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CE\(^2\): A Copula Entropic Mutual Information Estimator for Enhancing Adversarial Robustness

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Pattern Recognition and Computer Vision (PRCV 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14428))

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Abstract

Deep neural networks are vulnerable to adversarial examples, which exploit imperceptible perturbations to mislead classifiers. To improve adversarial robustness, recent methods have focused on estimating mutual information (MI). However, existing MI estimators struggle to provide stable and reliable estimates in high-dimensional data. To this end, we propose a Copula Entropic MI Estimator (CE\(^2\)) to address these limitations. CE\(^2\) leverages copula entropy to estimating MI in high dimensions, allowing target models to harness information from both clean and adversarial examples to withstand attacks. Our empirical experiments demonstrate that CE\(^2\) achieves a trade-off between variance and bias in MI estimates, resulting in stable and reliable estimates. Furthermore, the defense algorithm based on CE\(^2\) significantly enhances adversarial robustness against multiple attacks. The experimental results underscore the effectiveness of CE\(^2\) and its potential for improving adversarial robustness.

This work was supported in part by the National Natural Science Foundation of China (Grant No. 62006097, U1836218), in part by the Natural Science Foundation of Jiangsu Province (Grant No. BK20200593) and in part by the China Postdoctoral Science Foundation (Grant No. 2021M701456).

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Authors and Affiliations

  1. School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China

    Lin Liu, Cong Hu & Xiao-Jun Wu

Authors
  1. Lin Liu
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  2. Cong Hu
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  3. Xiao-Jun Wu
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Corresponding author

Correspondence to Cong Hu .

Editor information

Editors and Affiliations

  1. Nanjing University of Information Science and Technology, Nanjing, China

    Qingshan Liu

  2. Xiamen University, Xiamen, China

    Hanzi Wang

  3. Beijing University of Posts and Telecommunications, Beijing, China

    Zhanyu Ma

  4. Sun Yat-sen University, Guangzhou, China

    Weishi Zheng

  5. Peking University, Beijing, China

    Hongbin Zha

  6. Chinese Academy of Sciences, Beijing, China

    Xilin Chen

  7. Chinese Academy of Sciences, Beijing, China

    Liang Wang

  8. Xiamen University, Xiamen, China

    Rongrong Ji

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Liu, L., Hu, C., Wu, XJ. (2024). CE\(^2\): A Copula Entropic Mutual Information Estimator for Enhancing Adversarial Robustness. In: Liu, Q., et al. Pattern Recognition and Computer Vision. PRCV 2023. Lecture Notes in Computer Science, vol 14428. Springer, Singapore. https://doi.org/10.1007/978-981-99-8462-6_14

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  • DOI: https://doi.org/10.1007/978-981-99-8462-6_14

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  • Print ISBN: 978-981-99-8461-9

  • Online ISBN: 978-981-99-8462-6

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