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Why does batch normalization induce the model vulnerability on adversarial images?

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Abstract

Batch normalization is one of the most widely used components in deep neural networks. It can accelerate training, and boost model performance on normal samples. However, batch normalization induces vulnerability to models on adversarial examples, especially in medical images, and the reason is still not clear. In this paper, we aim to explain the vulnerability aroused by batch normalization under adversarial images. Specifically, we first discover that both natural and medical images contain a large number of trivial features, whose weights will be enlarged under adversarial attacks, and batch normalization can further enlarge their weights. Additionally, we find that batch normalization will reduce the inter-class margin of high-level features, leading to less tolerance to adversarial perturbations, thereby decreasing the model robustness. Moreover, we hypothesize that the smaller inter-class margin, the more difficult to attain the optimal classification space, which means batch normalization will restrict the performance of adversarial training. This further verifies that a narrower inter-class margin induced by batch normalization reduces the model robustness. Experiments on four benchmark datasets demonstrate our discovery, interpretation and hypothesis.

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Notes

  1. You can access it from https://www.kaggle.com/c/imagenet-object-localization-challenge/data

  2. You can access it from https://www.kaggle.com/nih-chest-xrays/data

  3. You can access it from https://www.kaggle.com/c/rsna-pneumonia-detection-challenge/data

  4. You can access it from https://cocodataset.org/#download

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Funding

This work is partially supported by the National Natural Science Foundation of China (Grant No: 61876046) and the Guangxi “Bagui” Teams for Innovation and Research.

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Authors and Affiliations

  1. School of Computer Science and Engineering at University of Electronic Science and Technology of China, Chengdu, 611731, China

    Fei Kong, Fangqi Liu & Xiaoshuang Shi

  2. Department of Computer Science at Drexel University, Philadelphia, PA, 19104, USA

    Kaidi Xu

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  1. Fei Kong
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  2. Fangqi Liu
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  3. Kaidi Xu
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  4. Xiaoshuang Shi
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Correspondence to Xiaoshuang Shi.

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This article belongs to the Topical Collection: Special Issue on Web-based Intelligent Financial Services.

Guest Editors: Hong-Ning Dai, Xiaohui Haoran, and Miguel Martinez.

This work is partially supported by the National Natural Science Foundation of China (Grant No: 61876046) and the Guangxi “Bagui” Teams for Innovation and Research.

Appendices

Appendix : A: Details about the Datasets

Table 5 and 6 show the selected categories and their numbers of images for training and testing. We select those classes because of their relatively large number of samples. It is easy to train our model and analyze our results on those samples.

Table 5 Selected categories and the number of selected images from the ILSVRC dataset
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Table 6 Selected categories and the number of selected images from the COCO dataset
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Appendix : B: Details of Network Architectures

Table 7 shows the details of convolutional layers of the model VGG. We mark the location for extracting mid-level features and high-level features by space. Table 8 displays the details of fully connection layers. Top block presents the details of VGG16, and the bottom block provides the details of VGG-C.

Table 7 Convolutional layers in VGG16 and VGG-C. In each Conv2d, the bias is True, the padding size is 1, the stride size is 1. out_ch means the number of channels of output, ks means the kernel size. Batch normalization and ReLU are followed by each Conv2d layer. The first and the second space mark that the layer above is middle-level feature and high-level feature
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Table 8 The used classifiers in VGG16 and VGG-C. VGG16 adopts the classifier in the top block (rows above space), and VGG-C employs the classifier in the bottom block (rows below space)
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Table 9 The used architecture of ResNet18. The first and the second space mark that the layer above is middle-level feature and high-level feature
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Appendix : C: The Architecture of Basic Block

Table 9 shows the details of ResNet18. We mark the location for extracting mid-level features and high-level features by space. Figure 5 presents the details of Basic Block used in Table 9.

Fig. 5
figure 5

The architecture of Basic Block

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Kong, F., Liu, F., Xu, K. et al. Why does batch normalization induce the model vulnerability on adversarial images?. World Wide Web 26, 1073–1091 (2023). https://doi.org/10.1007/s11280-022-01066-7

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