>k\λ</td></tr><tr><td>FULL</td><td>78.0%</td><td>0.887</td><td>—</td><td>—</td><td>—</td></tr><tr><td>REAL-x</td><td>75.0%</td><td>0.838</td><td>70.3%</td><td>0.777</td><td>2.5</td></tr><tr><td>L2X</td><td>75.0%</td><td>0.848</td><td>54.0%</td><td>0.581</td><td>10</td></tr><tr><td>INVASE</td><td>74.3%</td><td>0.819</td><td>52.3%</td><td>0.548</td><td>2.5</td></tr><tr><td>BASE-x</td><td>74.3%</td><td>0.818</td><td>51.7%</td><td>0.595</td><td>2.5</td></tr></table>
+
+Results. Table 3 shows that while each method makes selections that allow for high predictive performance (ACC  $\geq$ $73.0\%$ ), REAL-X yields superior performance upon EVAL-X evaluation. Looking at selections of random Chest X-rays in fig. 4, we see that L2X, BASE-X and INVASE seem to make counterintuitive selections that omit many of the important pixels, resulting in a sharp decline in eACC.
+
+Table 4: Average rankings by expert radiologists.  
+
+<table><tr><td>REAL-x</td><td>L2X</td><td>INVASE</td><td>BASE-x</td></tr><tr><td>1.08 (0.04)</td><td>3.57 (0.10)</td><td>2.85 (0.11)</td><td>2.29 (0.09)</td></tr></table>
+
+Physician Evaluation. We asked two expert radiologists to rank each method based on the explanations provided. We randomly selected 50 Chest X-rays from the test set and displayed the selections made by each method for each X-ray in a random order to each radiologist. For a given Chest X-ray, the radiologists then evaluated which selections provided sufficient information to diagnose cardiomegaly and ranked the four options provided, allowing for ties. In table 4 we report the average rank each method achieved. We see that REAL-X consistently provides explanations that are meaningful to board-certified radiologists.
+
+# 7 DISCUSSION
+
+We proposed REAL-X, an AEM that provides interpretations that give high likelihood to the data efficiently with a single forward pass. Further, we introduced EVAL-X as a method to evaluate interpretations, detecting when predictions are encoded in explanations without making out-of-distribution queries of a model. EVAL-X produces an evaluator model to approximate the true data generating distribution given any subset of the input. One future direction could be to produce feature attributions, such as Shapley values, recognizing the evaluator model as a function on subsets for any data point.
+
+With REAL-X, we employ amortization to provide fast interpretations. Amortization can help make many existing interpretation techniques scalable, though, as exemplified by JAMs, care must be taken to avoid encoding predictions within interpretations. For example, learning a locally linear model to explain each instance of data can be amortized by learning an global explanation model that takes an instance as input and outputs the parameters of a linear model that
+
+predicts the target for that instance. As with JAMs, the parameters outputted by the explanation model can be used to encode the target.
+
+In addition to extending our methodology to allow for feature attributions, one can explore tailoring it for use with specific data modalities. For example, saliency maps are generally more human interpretable if the segmentation is smooth instead of disjoint pixel selections, as in fig. 3. We leave these avenues for future work.
+
+# Acknowledgements
+
+We thank Dr. Lea Azour and Dr. William Moore for clinically evaluating each Chest X-ray explanation. We also thank the reviewers for their thoughtful feedback.
+
+Neil Jethani was partially supported by NIH T32 GM136573. Mukund Sudarshan was partially supported by a PhRMA Foundation Predoctoral Fellowship. Yin Aphinyanaphongs was partially supported by NIH 3UL1TR001445-05 and National Science Foundation award #1928614. Mukund Sudarshan and Rajesh Ranganath were partly supported by NIH/NHLBI Award R01HL148248, and by NSF Award 1922658 NRT-HDR: FUTURE Foundations, Translation, and Responsibility for Data Science.
+
+# Bibliography
+
+Adebayo, J., Gilmer, J., Muelly, M., Goodfellow, I., Hardt, M., and Kim, B. (2018). Sanity checks for saliency maps. In Advances in Neural Information Processing Systems, pages 9505-9515.  
+Chen, J., Song, L., Wainwright, M., and Jordan, M. (2018). Learning to explain: An information-theoretic perspective on model interpretation. In International Conference on Machine Learning, pages 883-892.  
+Dabkowski, P. and Gal, Y. (2017). Real time image saliency for black box classifiers.  
+Glynn, P. W. (1990). Likelihood ratio gradient estimation for stochastic systems. Communications of the ACM, 33(10):75-84.  
+Hooker, S., Erhan, D., Kindermans, P.-J., and Kim, B. (2019). A benchmark for interpretability methods in deep neural networks. In Wallach, H., Larochelle, H., Beygelzimer, A., d'Alché-Buc, F., Fox, E., and Garnett, R., editors, Advances in Neural Information Processing Systems 32, pages 9737-9748. Curran Associates, Inc.  
+Ishibuchi, H. and Nojima, Y. (2007). Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. International Journal of Approximate Reasoning, 44(1):4-31.  
+Jang, E., Gu, S., and Poole, B. (2017). Categorical reparameterization with gumbel-softmax. In International Conference on Learning Representations.
+
+Kingma, D. P. and Welling, M. (2014). Auto-encoding variational bayes.  
+Lakkaraju, H., Kamar, E., Caruana, R., and Leskovec, J. (2017). Interpretable & explorable approximations of black box models.  
+LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. (1998). Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278-2323.  
+Lipton, Z. C. (2017). The mythos of model interpretability.  
+Lundberg, S. M. and Lee, S. I. (2017). A unified approach to interpreting model predictions. In Advances in Neural Information Processing Systems, volume 2017-Decem, pages 4766-4775. Neural information processing systems foundation.  
+Maddison, C. J., Mnih, A., and Teh, Y. W. (2016). The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. 5th International Conference on Learning Representations, ICLR 2017 - Conference Track Proceedings.  
+Ribeiro, M. T., Singh, S., and Guestrin, C. (2016). " why should i trust you?" explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pages 1135-1144.  
+Samek, W., Binder, A., Montavon, G., Lapuschkin, S., and MÄÖller, K. R. (2017). Evaluating the Visualization of What a Deep Neural Network Has Learned. IEEE Transactions on Neural Networks and Learning Systems, 28(11):2660-2673.  
+Schwab, P. and Karlen, W. (2019). Cxplain: Causal explanations for model interpretation under uncertainty.  
+Selvaraju, R. R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., and Batra, D. (2019). Grad-cam: Visual explanations from deep networks via gradient-based localization. International Journal of Computer Vision, 128(2):336-359.  
+Shrikumar, A., Greenside, P., and Kundaje, A. (2017). Learning important features through propagating activation differences. In International Conference on Machine Learning, pages 3145-3153.  
+Silver, D., Schrittwieser, J., Simonyan, K., Antonoglou, I., Huang, A., Guez, A., Hubert, T., Baker, L., Lai, M., Bolton, A., et al. (2017). Mastering the game of go without human knowledge. nature, 550(7676):354-359.  
+Simonyan, K., Vedaldi, A., and Zisserman, A. (2013). Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps. 2nd International Conference on Learning Representations, ICLR 2014 - Workshop Track Proceedings.
+
+Springenberg, J. T., Dosovitskiy, A., Brox, T., and Ried-miller, M. (2014). Striving for Simplicity: The All Convolutional Net. 3rd International Conference on Learning Representations, ICLR 2015 - Workshop Track Proceedings.  
+Tucker, G., Mnih, A., Maddison, C. J., Lawson, J., and Sohl-Dickstein, J. (2017). Rebar: Low-variance, unbiased gradient estimates for discrete latent variable models. In Advances in Neural Information Processing Systems, pages 2627-2636.  
+Wang, X., Peng, Y., Lu, L., Lu, Z., Bagheri, M., and Summers, R. M. (2017). Chestx-ray8: Hospital-scale chest x-ray database and benchmarks on weakly-supervised classification and localization of common thorax diseases. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).  
+Williams, R. J. (1992). Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8(3-4):229-256.  
+Yoon, J., Jordan, J., and van der Schaar, M. (2019). INVASE: Instance-wise variable selection using neural networks. In International Conference on Learning Representations.  
+Zech, J. R., Badgeley, M. A., Liu, M., Costa, A. B., Titano, J. J., and Oermann, E. K. (2018). Variable generalization performance of a deep learning model to detect pneumonia in chest radiographs: a cross-sectional study. *PLoS medicine*, 15(11):e1002683.  
+Zeiler, M. D. and Fergus, R. (2014). Visualizing and understanding convolutional networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), volume 8689 LNCS, pages 818-833. Springer Verlag.  
+Zhou, J. and Troyanskaya, O. G. (2015). Predicting effects of noncoding variants with deep learning-based sequence model. Nature Methods, 12(10):931-934.  
+Zintgraf, L. M., Cohen, T. S., Adel, T., and Welling, M. (2017). Visualizing Deep Neural Network Decisions: Prediction Difference Analysis. 5th International Conference on Learning Representations, ICLR 2017 - Conference Track Proceedings.
+
+# Supplementary Materials
+
+# A Applying REBAR Gradient Estimation to REAL-X
+
+Computing the gradient of an expectation of a function with respect to the parameters of a discrete distribution requires calculating score function gradients. Score function gradients often have high variance. To reduce this variance, control variates are used within the objective. REBAR gradient calculation involves using a highly correlated control variate that approximates the discrete distribution with its continuous relaxation.
+
+The REAL-  $\mathrm{x}$  procedure involves
+
+$$
+\operatorname * {m a x} _ {\beta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \mathbb {E} _ {\boldsymbol {s} _ {i} \sim \mathcal {B} (f _ {\beta} (\boldsymbol {x}) _ {i})} \left[ \log q _ {\mathrm {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) - \lambda \| \boldsymbol {s} \| _ {0} \right].
+$$
+
+This is accomplished through stochastic gradient ascent by taking
+
+$$
+\nabla_ {\beta} \mathbb {E} _ {\mathbf {s} _ {i} \sim \mathcal {B} \left(f _ {\beta} (\boldsymbol {x}) _ {i}\right)} \left[ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta) - \lambda \| \boldsymbol {s} \| _ {0} \right], \tag {7}
+$$
+
+which requires score function gradient estimation.
+
+Let  $\mathbf{s}$  be a discrete random variable,  $\mathcal{L} = \mathbb{E}_{\mathbf{s} \sim q_{\beta}}[h(\mathbf{s})]$ , and  $\mathbb{E}[\hat{g}_{\beta}] = \nabla_{\beta}\mathcal{L}$ , the REBAR gradient estimator (Tucker et al., 2017) computes  $\hat{g}_{\beta}$ . Then, letting  $\mathbf{z}$  be a continuous relaxation of  $\mathbf{s}$ , REBAR estimates the gradient as
+
+$$
+\hat {g} _ {\beta} = \left[ h (\boldsymbol {s}) - h (\tilde {\boldsymbol {z}}) \right] \nabla_ {\beta} \log q _ {\beta} (\boldsymbol {s}) - \nabla_ {\beta} h (\tilde {\boldsymbol {z}}) + \nabla_ {\beta} h (\boldsymbol {z}),
+$$
+
+where  $\pmb {s} = B(\pmb {z}),\pmb {z}\sim q_{\beta}(\mathbf{z}),\tilde{\pmb{z}}\sim q_{\beta}(\mathbf{z}|\pmb {s})$
+
+To estimate eq. (7) using REBAR, REAL-x sets
+
+$$
+h (\boldsymbol {s}) = \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s}); \theta).
+$$
+
+Here,  $\mathbf{s}$  is Bernoulli distributed and REAL- $\mathbf{x}$  sets  $\mathbf{z}$  to be distributed as the binary equivalent of the Concrete distribution (Maddison et al., 2016; Jang et al., 2017), which we refer to as the RelaxedBernoulli distribution.  $\mathbf{s}$ ,  $\mathbf{z}$ , and  $\tilde{\mathbf{z}}$  are sampled as described by Tucker et al. (2017) such that
+
+$$
+p _ {i} = f _ {\beta} (\boldsymbol {x}) _ {i},
+$$
+
+$$
+\boldsymbol {s} _ {i} = B \left(\boldsymbol {z} _ {i}\right) = \mathbb {1} \left(\boldsymbol {z} _ {i} > 0\right), \tag {8}
+$$
+
+$$
+\boldsymbol {z} _ {i} \sim q _ {\beta} (\mathbf {z} \mid \boldsymbol {x}) = \text {R e l a x e d B e r n o u l l i} \left(p _ {i}; \tau = 0. 1\right), \tag {9}
+$$
+
+$$
+\tilde {\mathbf {z}} _ {i} \sim q _ {\beta} (\mathbf {z} \mid \mathbf {x}, \mathbf {s}) = \frac {1}{0 . 1} \left(\log \frac {p _ {i}}{1 - p _ {i}} + \log \frac {\mathbf {v} ^ {\prime}}{1 - \mathbf {v} ^ {\prime}}\right), \tag {10}
+$$
+
+$$
+\text {w h e r e} \boldsymbol {v} \sim \operatorname {U n i f} (0, 1) \text {a n d} \boldsymbol {v} ^ {\prime} = \left\{ \begin{array}{l l} \mathbf {v} (1 - p _ {i}) & \text {i f} \boldsymbol {s} _ {i} = 0 \\ \mathbf {v} p _ {i} + (1 - p _ {i}) & \text {i f} \boldsymbol {s} _ {i} = 1 \end{array} \right..
+$$
+
+Then to estimate eq. (7) notice that
+
+$$
+\nabla_ {\beta} \mathbb {E} _ {\mathbf {s} _ {i} \sim \mathcal {B} (f _ {\beta} (\boldsymbol {x}) _ {i})} [ \lambda \| \boldsymbol {s} \| _ {0} ] = \lambda \nabla_ {\beta} f _ {\beta} (\mathbf {x}).
+$$
+
+REAL-x, therefore, estimates eq. (7) by calculating  $\hat{g}_{\beta}$  as
+
+$$
+\begin{array}{l} \hat {g} _ {\beta} = \left[ \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {s})) - \log q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \tilde {\boldsymbol {z}})) \right] \nabla_ {\beta} \log q _ {\text {s e l}} (\boldsymbol {s} \mid \boldsymbol {x}; \beta) - \lambda \nabla_ {\beta} f _ {\beta} (\boldsymbol {x}) \\ - \nabla_ {\beta} q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \tilde {\boldsymbol {z}})) + \nabla_ {\beta} q _ {\text {p r e d}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {z})) \tag {11} \\ \end{array}
+$$
+
+# B Algorithms
+
+# B.1 Evaluation Algorithm
+
+Algorithm 2 Algorithm to Train Evaluator Model  $q_{\mathrm{eval - x}}$  
+Input:  $\mathcal{D}:= (\pmb{x},\pmb{y})$  where  $\pmb{x}\in \mathbb{R}^{N\times D}$  , feature matrix;  $\pmb{y}\in \mathbb{R}^N$  , labels   
+Output:  $q_{\mathrm{eval - x}}(\mathbf{y}|m(\mathbf{x},\cdot);\eta)$  , function that returns the probability of the target given a subset of features.   
+Select:  $\alpha$  , learning rate;  $M$  , mini-batch size   
+while Converge do Randomly sample mini-batch of size  $M$ $(\pmb {x}^{(i)},\pmb{y}^{(i)})_{i = 1}^{M}\sim \mathcal{D}$  for  $i = 1,\dots,M$  do Sample Selections:  $\pmb{r}^{(i)}\sim \mathrm{Bernoulli}(0.5)$  end Optimize:  $\eta = \eta +\alpha \nabla_{\eta}\left[\frac{1}{M}\sum_{i = 1}^{M}\log q_{\mathrm{eval - x}}(\pmb{y}^{(i)}|m(\pmb{x}^{(i)},\pmb{r}^{(i)});\eta)\right]$    
+end
+
+# C Lemmas
+
+Lemma 3. Let  $\mathbf{x} \in \mathbb{R}^D$ , target  $\mathbf{y} \in \{1, \dots, K\}$ , and  $\Delta$  be a set of  $K$  dimensional probability vectors, then for  $J = \arg \min_j \sum_{i=0}^j \binom{D}{i} \geq |\Delta|$  and  $\mathbf{x} \sim F$ , there exists a  $q_{sel}$  and  $q_{pred}$ , where  $\{q_{pred}(y = k \mid m(\mathbf{x}, \mathbf{s}))\}_{k=1}^K = \delta(\mathbf{x}) \in \Delta$  and  $E[||\mathbf{s}||_0] \leq J$ .
+
+# D Proofs
+
+# D.1 Proof of Lemma 1
+
+Lemma 1. Let  $\mathbf{x} \in \mathbb{R}^D$  and target  $\mathbf{y} \in \{1, \dots, K\}$ . If  $\mathbf{y}$  is a deterministic function of  $\mathbf{x}$  and  $K \leq D$ , then JAMs with monotone increase regularizers  $R$  will select at most one feature at optimality.
+
+As mentioning in section 3, the lemma considers the masking function from eq. (2) and on independent Bernoulli selector variables  $\mathbf{s}_j\sim$  Bernoulli  $(f_{\beta}(\mathbf{x})_j)$ .
+
+$\mathbf{s} \in \mathbb{R}^D$  is binary and, therefore, has the capacity to transmit D bits of information. Given that  $\mathbf{y} \in \{1, \dots, K\}$  is a deterministic function of  $\mathbf{x} \in \mathbb{R}^D$ , the true distribution is  $F(\mathbf{y} \mid \mathbf{x}) \in \{0, 1\}$  for each of the  $K$  realizations of  $\mathbf{y}$ . Therefore,  $m(\mathbf{x}, \mathbf{s})$  must pass at least  $\log_2 K$  bits of information to the predictor model  $q_{\mathrm{pred}}(\mathbf{y} \mid m(\mathbf{x}, \mathbf{s}))$ .
+
+With  $m$  of the form eq. (2), this information content can come from  $s$ .  $s$  has a capacity of  $\log_2\left(\sum_{i = 1}^n\binom{D}{i}\right)$  bits when restricted to realizations of  $s \sim q_{\mathrm{sel}}$  with at most  $n$  non-zero elements. The maximal number of non-zero elements  $J$  in any given realization of  $s$  required to minimally transmit  $\log_2K$  bits of information with  $s$  can be expressed as
+
+$$
+J = \operatorname *{arg  min}_{j}\sum_{i = 0}^{j}\left( \begin{array}{c}D\\ i \end{array} \right)\geq K.
+$$
+
+Given  $K \leq D$ , the maximal number of selections required is given by  $J = 1$ , where  $\binom{D}{1} = D \geq K$ . Therefore there exists a  $q_{\mathrm{pred}}$  and  $q_{\mathrm{sel}}$  such that  $\mathbb{E}[q_{\mathrm{pred}}(\boldsymbol{y} \mid m(\boldsymbol{x}, \boldsymbol{s}))] = \mathbb{E}[F(\boldsymbol{y} \mid \boldsymbol{x})]$  and  $\mathbb{E}[||\mathbf{s}||_0] \leq 1$ . For monotone increasing regularizer  $R$ , any solution that selects more than a single feature will have a lower JAM objective. Therefore, at optimally, JAMs will select at most a single feature.
+
+# D.2 Proof of Lemma 3
+
+Lemma 3. Let  $\mathbf{x} \in \mathbb{R}^D$ , target  $\mathbf{y} \in \{1, \dots, K\}$ , and  $\Delta$  be a set of  $K$  dimensional probability vectors, then for  $J = \arg \min_j \sum_{i=0}^j \binom{D}{i} \geq |\Delta|$  and  $\mathbf{x} \sim F$ , there exists a  $q_{sel}$  and  $q_{pred}$ , where  $\{q_{pred}(y = k \mid m(\mathbf{x}, \mathbf{s}))\}_{k=1}^K = \delta(\mathbf{x}) \in \Delta$  and  $E[||\mathbf{s}||_0] \leq J$ .
+
+This proof follows from the proof in appendix D.1. Given  $\mathbf{x} \in \mathbb{R}^D$  and target  $\mathbf{y} \in \{1, \dots, K\}$ , there exists a distribution  $q_{\mathrm{pred}}(\mathbf{y} \mid m(\mathbf{x}, \mathbf{s}))$  such that each realization of  $\mathbf{s} \in \{0, 1\}^D$  has a bijective mapping to a unique probability vector obtained as  $\{q_{\mathrm{pred}}(y = k \mid m(\mathbf{x}, \mathbf{s}))\}_{k=1}^{K} \in \mathbb{R}^K$ .
+
+As stated in the proof of lemma 1 s has a capacity of  $\log_2\left(\sum_{i=1}^{n}\binom{D}{i}\right)$  bits when restricted to realizations of  $s \sim q_{\mathrm{sel}}$  with at most  $n$  non-zero elements. Given a set of  $K$  dimensional probability vectors  $\Delta$ , the maximal number of non-zero selections in  $s$  required to produce at least  $|\Delta|$  unique realizations of  $s$ , denoted by  $J$ , can be expressed as
+
+$$
+J = \underset {j} {\arg \min} \sum_ {i = 0} ^ {j} \binom {D} {i} \geq | \Delta |.
+$$
+
+Then there exists a  $q_{\mathrm{pred}}$  and  $q_{\mathrm{sel}}$  such that there are at least  $|\Delta|$  unique probability vectors  $\{q_{\mathrm{pred}}(y = k \mid m(\mathbf{x}, \mathbf{s}))\}_{k=1}^{K} = \delta(\mathbf{x}) \in R^K$  where  $\delta(\mathbf{x}) \in \Delta$  and the average number of features selected  $E[||\mathbf{s}||_0] \leq J$ .
+
+# D.3 Proof of Lemma 2
+
+Lemma 2. Assume that the true  $F(\mathbf{y} \mid \mathbf{x})$  is computed as a tree, where the leaves  $\ell_i$  are the conditional distributions  $F_i(\mathbf{y} \mid \mathbf{x}_{S_i})$  of  $\mathbf{y}$  given distinct subsets of features  $S_i$  in  $\mathbf{x}$ . Given a monotone increasing regularizer  $R(|S_i|)$ , the preferred maximizer of the JAM objective excludes control flow features.
+
+The main intuition behind the proof of lemma 2 is as follows. The JAM objective results in a prediction model that does not require the control flow features to achieve optimal performance. As a result of the monotone increasing regularizer  $R$ , which assigns a cost for selecting each additional feature, the JAM objective omits control flow features. We now prove this idea formally.
+
+The tree is structured such that each leaf  $\ell_i$  in the tree has a corresponding conditional distribution  $F_{i}(\mathbf{y}\mid \mathbf{x}_{S_{i}})$  parameterized by a set of features  $S_{i}$  such that  $\forall j\neq i,S_{i}\neq S_{j}$ . Let the features found along the path from the root of the tree to the leaf, including those found at the leaf, be defined as  $\mathcal{T}_i$  for each leaf  $\ell_i$ . Those features that are not in the leaf and only appear in the non-leaf nodes of the tree are the control flow features defined as  $\mathcal{C}_i\coloneqq \mathcal{T}_i\backslash \mathcal{S}_i$ . For any input  $\pmb{x}$ , let  $\mathcal{T}(\pmb {x})$  be the features found along the path used in generating the response for that  $\pmb{x}$  and define the control flow features along the path as  $\mathcal{C}(\pmb {x})$  and set of leaf features  $S(x)$ .
+
+Consider the following cases where  $q_{\mathrm{sel}}(\mathbf{s} \mid \mathbf{x})$  selects the  $j$ th feature with probability
+
+$$
+\left\{ \begin{array}{l l} q _ {\text {s e l 1}} (\mathbf {s} _ {j} \mid \boldsymbol {x}) = \mathbb {1} [ j \in \mathcal {T} (\boldsymbol {x}) ] = \mathbb {1} [ j \in \{\mathcal {C} (\boldsymbol {x}) \cup \mathcal {S} (\boldsymbol {x}) \} ] & \text {(C a s e 1)} \\ q _ {\text {s e l 1}} (\mathbf {s} _ {j} \mid \boldsymbol {x}) = \mathbb {1} [ j \in \mathcal {S} (\boldsymbol {x}) ] & \text {(C a s e 2)} \end{array} , \right.
+$$
+
+where  $q_{\mathrm{sel1}}$  and  $q_{\mathrm{sel1}}$  denotes the  $q_{\mathrm{sel}}$  for case 1 and case 2 respectively.  $q_{\mathrm{pred1}}(\mathbf{y} \mid m(\mathbf{x}, \mathbf{s}))$  and  $q_{\mathrm{pred2}}(\mathbf{y} \mid m(\mathbf{x}, \mathbf{s}))$  are defined in the corresponding manner.
+
+In case 1, the predictor model  $q_{\mathrm{pred}1}$  receives all the relevant features from  $q_{\mathrm{sel}1}$ , such that  $\mathbb{E}_{\boldsymbol{x},\boldsymbol{y}\sim F}\mathbb{E}_{\boldsymbol{s}\sim q_{\mathrm{sel}1}(\boldsymbol{s}|\boldsymbol{x})}[\log q_{\mathrm{pred}1}(\boldsymbol{y}|\boldsymbol{m}(\boldsymbol{x},\boldsymbol{s}))]$  can predict as well as possible.
+
+In case 2, however, the predictor model  $q_{\mathrm{pred2}}(\mathbf{y} \mid m(\pmb{x}, \pmb{s}))$  does not receive the full set of relevant features from  $q_{\mathrm{sel2}}$ ; it only receives the leaf features. Since the leaf features are unique across leaves, the selections indicated by  $\pmb{s}$  provides enough information for the predictor model to consistently learn the correct data generating leaf conditional  $F(\mathbf{y} \mid \pmb{x}_{S(\pmb{x})})$ , meaning that it can predict as well as possible.
+
+Assuming the models maximize the JAM objective, in both cases  $q_{\mathrm{pred}}$  together with  $q_{\mathrm{sel}}$  correctly model  $F(\mathbf{y} \mid \mathbf{x})$ . Plugging this information into the JAM objective in eq. (3) yields the following:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {C a s e 1}} = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\mathcal {T} (\boldsymbol {x}) \sim q _ {\text {s e l l}} (\boldsymbol {s} \mid \boldsymbol {x})} \left[ \log q _ {\text {p r e d 1}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \mathcal {T} (\boldsymbol {x}))) - \lambda R (| \mathcal {T} (\boldsymbol {x}) |) \right] \\ = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} [ \log F (\boldsymbol {y} \mid \boldsymbol {x}) ] - \lambda \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\mathcal {T} (\boldsymbol {x}) \sim q _ {\text {s e l l}} (\boldsymbol {s} \mid \boldsymbol {x})} [ R (| \mathcal {T} (\boldsymbol {x}) |) ], \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {C a s e 2}} = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {S} (\boldsymbol {x}) \sim q _ {\text {s e l 2}} (\boldsymbol {s} \mid \boldsymbol {x})} [ \log q _ {\text {p r e d 2}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {S} (\boldsymbol {x}))) - \lambda R (| \boldsymbol {S} (\boldsymbol {x}) |) ] \\ = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} [ \log F (\boldsymbol {y} \mid \boldsymbol {x}) ] - \lambda \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\mathcal {S} (\boldsymbol {x}) \sim q _ {\mathrm {s e l 2}} (\boldsymbol {s} \mid \boldsymbol {x})} [ R (| \mathcal {S} (\boldsymbol {x}) |) ]. \\ \end{array}
+$$
+
+Given that  $R(.)$  is monotone increasing, the following inequality holds:
+
+$$
+\mathcal {L} _ {\text {C a s e 2}} \geq \mathcal {L} _ {\text {C a s e 1}}.
+$$
+
+For any  $\lambda > 0$  where control flow features are involved in the data generating process, that is  $\mathcal{C}_i \neq \emptyset$  for some  $i$ , this inequality is strict. Therefore, the solution that omits control flow features (Case 2) will have a higher objective value, which we describe as the preferred maximizer of the JAM objective. Thus, at optimality, control flow features will not be selected under the JAM objective with a monotone increasing regularizer.
+
+# E Optimality of the Evaluator Model
+
+The evaluator model  $q_{\mathrm{eval - x}}$  is learned such that eq. (5) is maximized as follows:
+
+$$
+\max  _ {\eta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \mathbb {E} _ {\boldsymbol {r} _ {i} \sim \text {B e r n o u l l i} (0. 5)} \left[ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \eta) \right].
+$$
+
+We aim to show that this expectation is maximal when  $q_{\mathrm{eval - x}}(\boldsymbol {y}\mid m(\boldsymbol {x},\boldsymbol {r})) = F(\boldsymbol {y}\mid \boldsymbol{x}_{\mathcal{R}})$  for any sample of  $\mathbf{r}$  identifying the corresponding subset of features  $\mathcal{R}$  in the input  $\boldsymbol{x}_{\mathcal{R}}$ .
+
+The expectations can be rewritten as
+
+$$
+\max  _ {\eta} \mathbb {E} _ {\boldsymbol {r} _ {i} \sim \text {B e r n o u l l i} (0. 5)} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \mid \boldsymbol {r} \sim F} \left[ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \eta) \right].
+$$
+
+Let the power set over feature selections  $\mathcal{P}_r = \{\pmb {r}\subset \{0,1\} ^D\}$  and equivalently for the corresponding feature subsets  $\mathcal{P}_R = \{\mathcal{R}\subset 2^D\}$ . Given  $\pmb {r}_i\sim$  Bernoulli(0.5), the probability
+
+$$
+p (\boldsymbol {r}) = \frac {1}{| \mathcal {P} _ {\boldsymbol {r}} |} = \frac {1}{| \mathcal {P} _ {R} |}.
+$$
+
+Recognizing that  $\mathbf{x},\mathbf{y}\perp \mathbf{r}$  , the expectation over  $\mathbf{r}$  can be expanded as
+
+$$
+\max  _ {\eta} \sum_ {\boldsymbol {r} \in \mathcal {P} _ {r}} \frac {1}{| \mathcal {P} _ {\boldsymbol {r}} |} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} [ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid m (\boldsymbol {x}, \boldsymbol {r}); \eta) ].
+$$
+
+Here, the expectation is with respect to a given  $\boldsymbol{r}$  in the power set  $\mathcal{P}_r$ . In this case, neither  $\boldsymbol{r}$  nor the subset of features masked by  $m(\boldsymbol{x}, \boldsymbol{r})$  provide any information about the target. Therefore, the likelihood is calculated with respect to the corresponding fixed subset  $\mathcal{R}$  as
+
+$$
+\max  _ {\eta} \sum_ {\mathcal {R} \in \mathcal {P} _ {R}} \frac {1}{| \mathcal {P} _ {R} |} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \left[ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid \boldsymbol {x} _ {\mathcal {R}}; \eta) \right].
+$$
+
+A finite sum is maximized when each individual element in the sum is maximized, therefore it suffices to find
+
+$$
+\max  _ {\eta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \left[ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid \boldsymbol {x} _ {\mathcal {R}}; \eta) \right] \quad \forall \mathcal {R} \in \mathcal {P} _ {R}
+$$
+
+Let  $q_{\mathrm{eval - x}} \coloneqq \{f_{\mathcal{R}}(\cdot ;\eta_{\mathcal{R}})\}_{\mathcal{R}\in \mathcal{P}_R}$ , such that when given  $\pmb{r}$  as an input for the corresponding  $\mathcal{R}$ ,  $f_{\mathcal{R}}(\cdot ;\eta_{\mathcal{R}})$  is used to generate the target. The key point here is that the subset  $\mathcal{R}$  provided to the model as  $\pmb{r}$  can uniquely identify which  $f_{\mathcal{R}}$  generates the target. Then, for any given  $R$ , each expectation is maximized when the corresponding  $f_{\mathcal{R}}$  is equal to the true data generating distribution given by
+
+$$
+\max  _ {\eta} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} \sim F} \left[ \log q _ {\text {e v a l - x}} (\boldsymbol {y} \mid \boldsymbol {x} _ {\mathcal {R}}; \eta) \right] = \max  _ {\eta_ {\mathcal {R}}} \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \left[ \log f _ {\mathcal {R}} (\boldsymbol {y} \mid \boldsymbol {x} _ {\mathcal {R}}; \eta_ {\mathcal {R}}) \right] = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \left[ \log F (\boldsymbol {y} \mid \boldsymbol {x} _ {R}) \right] \quad \forall \mathcal {R} \in \mathcal {P} _ {R}.
+$$
+
+# F Additional Experiments
+
+# F.1 EVAL-X vs. Models Explicitly Trained For Each Feature Subset.
+
+In this experiment, we evaluate EVAL-X. EVAL-X approximates  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$  for any subset of features  $\mathcal{R}$ , by training on randomly sampled subsets of the input  $\mathbf{x}$ . While, at optimally the training procedure for EVAL-X returns a model of  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$ , it may be difficult to approximate the distribution  $F(\mathbf{y} \mid \mathbf{x}_{\mathcal{R}})$  for every possible subset of features. We therefore trained separate models for each unique subset of features on our synthetic dataset described in section 6.3. Each of the datasets contain 11 input features with 2048 distinct feature subsets. For each dataset we trained 2048 distinct models on each feature subset. We then evaluated the selections made by each AEM on this collection of models and on EVAL-X. We compared the AUROC returned by EVAL-X (eAUROC) to those returned by the collection of models (cAUROC) in table 5. While EVAL-X returns underestimates relative to the collection of models, the difference is small and the trend amongst methods is conserved.
+
+Table 5: REAL-  $\mathrm{x}$  yields superior post-hoc evaluation on a collection of each models for each feature subset.  
+
+<table><tr><td></td><td colspan="2">S1</td><td colspan="2">S2</td><td colspan="2">S3</td></tr><tr><td>Method</td><td>eAUROC</td><td>cAUROC</td><td>eAUROC</td><td>cAUROC</td><td>eAUROC</td><td>cAUROC</td></tr><tr><td>REAL-x</td><td>0.774</td><td>0.798</td><td>0.804</td><td>0.807</td><td>0.873</td><td>0.876</td></tr><tr><td>L2X</td><td>0.742</td><td>0.759</td><td>0.771</td><td>0.776</td><td>0.848</td><td>0.849</td></tr><tr><td>INVASE</td><td>0.740</td><td>0.767</td><td>0.783</td><td>0.788</td><td>0.868</td><td>0.870</td></tr><tr><td>BASE-x</td><td>0.762</td><td>0.773</td><td>0.773</td><td>0.777</td><td>0.867</td><td>0.870</td></tr></table>
+
+# F.2 Training the Predictor Model First.
+
+We compared a REAL-X approach where  $q_{\mathrm{pred}}$  is first fully optimized, then  $q_{\mathrm{sel}}$  is optimized in a stepwise manor (REAL-x-STEP) to the approach outlined in algorithm 1, where both  $q_{\mathrm{sel}}$  and  $q_{\mathrm{pred}}$  are optimized simultaneous with each mini-batch. The AUROCs returned by EVAL-X for the synthetic datasets described in section 6.3 are presented in table 6. Both approaches perform similarly.
+
+Table 6: REAL-x and REAL-x-STEP perform similarly.  
+
+<table><tr><td></td><td colspan="2">S1</td><td colspan="2">S2</td><td colspan="2">S3</td></tr><tr><td>Metric</td><td>REAL-x</td><td>REAL-x-STEP</td><td>REAL-x</td><td>REAL-x-STEP</td><td>REAL-x</td><td>REAL-x-STEP</td></tr><tr><td>eAUROC</td><td>0.774</td><td>0.778</td><td>0.804</td><td>0.801</td><td>0.873</td><td>0.872</td></tr></table>

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+# Semantic Relation Reasoning for Shot-Stable Few-Shot Object Detection
+
+Chenchen Zhu Fangyi Chen Uzair Ahmed Zhiqiang Shen Marios Savvides Carnegie Mellon University
+
+{chenchez,fangyic,uzaira,zhiqians,marioss}@andrew.cmu.edu
+
+# Abstract
+
+Few-shot object detection is an imperative and long-lasting problem due to the inherent long-tail distribution of real-world data. Its performance is largely affected by the data scarcity of novel classes. But the semantic relation between the novel classes and the base classes is constant regardless of the data availability. In this work, we investigate utilizing this semantic relation together with the visual information and introduce explicit relation reasoning into the learning of novel object detection. Specifically, we represent each class concept by a semantic embedding learned from a large corpus of text. The detector is trained to project the image representations of objects into this embedding space. We also identify the problems of trivially using the raw embeddings with a heuristic knowledge graph and propose to augment the embeddings with a dynamic relation graph. As a result, our few-shot detector, termed SRR-FSD, is robust and stable to the variation of shots of novel objects. Experiments show that SRR-FSD can achieve competitive results at higher shots, and more importantly, a significantly better performance given both lower explicit and implicit shots. The benchmark protocol with implicit shots removed from the pretrained classification dataset can serve as a more realistic setting for future research.
+
+# 1. Introduction
+
+Deep learning algorithms usually require a large amount of annotated data to achieve superior performance. To acquire enough annotated data, one common way is by collecting abundant samples from the real world and paying annotators to generate ground-truth labels. However, even if all the data samples are well annotated based on our requirements, we still face the problem of few-shot learning. Because long-tail distribution is an inherent characteristic of the real world, there always exist some rare cases that have just a few samples available, such as rare animals, uncommon road conditions. In other words, we are unable to alleviate the situation of scarce cases by simply spending more money on annotation even big data is accessible.
+
+![](images/15f2e343d1947549a2bd3869b6ffdde3de95ed9f719be010081a22b4e40356da.jpg)  
+Figure 1. FSOD performance (mAP50) on VOC [13] Novel Set 1 at different shot numbers. Solid line (original) means the pretrained model used for initializing the detector backbone is trained on the original ImageNet [10]. Dashed line (rm-nov) means classes in Novel Set 1 are removed from the ImageNet for the pretrained backbone model. Our SRR-FSD is more stable to the variation of explicit shots (x-axis) and implicit shots (original vs. rm-nov).
+
+Therefore, the study of few-shot learning is an imperative and long-lasting task.
+
+Recently, efforts have been put into the study of few-shot object detection (FSOD) [5, 20, 11, 19, 44, 41, 14, 46, 39, 42, 43]. In FSOD, there are base classes in which sufficient objects are annotated with bounding boxes and novel classes in which very few labeled objects are available. The novel class set does not share common classes with the base class set. The few-shot detectors are expected to learn from limited data in novel classes with the aid of abundant data in base classes and to be able to detect all novel objects in a held-out testing set. To achieve this, most recent few-shot detection methods adopt the ideas from meta-learning and metric learning for few-shot recognition and apply them to conventional detection frameworks, e.g. Faster R-CNN [35], YOLO [34].
+
+Although recent FSOD methods have improved the base
+
+![](images/9521e5b7f8e094d117d44ddef28cd49ce9f35e426ab1b3901f98e1c9338cb14c.jpg)  
+Figure 2. Key insight: the semantic relation between base and novel classes is constant regardless of the data availability of novel classes, which can aid the learning together with visual information.
+
+line considerably, data scarcity is still a bottleneck that hurts the detector's generalization from a few samples. In other words, the performance is very sensitive to the number of both explicit and implicit shots and drops drastically as data becomes limited. The explicit shots refer to the available labeled objects from the novel classes. For example, the 1-shot performance of some FSOD methods is less than half of the 5-shot or 10-shot performance, as shown in Figure 1. In terms of implicit shots, initializing the backbone network with a model pretrained on a large-scale image classification dataset is a common practice for training an object detector. However, the classification dataset contains many implicit shots of object classes overlapped with the novel classes. So the detector can have early access to novel classes and encode their knowledge in the parameters of the backbone. Removing those implicit shots from the pretrained dataset also has a negative impact on the performance as shown in Figure 1. The variation of explicit and implicit shots could potentially lead to system failure when dealing with extreme cases in the real world.
+
+We believe the reason for shot sensitivity is due to exclusive dependence on the visual information. Novel objects are learned through images only and the learning is independent between classes. As a result, visual information becomes limited as image data becomes scarce. However, one thing remains constant regardless of the availability of visual information, i.e. the semantic relation between base and novel classes. For example in Figure 2, if we have the prior knowledge that the novel class "bicycle" looks similar to "motorbike", can have interaction with "person", and can carry a "bottle", it would be easier to learn the concept "bicycle" than solely using a few images. Such explicit relation reasoning is even more crucial when visual information is hard to access [40].
+
+So how can we introduce semantic relation to few-shot detection? In natural language processing, semantic con
+
+cepts are represented by word embeddings [27, 31] from language models, which have been used in zero-shot learning methods [40, 1]. And explicit relationships are represented by knowledge graphs [28, 4], which are adopted by some zero-shot or few-shot recognition algorithms [40, 30]. However, these techniques are rarely explored in the FSOD task. Also, directly applying them to few-shot detectors leads to non-trivial practical problems, i.e. the domain gap between vision and language, and the heuristic definition of knowledge graph for classes in FSOD datasets (see Section 3.2 and 3.3 for details).
+
+In this work, we explore the semantic relation for FSOD. We propose a Semantic Relation Reasoning Few-Shot Detector (SRR-FSD), which learns novel objects from both the visual information and the semantic relation in an end-to-end style. Specifically, we construct a semantic space using the word embeddings. Guided by the word embeddings of the classes, the detector is trained to project the objects from the visual space to the semantic space and to align their image representations with the corresponding class embeddings. To address the aforementioned problems, we propose to learn a dynamic relation graph driven by the image data instead of pre-defining one based on heuristics. Then the learned graph is used to perform relation reasoning and augment the raw embeddings for reduced domain gap.
+
+With the help of the semantic relation reasoning, our SRR-FSD demonstrates the shot-stable property in two aspects, see the red solid and dashed lines in Figure 1. In the common few-shot settings (solid lines), SRR-FSD achieves competitive performance at higher shots and significantly better performance at lower shots compared to state-of-the-art few-shot detectors. In a more realistic setting (dashed lines) where implicit shots of novel concepts are removed from the classification dataset for the pretrained model, SRR-FSD steadily maintains the performance while some previous methods have results degraded by a large margin due to the loss of implicit shots. We hope the suggested realistic setting can serve as a new benchmark protocol for future research.
+
+We summarize our contributions as follows:
+
+- To our knowledge, our work is the first to investigate semantic relation reasoning for the few-shot detection task and show its potential to improve a strong baseline.  
+- Our SRR-FSD achieves stable performance w.r.t the shot variation, outperforming state-of-the-art FSOD methods under several existing settings especially when the novel class data is extremely limited.  
+- We suggest a more realistic FSOD setting in which implicit shots of novel classes are removed from the classification dataset for the pretrained model, and show
+
+that our SRR-FSD can maintain a more steady performance compared to previous methods if using the new pretrained model.
+
+# 2. Related Work
+
+Object Detection Object detection is a fundamental computer vision task, serving as a necessary step for various down-streaming instance-based understanding. Modern CNN-based detectors can be roughly divided into two categories. One is single-stage detector such as YOLO [34], SSD [26], RetinaNet [24], and FreeAnchor [47] which directly predict the class confidence scores and the bounding box coordinates over a dense grid. The other is multi-stage detector such as Faster R-CNN [35], R-FCN [9], FPN [23], Cascade R-CNN [2], and Libra R-CNN [29] which predict class-agnostic regions of interest and refine those region proposals for one or multiple times. All these methods rely on pre-defined anchor boxes to have an initial estimation of the size and aspect ratio of the objects. Recently, anchor-free detectors eliminate the performance-sensitive hyperparameters for the anchor design. Some of them detect the key points of bounding boxes [22, 48, 12]. Some of them encode and decode the bounding boxes as anchor points and point-to-boundary distances [38, 50, 36, 45, 49]. DETR [3] reformulates object detection as a direct set prediction problem and solve it with transformers. However, these detectors are trained with full supervision where each class has abundant annotated object instances.
+
+Few-Shot Detection Recently, there have been works focusing on solving the detection problem in the limited data scenario. LSTD [5] proposes the transfer knowledge regularization and background depression regularization to promote the knowledge transfer from the source domain to the target domain. [11] proposes to iterate between model training and high-confidence sample selection. RepMet [20] adopts a distance metric learning classifier into the RoI classification head. FSRW [19] and Meta R-CNN [44] predict per-class attentive vectors to reweight the feature maps of the corresponding classes. MetaDet [41] leverages meta-level knowledge about model parameter generation for category-specific components of novel classes. In [14], the similarity between the few shot support set and query set is explored to detect novel objects. Context-Transformer [46] relies on discriminative context clues to reduce object confusion. TFA [39] only fine-tunes the last few layers of the detector. Two very recent papers are MPSR [42] and FSDetView [43]. MPSR develops an auxiliary branch to generate multi-scale positive samples as object pyramids and to refine the prediction at various scales. FSDetView proposes a joint feature embedding module to share the feature from base classes. However, all these methods depend purely on visual information and suffer from shot variation.
+
+Semantic Reasoning in Vision Tasks Semantic word
+
+embeddings have been used in zero-shot learning tasks to learn a mapping from the visual feature space to the semantic space, such as zero-shot recognition [40] and zero-shot object detection [1, 32]. In [7], semantic embeddings are used as the ground-truth of the encoder TriNet to guide the feature augmentation. In [15], semantic embeddings guide the feature synthesis for unseen classes by perturbing the seen feature with the projected difference between a seen class embedding and a unseen class embedding. In zero-shot or few-shot recognition [40, 30], word embeddings are often combined with knowledge graphs to perform relation reasoning via the graph convolution operation [21]. Knowledge graphs are usually defined based on heuristics from databases of common sense knowledge rules [28, 4]. [8] proposed a knowledge graph based on object co-occurrence for the multi-label recognition task. To our knowledge, the use of word embeddings and knowledge graphs are rarely explored in the FSOD task. Any-Shot Detector (ASD) [33] is the only work that uses word embeddings for the FSOD task. But ASD focuses more on the zero-shot detection and it does not consider the explicit relation reasoning between classes because each word embedding is treated independently.
+
+# 3. Semantic Relation Reasoning Few-Shot Detector
+
+In this section, we first briefly introduce the preliminaries for few-shot object detection including the problem setup and the general training pipelines. Then based on Faster R-CNN [35], we build our SRR-FSD by integrating semantic relation with the visual information and allowing it to perform relation reasoning in the semantic space. We also discuss the problems of trivially using the raw word embeddings and the predefined knowledge graphs. Finally, we introduce the two-phase training processes. An overview of our SRR-FSD is illustrated in Figure 3.
+
+# 3.1. FSOD Preliminaries
+
+Conventional object detection problem has a base class set  $\mathcal{C}_b$  in which there are many instances, and a base dataset  $\mathcal{D}_b$  with abundant images.  $\mathcal{D}_b$  consists of a set of annotated images  $\{(x_i,y_i)\}$  where  $x_{i}$  is the image and  $y_{i}$  is the annotation of labels from  $\mathcal{C}_b$  and bounding boxes for objects in  $x_{i}$ . For few-shot object detection (FSOD) problem, in addition to  $\mathcal{C}_b$  and  $\mathcal{D}_b$  it also has a novel class set  $\mathcal{C}_n$  and a novel dataset  $\mathcal{D}_n$ , with  $\mathcal{C}_b\cap \mathcal{C}_n = \emptyset$ . In  $\mathcal{D}_n$ , objects have labels belong to  $\mathcal{C}_n$  and the number of objects for each class is  $k$  for  $k$ -shot detection. A few-shot detector is expected to learn from  $\mathcal{D}_b$  and to quickly generalize to  $\mathcal{D}_n$  with a small  $k$  such that it can detect all objects in a held-out testing set with object classes in  $\mathcal{C}_b\cup \mathcal{C}_n$ . We assume all classes in  $\mathcal{C}_b\cup \mathcal{C}_n$  have semantically meaningful names so the corresponding semantic embeddings can be retrieved.
+
+![](images/99d6c5e5736ebf4124e07b453340cae11f554ee8970e69284349ca5077d4ce15.jpg)  
+Figure 3. Overview of the SRR-FSD. A semantic space is built from the word embeddings of all corresponding classes in the dataset and is augmented through a relation reasoning module. Visual features are learned to be projected into the augmented space. “ $\otimes$ ”: dot product. “FC”: fully-connected layer. “P”: lernable projection matrix.
+
+A typical few-shot detector has two training phases. The first one is the base training phase where the detector is trained on  $\mathcal{D}_b$  similarly to conventional object detectors. Then in the second phase, it is further fine-tuned on the union of  $\mathcal{D}_b$  and  $\mathcal{D}_n$ . To avoid the dominance of objects from  $\mathcal{D}_b$ , a small subset is sampled from  $\mathcal{D}_b$  such that the training set is balanced concerning the number of objects per class. As the total number of classes is increased by the size of  $\mathcal{C}_n$  in the second phase, more class-specific parameters are inserted in the detector and trained to be responsible for the detection of novel objects. The class-specific parameters are usually in the box classification and localization layers at the very end of the network.
+
+# 3.2. Semantic Space Projection
+
+Our few-shot detector is built on top of Faster R-CNN [35], a popular two-stage general object detector. In the second-stage of Faster R-CNN, a feature vector is extracted for each region proposal and forwarded to a classification subnet and a regression subnet. In the classification subnet, the feature vector is transformed into a  $d$ -dimensional vector  $\mathbf{v} \in \mathcal{R}^d$  through fully-connected layers. Then  $\mathbf{v}$  is multiplied by a learnable weight matrix  $\mathbf{W} \in \mathcal{R}^{N \times d}$  to output a probability distribution as in Eq. (1).
+
+$$
+\mathbf {p} = \operatorname {s o f t m a x} (\mathbf {W} \mathbf {v} + \mathbf {b}) \tag {1}
+$$
+
+where  $N$  is the number of classes and  $\mathbf{b} \in \mathcal{R}^N$  is a learnable bias vector. Cross-entropy loss is used during training.
+
+To learn objects from both the visual information and the semantic relation, we first construct a semantic space and project the visual feature  $\mathbf{v}$  into this semantic space. Specifically, we represent the semantic space using a set of  $d_{e}$ -dimensional word embeddings  $\mathbf{W}_{e} \in \mathcal{R}^{N \times d_{e}}$  [27] corresponding to the  $N$  object classes (including the background class). And the detector is trained to learn a linear projection  $\mathbf{P} \in \mathcal{R}^{d_{e} \times d}$  in the classification subnet (see Fig-
+
+ure 3) such that  $\mathbf{v}$  is expected to align with its class's word embedding after projection. Mathematically, the prediction of the probability distribution turns into Eq. (2) from Eq. (1).
+
+$$
+\mathbf {p} = \operatorname {s o f t m a x} \left(\mathbf {W} _ {e} \mathbf {P} \mathbf {v} + \mathbf {b}\right) \tag {2}
+$$
+
+During training,  $\mathbf{W}_e$  is fixed and the learnable variable is  $\mathbf{P}$ . A benefit is that generalization to novel objects involves no new parameters in  $\mathbf{P}$ . We can simply expand  $\mathbf{W}_e$  with embeddings of novel classes. We still keep the  $\mathbf{b}$  to model the category imbalance in the detection dataset.
+
+Domain gap between vision and language.  $\mathbf{W}_e$  encodes the knowledge of semantic concepts from natural language. While it is applicable in zero-shot learning, it will introduce the bias of the domain gap between vision and language to the FSOD task. Because unlike zero-shot learning where unseen classes have no support from images, the few-shot detector can rely on both the images and the embeddings to learn the concept of novel objects. When there are very few images to rely on, the knowledge from embeddings can guide the detector towards a decent solution. But when more images are available, the knowledge from embeddings may be misleading due to the domain gap, resulting in a suboptimal solution. Therefore, we need to augment the semantic embeddings to reduce the domain gap. Some previous works like ASD [33] apply a trainable transformation to each word embedding independently. But we leveraging the explicit relationship between classes is more effective for embedding augmentation, leading to the proposal of the dynamic relation graph in Section 3.3.
+
+# 3.3. Relation Reasoning
+
+The semantic space projection learns to align the concepts from the visual space with the semantic space. But it still treats each class independently and there is no knowledge propagation among classes. Therefore, we further introduce a knowledge graph to model their relationships. The knowledge graph  $\mathbf{G}$  is a  $N\times N$  adjacency matrix representing the connection strength for every neighboring class pairs.  $\mathbf{G}$  is involved in classification via the graph convolution operation [21]. Mathematically, the updated probability prediction is shown in Eq. (3).
+
+$$
+\mathbf {p} = \operatorname {s o f t m a x} \left(\mathbf {G W} _ {e} \mathbf {P v} + \mathbf {b}\right) \tag {3}
+$$
+
+The heuristic definition of the knowledge graph. In zero-shot or few-shot recognition algorithms, the knowledge graph  $\mathbf{G}$  is predefined base on heuristics. It is usually constructed from a database of common sense knowledge rules by sampling a sub-graph through the rule paths such that semantically related classes have strong connections. For example, classes from the ImageNet dataset [10] have a knowledge graph sampled from the WordNet [28]. However, classes in FSOD datasets are not highly semantically
+
+![](images/21483353df342d4676557fc740cadfd37d05c63d901e482f4d6f45afd61e0326.jpg)  
+Figure 4. Network architecture of the relation reasoning module for learning the relation graph. “ $\otimes$ ”: dot product. “ $\oplus$ ”: element-wise plus.
+
+related, nor do they form a hierarchical structure like the ImageNet classes. The only applicable heuristics we found are based on object co-occurrence from [8]. Although the statistics of the co-occurrence are straightforward to compute, the co-occurrence is not necessarily equivalent to semantic relation.
+
+Instead of predefining a knowledge graph based on heuristics, we propose to learn a dynamic relation graph driven by the data to model the relation reasoning between classes. The data-driven graph is also responsible for reducing the domain gap between vision and language because it is trained with image inputs. Inspired by the concept of the transformer, we implement the dynamic graph with the self-attention architecture [37] as shown in Figure 4. The original word embeddings  $\mathbf{W}_e$  are transformed by three linear layers  $f, g, h$ , and a self-attention matrix is computed from the outputs of  $f, g$ . The self-attention matrix is multiplied with the output of  $h$  followed by another linear layer  $l$ . A residual connection [16] adds the output of  $l$  with the original  $\mathbf{W}_e$ . Another advantage of learning a dynamic graph is that it can easily adapt to new coming classes. Because the graph is not fixed and is generated on the fly from the word embeddings. We do not need to redefine a new graph and retrain the detector from the beginning. We can simply insert corresponding embeddings of new classes and fine-tune the detector.
+
+# 3.4. Decoupled Fine-tuning
+
+In the second fine-tuning phase, we only unfreeze the last few layers of our SRR-FSD similar to TFA [39]. For the classification subnet, we fine-tune the parameters in the relation reasoning module and the projection matrix  $\mathbf{P}$ . For the localization subnet, it is not dependent on the word embeddings but it shares features with the classification subnet. We find that the learning of localization on novel objects can interfere with the classification subnet via the shared features, leading to many false positives. Decoupling the shared fully-connected layers between the two subnets can effectively make each subnet learn better features for its task. In other words, the classification subnet and the localization subnet have individual fully-connected layers and
+
+they are fine-tuned independently.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Our SRR-FSD is implemented based on Faster R-CNN [35] with ResNet-101 [16] and Feature Pyramid Network [23] as the backbone using the MMDetection [6] framework. All models are trained with Stochastic Gradient Descent (SGD) and a batch size of 16. For the word embeddings, we use the L2-normalized 300-dimensional Word2Vec [27] vectors from the language model trained on large unannotated texts like Wikipedia. In the relation reasoning module, we reduce the dimension of word embeddings to 32 which is empirically selected. In the first base training phase, we set the learning rate, the momentum, and the weight decay to 0.02, 0.9, and 0.0001, respectively. In the second fine-tuning phase, we reduce the learning rate to 0.001 unless otherwise mentioned. The input image is sampled by first randomly choosing between the base set and the novel set with a  $50\%$  probability and then randomly selecting an image from the chosen set.
+
+# 4.2. Existing Settings
+
+We follow the existing settings in previous FSOD methods [19, 41, 44, 39] to evaluate our SRR-FSD on the VOC [13] and COCO [25] datasets. For fair comparison and reduced randomness, we use the same data splits and a fixed list of novel samples provided by [19].
+
+VOC The 07 and 12 train/val sets are used for training and the 07 test set is for testing. Out of its 20 object classes, 5 classes are selected as novel and the remaining 15 are base classes, with 3 different base/novel splits. The novel classes each have  $k$  annotated objects, where  $k$  equals 1, 2, 3, 5, 10. In the first base training phase, our SRR-FSD is trained for 18 epochs with the learning rate multiplied by 0.1 at the 12th and 15th epoch. In the second fine-tuning phase, we train for  $500 \times |\mathcal{D}_n|$  steps where  $|\mathcal{D}_n|$  is the number of images in the  $k$ -shot novel dataset.
+
+We report the mAP50 of the novel classes on VOC with 3 splits in Table 1. In all different base/novel splits, our SRR-FSD achieves a more shot-stable performance. At higher shots like 5-shot and 10-shot, our performance is competitive compared to previous state-of-the-art methods. At more challenging conditions with shots less than 5, our approach can outperform the second-best by a large margin (up to  $10+$  mAP). Compared to ASD [33] which only reports results of 3-shot and 5-shot in the Novel Set 1, ours is 24.2 and 6.0 better respectively in mAP. We do not include ASD in Table 1 because its paper does not provide the complete results on VOC.
+
+Learning without forgetting is another merit of our SRR-FSD. After generalization to novel objects, the performance
+
+<table><tr><td rowspan="2">Method / shot</td><td colspan="5">Novel Set 1</td><td colspan="5">Novel Set 2</td><td colspan="5">Novel Set 3</td></tr><tr><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>FSRW [19]</td><td>14.8</td><td>15.5</td><td>26.7</td><td>33.9</td><td>47.2</td><td>15.7</td><td>15.3</td><td>22.7</td><td>30.1</td><td>40.5</td><td>21.3</td><td>25.6</td><td>28.4</td><td>42.8</td><td>45.9</td></tr><tr><td>MetaDet [41]</td><td>18.9</td><td>20.6</td><td>30.2</td><td>36.8</td><td>49.6</td><td>21.8</td><td>23.1</td><td>27.8</td><td>31.7</td><td>43.0</td><td>20.6</td><td>23.9</td><td>29.4</td><td>43.9</td><td>44.1</td></tr><tr><td>Meta R-CNN [44]</td><td>19.9</td><td>25.5</td><td>35.0</td><td>45.7</td><td>51.5</td><td>10.4</td><td>19.4</td><td>29.6</td><td>34.8</td><td>45.4</td><td>14.3</td><td>18.2</td><td>27.5</td><td>41.2</td><td>48.1</td></tr><tr><td>TFA [39]</td><td>39.8</td><td>36.1</td><td>44.7</td><td>55.7</td><td>56.0</td><td>23.5</td><td>26.9</td><td>34.1</td><td>35.1</td><td>39.1</td><td>30.8</td><td>34.8</td><td>42.8</td><td>49.5</td><td>49.8</td></tr><tr><td>SRR-FSD (Ours)</td><td>47.8</td><td>50.5</td><td>51.3</td><td>55.2</td><td>56.8</td><td>32.5</td><td>35.3</td><td>39.1</td><td>40.8</td><td>43.8</td><td>40.1</td><td>41.5</td><td>44.3</td><td>46.9</td><td>46.4</td></tr></table>
+
+Table 1. FSOD evaluation on VOC. We report the mAP with IoU threshold 0.5 (mAP50) under 3 different sets of 5 novel classes with a small number of shots.
+
+<table><tr><td>Shot</td><td>Method</td><td>Base AP50</td><td>Novel AP50</td></tr><tr><td rowspan="4">3</td><td>Meta R-CNN [44]</td><td>64.8</td><td>35.0</td></tr><tr><td>TFA [39]</td><td>79.1</td><td>44.7</td></tr><tr><td>Ours base only</td><td>77.7</td><td>n/a</td></tr><tr><td>SRR-FSD (Ours)</td><td>78.2</td><td>51.3</td></tr><tr><td rowspan="4">10</td><td>Meta R-CNN [44]</td><td>67.9</td><td>51.5</td></tr><tr><td>TFA [39]</td><td>78.4</td><td>56.0</td></tr><tr><td>Ours base only</td><td>77.7</td><td>n/a</td></tr><tr><td>SRR-FSD (Ours)</td><td>78.2</td><td>56.8</td></tr></table>
+
+Table 2. FSOD performance for the base and novel classes on Novel Set 1 of VOC. Our SRR-FSD has the merit of learning without forgetting.
+
+on the base objects does not drop at all as shown in Table 2. Both base AP and novel AP of our SRR-FSD compare favorably to previous methods based on the same Faster R-CNN with ResNet-101. The base AP even increases a bit probably due to the semantic relation reasoning from limited novel objects to base objects.
+
+COCO The minival set with 5000 images is used for testing and the rest images in train/val sets are for training. Out of the 80 classes, 20 of them overlapped with VOC are the novel classes with  $k = 10$ , 30 shots per class and the remaining 60 classes are base. We train the SRR-FSD on the base dataset for 12 epochs using the same setting as MMDetection [6] and fine-tune it for a fixed number of  $10 \times |\mathcal{D}_b|$  steps where  $|\mathcal{D}_b|$  is the number of images in the base dataset. Unlike VOC, the base dataset in COCO contains unlabeled novel objects, so the region proposal network (RPN) treats them as the background. To avoid omitting novel objects in the fine-tuning phase, we unfreeze the RPN and the following layers. Table 3 presents the COCO-style averaged AP. Again we consistently outperform previous methods including FSRW [19], MetaDet [41], Meta R-CNN [44], TFA [39], and MPSR [42].
+
+COCO to VOC For the cross-domain FSOD setting, we follow [19, 41] to use the same base dataset with 60 classes as in the previous COCO within-domain setting. The novel dataset consists of 10 samples for each of the 20 classes from the VOC dataset. The learning schedule is the same as the previous COCO within-domain setting except the learning rate is 0.005. Figure 5 shows that our SRR-FSD
+
+<table><tr><td>Shot</td><td>Method</td><td>AP</td><td>AP50</td><td>AP75</td></tr><tr><td rowspan="6">10</td><td>FSRW [19]</td><td>5.6</td><td>12.3</td><td>4.6</td></tr><tr><td>MetaDet [41]</td><td>7.1</td><td>14.6</td><td>6.1</td></tr><tr><td>Meta R-CNN [44]</td><td>8.7</td><td>19.1</td><td>6.6</td></tr><tr><td>TFA [39]</td><td>10.0</td><td>-</td><td>9.3</td></tr><tr><td>MPSR [42]</td><td>9.8</td><td>17.9</td><td>9.7</td></tr><tr><td>SRR-FSD (Ours)</td><td>11.3</td><td>23.0</td><td>9.8</td></tr><tr><td rowspan="6">30</td><td>FSRW [19]</td><td>9.1</td><td>19.0</td><td>7.6</td></tr><tr><td>MetaDet [41]</td><td>11.3</td><td>21.7</td><td>8.1</td></tr><tr><td>Meta R-CNN [44]</td><td>12.4</td><td>25.3</td><td>10.8</td></tr><tr><td>TFA [39]</td><td>13.7</td><td>-</td><td>13.4</td></tr><tr><td>MPSR [42]</td><td>14.1</td><td>25.4</td><td>14.2</td></tr><tr><td>SRR-FSD (Ours)</td><td>14.7</td><td>29.2</td><td>13.5</td></tr></table>
+
+Table 3. FSOD performance of the novel classes on COCO.
+
+![](images/5739632373ec6ee9201e4a2c930794e0055121335b10a86f6e6b68547222e425.jpg)  
+Figure 5. 10-shot cross domain performance on the 20 novel classes under COCO to VOC.
+
+achieves the best performance with a healthy  $44.5\mathrm{mAP}$ , indicating better generalization ability in cross-domain situations.
+
+# 4.3. A More Realistic Setting
+
+The training of the few-shot detector usually involves initializing the backbone network with a model pretrained on large-scale object classification datasets such as ImageNet [10]. The set of object classes in ImageNet, i.e.  $\mathcal{C}_0$ , is highly overlapped with the novel class set  $\mathcal{C}_n$  in the existing settings. This means that the pretrained model can get early access to large amounts of object samples, i.e. implicit
+
+<table><tr><td rowspan="2">Method / shot</td><td colspan="5">Novel Set 1</td><td colspan="5">Novel Set 2</td><td colspan="5">Novel Set 3</td></tr><tr><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>FSRW [19]</td><td>13.9</td><td>21.1</td><td>20.0</td><td>29.9</td><td>40.8</td><td>13.5</td><td>14.2</td><td>20.6</td><td>20.7</td><td>36.8</td><td>16.2</td><td>22.2</td><td>26.8</td><td>37.0</td><td>41.5</td></tr><tr><td>Meta R-CNN [44]</td><td>11.5</td><td>22.2</td><td>24.7</td><td>36.4</td><td>45.2</td><td>10.1</td><td>16.9</td><td>22.7</td><td>29.6</td><td>40.1</td><td>10.0</td><td>21.7</td><td>27.1</td><td>32.8</td><td>41.6</td></tr><tr><td>TFA [39]</td><td>35.8</td><td>39.5</td><td>44.2</td><td>50.8</td><td>55.3</td><td>18.8</td><td>26.0</td><td>33.2</td><td>31.3</td><td>39.2</td><td>25.6</td><td>32.6</td><td>36.4</td><td>43.7</td><td>48.5</td></tr><tr><td>SRR-FSD (Ours)</td><td>46.3</td><td>51.1</td><td>52.6</td><td>56.2</td><td>57.3</td><td>31.0</td><td>29.9</td><td>34.7</td><td>37.3</td><td>41.7</td><td>39.2</td><td>40.5</td><td>39.7</td><td>42.2</td><td>45.2</td></tr></table>
+
+Table 4. FSOD performance (mAP50) on VOC under a more realistic setting where novel classes are removed from the pretrained classification dataset to guarantee  $\mathcal{C}_0 \cap \mathcal{C}_n = \emptyset$ . Our SRR-FSD is more robust to the loss of implicit shots comparing with Table 1.
+
+shots, from novel classes and encode their knowledge in the parameters before it is further trained for the detection task. Even the pretrained model is optimized for the recognition task, the extracted features still have a big impact on the detection of novel objects (see Figure 1). However, some rare classes may have highly limited or valuable data in the real world that pretraining a classification network on it is not realistic.
+
+Therefore, we suggest a more realistic setting for FSOD, which extends the existing settings. In addition to  $\mathcal{C}_b\cap \mathcal{C}_n = \emptyset$ , we also require that  $\mathcal{C}_0\cap \mathcal{C}_n = \emptyset$ . To achieve this, we systematically and hierarchically remove novel classes from  $\mathcal{C}_0$ . For each class in  $\mathcal{C}_n$ , we find its corresponding synset in ImageNet and obtain its full hyponym (the synset of the whole subtree starting from that synset) using the ImageNet API<sup>1</sup>. The images of this synset and its full hyponym are removed from the pretrained dataset. And the classification model is trained on a dataset with no novel objects. We provide the list of WordNet IDs for each novel class to be removed in Appendix A.
+
+We notice that CoAE [18] also proposed to remove all COCO-related ImageNet classes to ensure the model does not "foresee" the unseen classes. As a result, a total of 275 classes are removed from ImageNet including both the base and novel classes in VOC [13], which correspond to more than 300k images. We think the loss of this much data may lead to a worse pretrained model in general. So the pretrained model may not be able to extract features strong enough for down-streaming vision tasks compared with the model trained on full ImageNet. Our setting, on the other hand, tries to alleviate this effect as much as possible by only removing the novel classes in VOC Novel Set 1, 2, and 3 respectively, which correspond to an average of 50 classes from ImageNet.
+
+Under the new realistic setting, we re-evaluate previous methods using their official source code and report the performance on the VOC dataset in Table 4. Our SRR-FSD demonstrates superior performance to other methods under most conditions, especially at challenging lower shot scenarios. More importantly, our SRR-FSD is less affected by the loss of implicit shots. Compared with results in Table 1, our performance is more stably maintained when novel
+
+objects are only available in the novel dataset.
+
+# 4.4. Ablation Study
+
+In this section, we study the contribution of each component. Experiments are conducted on the VOC dataset. Our baseline is the Faster R-CNN [35] with ResNet-101 [16] and FPN [23]. We gradually apply the Semantic Space Projection (SSP 3.2), Relation Reasoning (RR 3.3) and Decoupled Fine-tuning (DF 3.4) to the baseline and report the performance in Table 5. We also compare three different ways of augmenting the raw word embeddings in Table 6, including the trainable transformation from ASD [33], the heuristic knowledge graph from [8], and the dynamic graph from our proposed relation reasoning module.
+
+Semantic space projection guides shot-stable learning. The baseline Faster R-CNN can already achieve satisfying results at 5-shot and 10-shot. But at 1-shot and 2-shot, performance starts to fall apart due to exclusive dependence on images. The semantic space projection, on the other hand, makes the learning more stable to the variation of shot numbers (see 1st and 2nd entries in Table 5). The space projection guided by the semantic embeddings is learned well enough in the base training phase so it can be quickly adapted to novel classes with a few instances. We can observe a major boost at lower shot conditions compared to baseline, i.e.  $7.9\mathrm{mAP}$  and  $2.4\mathrm{mAP}$  gain at 1-shot and 2-shot respectively. However, the raw semantic embeddings limit the performance at higher shot conditions. The performance at 5-shot and 10-shot drops below the baseline. This verifies our argument about the domain gap between vision and language. At lower shots, there is not much visual information to rely on so the language information can guide the detector to a decent solution. But when more images are available, the visual information becomes more precise then the language information starts to be misleading. Therefore, we propose to refine the word embeddings for a reduced domain gap.
+
+Relation reasoning promotes adaptive knowledge propagation. The relation reasoning module explicitly learns a relation graph that builds direct connections between base classes and novel classes. So the detector can learn the novel objects using the knowledge of base objects besides the visual information. Additionally, the relation
+
+<table><tr><td rowspan="2"></td><td colspan="3">Components</td><td colspan="5">Shots in Novel Set 1</td></tr><tr><td>SSP</td><td>RR</td><td>DF</td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td rowspan="3">Faster R-CNN [35]</td><td rowspan="2">✓</td><td></td><td></td><td>32.6</td><td>44.4</td><td>46.3</td><td>49.6</td><td>55.6</td></tr><tr><td></td><td></td><td>40.5</td><td>46.8</td><td>46.5</td><td>47.1</td><td>52.2</td></tr><tr><td>✓</td><td>✓</td><td></td><td>44.1</td><td>46.0</td><td>47.8</td><td>51.7</td><td>54.7</td></tr><tr><td>SRR-FSD</td><td>✓</td><td>✓</td><td>✓</td><td>47.8</td><td>50.5</td><td>51.3</td><td>55.2</td><td>56.8</td></tr></table>
+
+Table 5. Ablative performance (mAP50) on the VOC Novel Set 1 by gradually applying the proposed components to the baseline Faster R-CNN. SSP: semantic space projection. RR: relation reasoning. DF: decoupled fine-tuning.  
+
+<table><tr><td></td><td colspan="5">Shots in Novel Set 1</td></tr><tr><td></td><td>1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>+SSP</td><td>40.5</td><td>46.8</td><td>46.5</td><td>47.1</td><td>52.2</td></tr><tr><td>+SSP +TT [33]</td><td>39.3</td><td>45.7</td><td>43.9</td><td>49.4</td><td>52.4</td></tr><tr><td>+SSP +HKG [8]</td><td>41.6</td><td>45.5</td><td>47.8</td><td>49.7</td><td>52.5</td></tr><tr><td>+SSP +RR</td><td>44.1</td><td>46.0</td><td>47.8</td><td>51.7</td><td>54.7</td></tr></table>
+
+Table 6. Comparison of three ways of refining the word embeddings, including the trainable transformation from ASD [33], the heuristic knowledge graph from [8], and the dynamic relation graph from our relation reasoning module. SSP: semantic space projection. RR: relation reasoning. TT: trainable transformation. HKG: heuristic knowledge graph.
+
+reasoning module also functions as a refinement to the raw word embeddings with a data-driven relation graph. Since the relation graph is updated with image inputs, the refinement tends to adapt the word embeddings for the vision domain. Results in Table 5 (2nd and 3rd entries) confirm that applying relation reasoning improves the detection accuracy of novel objects under different shot conditions. We also compare it with two other ways of refining the raw word embeddings in Table 6. One is the trainable transformation (TT) from ASD [33] where word embeddings are updated with a trainable metric and a word vocabulary. Note that this transformation is applied to each embedding independently which does not consider the explicit relationships between them. The other one is the heuristic knowledge graph (HKG) defined based on the co-occurrence of objects from [8]. It turns out both the trainable transformation and the predefined heuristic knowledge graph are not as effective as the dynamic relation graph in the relation reasoning module. The effect of the trainable transformation is similar to unfreezing more parameters of the last few layers during fine-tuning as shown in Appendix E, which leads to overfitting when the shot is low. And the predefined knowledge graph is fixed during training thus cannot be adaptive to the inputs. In other words, the dynamic relation graph is better because it can not only perform explicit relation reasoning but also augment the raw embeddings for reduced domain gap between vision and language.
+
+Decoupled fine-tuning reduces false positives. We analyze the false positives generated by our SRR-FSD with and without decoupled fine-tuning (DF) using the detector
+
+![](images/8d0fcbb2464f1200a62a4c4948699dd5925458780875f0745a6489d61dbeb41d.jpg)  
+Figure 6. Error analysis of false positives in VOC Novel Set 1 with and without decouple fine-tuning (DF). Detectors are trained with 3 shots. Pie charts indicate the fraction of correct detections (Cor) and top-ranked false positives that are due to poor localization (Loc), confusion with similar objects (Sim), confusion with other VOC objects (Oth), or confusion with background or unlabeled objects (BG).
+
+diagnosing tool [17]. The effect of DF on reducing the false positives in novel classes is visualized in Figure 6. It shows that most of the false positives are due to misclassification into similar categories. With DF, the classification subnet can be trained independently from the localization subnet to learn better features specifically for classification.
+
+# 5. Conclusion
+
+In this work, we propose semantic relation reasoning for few-shot object detection. The key insight is to explicitly integrate semantic relation between base and novel classes with the available visual information, which can help to learn the novel concepts better especially when the novel class data is extremely limited. We apply the semantic relation reasoning to the standard two-stage Faster R-CNN and demonstrate robust few-shot performance against the variation of shot numbers. Compared to previous methods, our approach achieves state-of-the-art results on several few-shot detection settings, as well as a more realistic setting where novel concepts encoded in the pretrained backbone model are eliminated. We hope this realistic setting can be a better evaluation protocol for future few-shot detectors. Last but not least, the key components of our approach, i.e. semantic space projection and relation reasoning, can be straightly applied to the classification subnet of other few-shot detectors.
+
+# A. Removing Novel Classes from ImageNet
+
+We propose a realistic setting for evaluating the few-shot object detection methods, where novel classes are completely removed from the classification dataset used for training a model to initialize the backbone network in the detector. This can guarantee that the object concept of novel classes will not be encoded in the pretrained model before training the few-shot detector. Because the novel class data is so rare in the real world that pretraining a classifier on it is not realistic.
+
+ImageNet [10] is widely used for pretraining the classification model. It has 1000 classes organized according to the WordNet hierarchy. Each class has over 1000 images for training. We systematically and hierarchically remove novel classes by finding each synset and its corresponding full hyponym (synset of the whole sub-tree starting from that synset) using the ImageNet API  $^{2}$ . So each novel class may contain multiple ImageNet classes.
+
+For the novel classes in the VOC dataset [13], their corresponding WordNet IDs to be removed are as follows.
+
+- aeroplane: n02690373, n02692877, n04552348  
+- bird: n01514668, n01514859, n01518878, n01530575, n01531178, n01532829, n01534433, n01537544, n01558993, n01560419, n01580077, n01582220, n01592084, n01601694, n01608432, n01614925, n01616318, n01622779, n01795545, n01796340, n01797886, n01798484, n01806143, n01806567, n01807496, n01817953, n01818515, n01819313, n01820546, n01824575, n01828970, n01829413, n01833805, n01843065, n01843383, n01847000, n01855032, n01855672, n01860187, n02002556, n02002724, n02006656, n02007558, n02009229, n02009912, n02011460, n02012849, n02013706, n02017213, n02018207, n02018795, n02025239, n02027492, n02028035, n02033041, n02037110, n02051845, n02056570, n02058221
+
+- boat: n02687172, n02951358, n03095699, n03344393, n03447447, n03662601, n03673027, n03873416, n03947888, n04147183, n04273569, n04347754, n04606251, n04612504  
+- bottle: n02823428, n03062245, n03937543, n03983396, n04522168, n04557648, n04560804, n04579145, n04591713  
+bus: n03769881, n04065272, n04146614, n04487081  
+- cat: n02123045, n02123159, n02123394, n02123597, n02124075, n02125311, n02127052  
+cow: n02403003, n02408429, n02410509
+
+horse: n02389026, n02391049  
+motorbike: n03785016, n03791053  
+- sheep: n02412080, n02415577, n02417914, n02422106, n02422699, n02423022  
+- sofa: n04344873
+
+For the novel classes in the COCO dataset [25], they are very common in the real world. Removing them from the ImageNet does not make sense as much as removing data-scarce classes. So we suggest for large-scale datasets like COCO, we should follow the long-tail distribution of their class frequency and select the data-scarce classes on the distribution tail to be the novel classes.
+
+# B. Visualization of Relation Reasoning
+
+Figure 7 visualizes the correlation maps between the semantic embeddings of novel and base classes before and after the relation reasoning, as well as the difference between the two maps. Nearly all the correlations are increased slightly, indicating better knowledge propagation between the two groups of classes. Additionally, it is interesting to see that some novel classes get more correlated than others, e.g. "sofa" with "bottle" and "sofa" with "table", probably because "sofa" can often be seen together with "bottle" and "table" in the living room but the original semantic embeddings cannot capture these relationships.
+
+# C. Using Other Word Embeddings
+
+In the semantic space projection, we represent the semantic space using word embeddings from the Word2Vec [27]. We could simply set the  $\mathbf{W}_e$  to be random vectors. Additionally, there are other language models for obtaining vector representations for words, such as the GloVe [31]. The GloVe is trained with aggregated global word-word cooccurrence statistics from a corpus, and the resulting representations showcase interesting linear substructures of the word vector space. We also explored using word embedding with different dimensions from the GloVe in the semantic space projection step and compared with the results by the Word2Vec. Performance on the VOC Novel Set 1 is reported in Table 7. The Word2Vec can provide better representations than the GloVe of both 300 dimensions and 200 dimensions. The performance of random embeddings is significantly worse than the meaningful Word2Vec and GloVe, which again verifies the importance of semantic information for shot-stable FSOD.
+
+# D. Reduced Dimension in Relation Reasoning
+
+In the relation reasoning module, the dimension of word embeddings is reduced by linear layers before computing
+
+![](images/22a394db07435b0ac5007abdffbb367248b45c75924358a10485a3c93fcf0e23.jpg)  
+(a) Before relation reasoning
+
+![](images/00870188fab5844d8174f8d6fd97f0a1cbbbd125386bc7c2aced6a04702d4731.jpg)  
+(b) After relation reasoning
+
+![](images/7513b994a7c6edb10f7c79b4242aef6eb0cda48d359512b1088e6744d9d69954.jpg)  
+(c) Difference between above correlation maps  
+Figure 7. Correlation of the semantic embeddings before and after the relation reasoning between the base classes and the novel classes on the VOC dataset. The novel classes are from Novel Set 1. The last figure shows how does the correlation change subtly. Some novel classes are getting more correlated with base classes after relation reasoning, e.g. "sofa" with "bottle" and "table". Best viewed in color.
+
+<table><tr><td rowspan="2">Word embeddings</td><td colspan="5">Novel Set 1</td></tr><tr><td>shot=1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>Random-300d</td><td>33.2</td><td>37.5</td><td>43.0</td><td>47.0</td><td>51.5</td></tr><tr><td>Word2Vec-300d [27]</td><td>42.8</td><td>47.1</td><td>49.0</td><td>50.8</td><td>52.8</td></tr><tr><td>GloVe-300d [31]</td><td>38.8</td><td>44.8</td><td>46.6</td><td>49.0</td><td>54.3</td></tr><tr><td>GloVe-200d [31]</td><td>39.7</td><td>44.6</td><td>45.8</td><td>49.4</td><td>53.0</td></tr></table>
+
+Table 7. FSOD performance (mAP50) on the VOC Novel Set 1 under different word embeddings in the semantic space projection. All models are using the ResNet-50 network. 300d and 200d mean the numbers of embedding dimension are 300 and 200 respectively. The Word2Vec provides better representations than the GloVe.
+
+the attention map, which saves computational time. We empirically test different dimensions and select the one with the best performance, i.e. when the dimension is 32. But other choices are just slightly worse. Table 8 reports the results on VOC dataset under different dimensions. All the experiments are following the same setting as in the main paper. The only exception is that we use ResNet-50 [16] to
+
+<table><tr><td rowspan="2">Dimension</td><td colspan="5">Novel Set 1</td></tr><tr><td>shot=1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>128</td><td>40.9</td><td>44.6</td><td>44.3</td><td>48.1</td><td>54.1</td></tr><tr><td>64</td><td>42.0</td><td>47.4</td><td>48.9</td><td>51.7</td><td>54.1</td></tr><tr><td>32</td><td>42.4</td><td>46.8</td><td>48.1</td><td>51.9</td><td>54.7</td></tr><tr><td>16</td><td>44.1</td><td>46.0</td><td>47.8</td><td>51.7</td><td>54.7</td></tr></table>
+
+Table 8. FSOD performance (mAP50) on the VOC Novel Set 1 under different reduced feature dimension in the relation reasoning module. Bold font indicates best or second best results. All models are using the ResNet-50 network.  
+
+<table><tr><td rowspan="2">Tunable Parameters</td><td colspan="5">Novel Set 1</td></tr><tr><td>shot=1</td><td>2</td><td>3</td><td>5</td><td>10</td></tr><tr><td>Last layer (TFA [39])</td><td>39.8</td><td>36.1</td><td>44.7</td><td>55.7</td><td>56.0</td></tr><tr><td>+FCs</td><td>36.9</td><td>34.9</td><td>45.3</td><td>53.0</td><td>55.9</td></tr><tr><td>+FCs +RPN</td><td>37.2</td><td>39.8</td><td>44.3</td><td>52.7</td><td>56.2</td></tr><tr><td>+FCs +RPN +Backbone</td><td>16.2</td><td>19.5</td><td>24.8</td><td>39.2</td><td>44.6</td></tr></table>
+
+Table 9. FSOD results (mAP50) on the VOC Novel Set 1 with more and more tunable parameters in the finetuning stage. The baseline is TFA [39] which only finetunes the last classification layer in the Faster R-CNN. We gradually unfreeze more previous layers including two fully-connected layers (FCs) after the RoI-pooling, layers in region proposal network (RPN), and layers in the Backbone. This proves that finetuning more parameters does not guarantee better performance in few-shot detection.
+
+reduce the computational cost of tuning hyperparameters.
+
+# E. Finetuning More Parameters
+
+Similar to TFA [39], we have a finetuning stage to make the detector generalized to novel classes. For the classification subnet, we finetune the parameters in the relation reasoning module and the projection matrix while all the parameters in previous layers are frozen. Some may argue that the improvement of our SRR-FSD over the baseline is due to more parameters finetuned in the relation reasoning module compared to the Faster R-CNN [35] baseline. But we show that finetuning more parameters does not necessarily lead to better results in Table 9. We take the TFA model which is essentially a Faster R-CNN finetuned with only the last layer trainable and gradually unfreeze the previous layers. It turns out more parameters involved in finetuning do not change the results substantially and that too many parameters will lead to severe overfitting.
+
+# F. Complete Results on VOC
+
+In Table 10, we present the complete results on the VOC [13] dataset as in FSRW [19] and Meta R-CNN [44]. We also include the very recent MPSR [42] for comparison. MPSR develops an auxiliary branch to generate multi-scale positive samples as object pyramids and to refine the prediction at various scales. Note that MPSR improves its base
+
+<table><tr><td rowspan="2">Shot</td><td rowspan="2">Method</td><td colspan="5">Novel Set 1</td><td colspan="5">Novel Set 2</td><td colspan="5">Novel Set 3</td><td></td><td></td><td></td></tr><tr><td>bird bus</td><td>cow</td><td>mbike</td><td>sofa</td><td>mean</td><td>aero</td><td>bottle</td><td>cow</td><td>horse</td><td>sofa</td><td>mean</td><td>boat</td><td>cat</td><td>mbike</td><td>sheep</td><td>sofa</td><td>mean</td><td></td></tr><tr><td rowspan="4">1</td><td>FSRW</td><td>13.5</td><td>10.6</td><td>31.5</td><td>13.8</td><td>4.3</td><td>14.8</td><td>11.8</td><td>9.1</td><td>15.6</td><td>23.7</td><td>18.2</td><td>15.7</td><td>10.8</td><td>44.0</td><td>17.8</td><td>18.1</td><td>5.3</td><td>19.2</td></tr><tr><td>Meta R-CNN</td><td>6.1</td><td>32.8</td><td>15.0</td><td>35.4</td><td>0.2</td><td>19.9</td><td>23.9</td><td>0.8</td><td>23.6</td><td>3.1</td><td>0.7</td><td>10.4</td><td>0.6</td><td>31.1</td><td>28.9</td><td>11.0</td><td>0.1</td><td>14.3</td></tr><tr><td>MPSR</td><td>33.5</td><td>41.2</td><td>57.6</td><td>54.5</td><td>21.6</td><td>41.7</td><td>21.2</td><td>9.1</td><td>36.0</td><td>30.9</td><td>25.1</td><td>24.4</td><td>14.9</td><td>47.8</td><td>57.7</td><td>34.7</td><td>22.8</td><td>35.6</td></tr><tr><td>SRR-FSD (Ours)</td><td>38.1</td><td>53.8</td><td>58.7</td><td>64.1</td><td>24.4</td><td>47.8</td><td>27.9</td><td>4.6</td><td>50.5</td><td>53.9</td><td>25.5</td><td>32.5</td><td>16.2</td><td>57.2</td><td>62.9</td><td>48.3</td><td>16.0</td><td>40.1</td></tr><tr><td rowspan="4">2</td><td>FSRW</td><td>21.2</td><td>12.0</td><td>16.8</td><td>17.9</td><td>9.6</td><td>15.5</td><td>28.6</td><td>0.9</td><td>27.6</td><td>0.0</td><td>19.5</td><td>15.3</td><td>5.3</td><td>46.4</td><td>18.4</td><td>26.1</td><td>12.4</td><td>21.7</td></tr><tr><td>Meta R-CNN</td><td>17.2</td><td>34.4</td><td>43.8</td><td>31.8</td><td>0.4</td><td>25.5</td><td>12.4</td><td>0.1</td><td>44.4</td><td>50.1</td><td>0.1</td><td>19.4</td><td>10.6</td><td>24.0</td><td>36.2</td><td>19.2</td><td>0.8</td><td>18.2</td></tr><tr><td>MPSR</td><td>38.2</td><td>28.6</td><td>56.5</td><td>57.3</td><td>32.0</td><td>42.5</td><td>36.5</td><td>9.1</td><td>45.1</td><td>21.6</td><td>34.2</td><td>29.3</td><td>17.9</td><td>49.6</td><td>59.2</td><td>49.2</td><td>32.9</td><td>41.8</td></tr><tr><td>SRR-FSD (Ours)</td><td>35.8</td><td>57.7</td><td>59.3</td><td>61.8</td><td>38.0</td><td>50.5</td><td>34.4</td><td>5.7</td><td>57.1</td><td>44.0</td><td>35.5</td><td>35.3</td><td>15.5</td><td>51.4</td><td>62.6</td><td>44.4</td><td>33.7</td><td>41.5</td></tr><tr><td rowspan="4">3</td><td>FSRW</td><td>26.1</td><td>19.1</td><td>40.7</td><td>20.4</td><td>27.1</td><td>26.7</td><td>29.4</td><td>4.6</td><td>34.9</td><td>6.8</td><td>37.9</td><td>22.7</td><td>11.2</td><td>39.8</td><td>20.9</td><td>23.7</td><td>33.0</td><td>25.7</td></tr><tr><td>Meta R-CNN</td><td>30.1</td><td>44.6</td><td>50.8</td><td>38.8</td><td>10.7</td><td>35.0</td><td>25.2</td><td>0.1</td><td>50.7</td><td>53.2</td><td>18.8</td><td>29.6</td><td>16.3</td><td>39.7</td><td>32.6</td><td>38.8</td><td>10.3</td><td>27.5</td></tr><tr><td>MPSR</td><td>35.1</td><td>60.6</td><td>56.6</td><td>61.5</td><td>43.4</td><td>51.4</td><td>49.2</td><td>9.1</td><td>47.1</td><td>46.3</td><td>44.3</td><td>39.2</td><td>14.4</td><td>60.6</td><td>57.1</td><td>37.2</td><td>42.3</td><td>42.3</td></tr><tr><td>SRR-FSD (Ours)</td><td>35.2</td><td>55.6</td><td>61.3</td><td>62.9</td><td>41.5</td><td>51.3</td><td>42.3</td><td>11.5</td><td>57.0</td><td>43.6</td><td>41.2</td><td>39.1</td><td>23.1</td><td>50.6</td><td>60.0</td><td>49.3</td><td>38.6</td><td>44.3</td></tr><tr><td rowspan="4">5</td><td>FSRW</td><td>31.5</td><td>21.1</td><td>39.8</td><td>40.0</td><td>37.0</td><td>33.9</td><td>33.1</td><td>9.4</td><td>38.4</td><td>25.4</td><td>44.0</td><td>30.1</td><td>14.2</td><td>57.3</td><td>50.8</td><td>38.9</td><td>41.6</td><td>40.6</td></tr><tr><td>Meta R-CNN</td><td>35.8</td><td>47.9</td><td>54.9</td><td>55.8</td><td>34.0</td><td>45.7</td><td>28.5</td><td>0.3</td><td>50.4</td><td>56.7</td><td>38.0</td><td>34.8</td><td>16.6</td><td>45.8</td><td>53.9</td><td>41.5</td><td>48.1</td><td>41.2</td></tr><tr><td>MPSR</td><td>39.7</td><td>65.5</td><td>55.1</td><td>68.5</td><td>47.4</td><td>55.2</td><td>47.8</td><td>10.4</td><td>45.2</td><td>47.5</td><td>48.8</td><td>39.9</td><td>20.9</td><td>56.6</td><td>68.1</td><td>48.4</td><td>45.8</td><td>48.0</td></tr><tr><td>SRR-FSD (Ours)</td><td>46.1</td><td>58.6</td><td>64.6</td><td>63.5</td><td>43.2</td><td>55.2</td><td>44.2</td><td>12.3</td><td>56.5</td><td>51.3</td><td>39.8</td><td>40.8</td><td>20.4</td><td>55.5</td><td>65.4</td><td>51.9</td><td>41.3</td><td>46.9</td></tr><tr><td rowspan="4">10</td><td>FSRW</td><td>30.0</td><td>62.7</td><td>43.2</td><td>60.6</td><td>39.6</td><td>47.2</td><td>43.2</td><td>13.9</td><td>41.5</td><td>58.1</td><td>39.2</td><td>39.2</td><td>20.1</td><td>51.8</td><td>55.6</td><td>42.4</td><td>36.6</td><td>41.3</td></tr><tr><td>Meta R-CNN</td><td>52.5</td><td>55.9</td><td>52.7</td><td>54.6</td><td>41.6</td><td>51.5</td><td>52.8</td><td>3.0</td><td>52.1</td><td>70.0</td><td>49.2</td><td>45.4</td><td>13.9</td><td>72.6</td><td>58.3</td><td>47.8</td><td>47.6</td><td>48.1</td></tr><tr><td>MPSR</td><td>48.3</td><td>73.7</td><td>68.2</td><td>70.8</td><td>48.2</td><td>61.8</td><td>51.8</td><td>16.7</td><td>53.1</td><td>66.4</td><td>51.2</td><td>47.8</td><td>24.4</td><td>55.8</td><td>67.5</td><td>50.4</td><td>50.5</td><td>49.7</td></tr><tr><td>SRR-FSD (Ours)</td><td>45.0</td><td>67.4</td><td>63.1</td><td>65.2</td><td>43.3</td><td>56.8</td><td>46.2</td><td>18.4</td><td>54.0</td><td>59.1</td><td>41.4</td><td>43.8</td><td>17.1</td><td>55.1</td><td>67.4</td><td>47.5</td><td>44.7</td><td>46.4</td></tr></table>
+
+Table 10. AP50 performance of each novel class on the few-shot VOC dataset. Bold font indicates the best result in the group. Our SRR-FSD trained with visual information and semantic relation demonstrates shot-stable performance.
+
+line by a considerable margin but its research direction is orthogonal and complimentary to ours because it is still exclusively dependent on visual information. Therefore, our approach combining visual information and semantic relation reasoning can achieve superior performance at extremely low shot (e.g. 1, 2) conditions.
+
+# G. Interpretation of the Dynamic Relation Graph
+
+In the relation reasoning module, we propose to learn a dynamic relation graph driven by the data, which is conceptually different from the predefined fixed knowledge graphs used in [40, 8, 30]. We implement the dynamic graph with the self-attention architecture [37]. Although it is in the form of a feedforward network, it can also be interpreted as a computation related to the knowledge graph. If we denote the transformations in the linear layers  $f$ ,  $g$ ,  $h$ ,  $l$  as  $\mathbf{T}_f$ ,  $\mathbf{T}_g$ ,  $\mathbf{T}_h$ ,  $\mathbf{T}_l$  respectively, we can formulate the relation reasoning in Eq. (4)
+
+$$
+\mathbf {W} _ {e} ^ {\prime} = \delta (\mathbf {W} _ {e} \mathbf {T} _ {f} \mathbf {T} _ {g} ^ {T} \mathbf {W} _ {e} ^ {T}) \mathbf {W} _ {e} \mathbf {T} _ {h} \mathbf {T} _ {l} + \mathbf {W} _ {e} (4)
+$$
+
+where  $\mathbf{W}_e^{\prime}$  is the matrix of augmented word embeddings after the relation reasoning which will be used as the weights to compute classification scores and  $\delta$  is the softmax function operated on the last dimension of the input matrix. The item  $\delta (\mathbf{W}_e\mathbf{T}_f\mathbf{T}_g^T\mathbf{W}_e^T)$  can be interpreted as a  $N\times N$  dynamic knowledge graph in which the learnable parameters
+
+are  $\mathbf{T}_f$  and  $\mathbf{T}_g$ . And it is involved in the computation of the classification scores via the graph convolution operation [21], which connects the  $N$  word embeddings in  $\mathbf{W}_e$  to allow knowledge propagation among them. The item  $\mathbf{T}_h\mathbf{T}_l$  can be viewed as a learnable transformation applied to each embedding independently.
+
+# References
+
+[1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chellappa, and Ajay Divakaran. Zero-shot object detection. In Proceedings of the European Conference on Computer Vision (ECCV), pages 384-400, 2018. 2, 3  
+[2] Zhaowei Cai and Nuno Vasconcelos. Cascade r-cnn: Delving into high quality object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6154-6162, 2018. 3  
+[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. arXiv preprint arXiv:2005.12872, 2020. 3  
+[4] Andrew Carlson, Justin Betteridge, Bryan Kisiel, Burr Settles, Estevam R Hruschka Jr, and Tom M Mitchell. Toward an architecture for never-ending language learning. In Aaai, volume 5. Atlanta, 2010. 2, 3  
+[5] Hao Chen, Yali Wang, Guoyou Wang, and Yu Qiao. Lstd: A low-shot transfer detector for object detection. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018. 1, 3
+
+[6] Kai Chen, Jiaqi Wang, Jiangmiao Pang, Yuhang Cao, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jiarui Xu, et al. Mmdetection: Open mmlab detection toolbox and benchmark. arXiv preprint arXiv:1906.07155, 2019. 5, 6  
+[7] Zitian Chen, Yanwei Fu, Yinda Zhang, Yu-Gang Jiang, Xi-angyang Xue, and Leonid Sigal. Multi-level semantic feature augmentation for one-shot learning. IEEE Transactions on Image Processing, 28(9):4594-4605, 2019. 3  
+[8] Zhao-Min Chen, Xiu-Shen Wei, Peng Wang, and Yanwen Guo. Multi-label image recognition with graph convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5177-5186, 2019. 3, 5, 7, 8, 11  
+[9] Jifeng Dai, Yi Li, Kaiming He, and Jian Sun. R-fcn: Object detection via region-based fully convolutional networks. In Advances in neural information processing systems, pages 379-387, 2016. 3  
+[10] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. IEEE, 2009. 1, 4, 6, 9  
+[11] Xuanyi Dong, Liang Zheng, Fan Ma, Yi Yang, and Deyu Meng. Few-example object detection with model communication. IEEE transactions on pattern analysis and machine intelligence, 41(7):1641-1654, 2018. 1, 3  
+[12] Kaiwen Duan, Song Bai, Lingxi Xie, Honggang Qi, Qingming Huang, and Qi Tian. Centernet: Object detection with keypoint triplets. In Proceedings of the IEEE International Conference on Computer Vision, 2019. 3  
+[13] Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The pascal visual object classes (voc) challenge. International journal of computer vision, 88(2):303-338, 2010. 1, 5, 7, 9, 10  
+[14] Qi Fan, Wei Zhuo, Chi-Keung Tang, and Yu-Wing Tai. Few-shot object detection with attention-rpn and multi-relation detector. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4013–4022, 2020. 1, 3  
+[15] Jiechao Guan, Zhiwu Lu, Tao Xiang, Aoxue Li, An Zhao, and Ji-Rong Wen. Zero and few shot learning with semantic feature synthesis and competitive learning. IEEE transactions on pattern analysis and machine intelligence, 2020. 3  
+[16] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 5, 7, 10  
+[17] Derek Hoiem, Yodsawalai Chodpathumwan, and Qieyun Dai. Diagnosing error in object detectors. In European conference on computer vision, pages 340-353. Springer, 2012. 8  
+[18] Ting-I Hsieh, Yi-Chen Lo, Hwann-Tzong Chen, and Tyng-Luh Liu. One-shot object detection with co-attention and co-excitation. In Advances in Neural Information Processing Systems, pages 2725–2734, 2019. 7  
+[19] Bingyi Kang, Zhuang Liu, Xin Wang, Fisher Yu, Jiashi Feng, and Trevor Darrell. Few-shot object detection via feature
+
+reweighting. In Proceedings of the IEEE International Conference on Computer Vision, pages 8420-8429, 2019. 1, 3, 5, 6, 7, 10  
+[20] Leonid Karlinsky, Joseph Shtok, Sivan Harary, Eli Schwartz, Amit Aides, Rogerio Feris, Raja Giryes, and Alex M Bronstein. Repmet: Representative-based metric learning for classification and few-shot object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5197-5206, 2019. 1, 3  
+[21] T.N. Kipf and M. Welling. Semi-supervised classification with graph convolutional network. In International Conference on Learning Representations (ICLR), 2017. 3, 4, 11  
+[22] Hei Law and Jia Deng. Cornernet: Detecting objects as paired keypoints. In Proceedings of the European Conference on Computer Vision (ECCV), pages 734-750, 2018. 3  
+[23] Tsung-Yi Lin, Piotr Dólar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2117-2125, 2017. 3, 5, 7  
+[24] Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dólar. Focal loss for dense object detection. In Proceedings of the IEEE international conference on computer vision, pages 2980-2988, 2017. 3  
+[25] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 5, 9  
+[26] Wei Liu, Dragomir Anguelov, Dumitru Erhan, Christian Szegedy, Scott Reed, Cheng-Yang Fu, and Alexander C Berg. Ssd: Single shot multibox detector. In European conference on computer vision, pages 21-37. Springer, 2016. 3  
+[27] Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems, pages 3111-3119, 2013. 2, 4, 5, 9, 10  
+[28] George A Miller. Wordnet: a lexical database for english. Communications of the ACM, 38(11):39-41, 1995. 2, 3, 4  
+[29] Jiangmiao Pang, Kai Chen, Jianping Shi, Huajun Feng, Wanli Ouyang, and Dahua Lin. Libra r-cnn: Towards balanced learning for object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 821-830, 2019. 3  
+[30] Zhimao Peng, Zechao Li, Junge Zhang, Yan Li, Guo-Jun Qi, and Jinhui Tang. Few-shot image recognition with knowledge transfer. In Proceedings of the IEEE International Conference on Computer Vision, pages 441-449, 2019. 2, 3, 11  
+[31] Jeffrey Pennington, Richard Socher, and Christopher D Manning. Glove: Global vectors for word representation. In Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), pages 1532–1543, 2014. 2, 9, 10  
+[32] Shafin Rahman, Salman Khan, and Nick Barnes. Improved visual-semantic alignment for zero-shot object detection. In AAAI, pages 11932–11939, 2020. 3
+
+[33] Shafin Rahman, Salman Khan, Nick Barnes, and Fahad Shahbaz Khan. Any-shot object detection. arXiv preprint arXiv:2003.07003, 2020. 3, 4, 5, 7, 8  
+[34] Joseph Redmon and Ali Farhadi. Yolo9000: better, faster, stronger. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7263-7271, 2017. 1, 3  
+[35] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In Advances in neural information processing systems, pages 91-99, 2015. 1, 3, 4, 5, 7, 8, 10  
+[36] Zhi Tian, Chunhua Shen, Hao Chen, and Tong He. Fcos: Fully convolutional one-stage object detection. In Proceedings of the IEEE International Conference on Computer Vision, 2019. 3  
+[37] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pages 5998-6008, 2017. 5, 11  
+[38] Jiaqi Wang, Kai Chen, Shuo Yang, Chen Change Loy, and Dahua Lin. Region proposal by guided anchoring. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2965-2974, 2019. 3  
+[39] Xin Wang, Thomas E Huang, Trevor Darrell, Joseph E Gonzalez, and Fisher Yu. Frustratingly simple few-shot object detection. arXiv preprint arXiv:2003.06957, 2020. 1, 3, 5, 6, 7, 10  
+[40] Xiaolong Wang, Yufei Ye, and Abhinav Gupta. Zero-shot recognition via semantic embeddings and knowledge graphs. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6857-6866, 2018. 2, 3, 11  
+[41] Yu-Xiong Wang, Deva Ramanan, and Martial Hebert. Meta-learning to detect rare objects. In Proceedings of the IEEE International Conference on Computer Vision, pages 9925-9934, 2019. 1, 3, 5, 6  
+[42] Jiaxi Wu, Songtao Liu, Di Huang, and Yunhong Wang. Multi-scale positive sample refinement for few-shot object detection. In European conference on computer vision. Springer, 2020. 1, 3, 6, 10  
+[43] Yang Xiao and Renaud Marlet. Few-shot object detection and viewpoint estimation for objects in the wild. In European conference on computer vision. Springer, 2020. 1, 3  
+[44] Xiaopeng Yan, Ziliang Chen, Anni Xu, Xiaoxi Wang, Xiaodan Liang, and Liang Lin. Meta r-cnn: Towards general solver for instance-level low-shot learning. In Proceedings of the IEEE International Conference on Computer Vision, pages 9577-9586, 2019. 1, 3, 5, 6, 7, 10  
+[45] Ze Yang, Shaohui Liu, Han Hu, Liwei Wang, and Stephen Lin. Repoints: Point set representation for object detection. In Proceedings of the IEEE International Conference on Computer Vision, 2019. 3  
+[46] Ze Yang, Yali Wang, Xianyu Chen, Jianzhuang Liu, and Yu Qiao. Context-transformer: Tackling object confusion for few-shot detection. In AAAI, pages 12653-12660, 2020. 1, 3  
+[47] Xiaosong Zhang, Fang Wan, Chang Liu, Rongrong Ji, and Qixiang Ye. Freeanchor: Learning to match anchors for vi
+
+sual object detection. In Advances in neural information processing systems, 2019. 3  
+[48] Xingyi Zhou, Jiacheng Zhuo, and Philipp Krahenbuhl. Bottom-up object detection by grouping extreme and center points. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 850-859, 2019. 3  
+[49] Chenchen Zhu, Fangyi Chen, Zhiqiang Shen, and Marios Savvides. Soft anchor-point object detection. In Proceedings of the European Conference on Computer Vision (ECCV), 2020. 3  
+[50] Chenchen Zhu, Yihui He, and Marios Savvides. Feature selective anchor-free module for single-shot object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2019. 3

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