Cheng-Cheng Ma, Bao-Yuan Wu, Yan-Bo Fan, Yong Zhang, Zhi-Feng Li. Effective and Robust Detection of Adversarial Examples via Benford-Fourier Coefficients. Machine Intelligence Research. https://doi.org/10.1007/s11633-022-1328-1
Citation: Cheng-Cheng Ma, Bao-Yuan Wu, Yan-Bo Fan, Yong Zhang, Zhi-Feng Li. Effective and Robust Detection of Adversarial Examples via Benford-Fourier Coefficients. Machine Intelligence Research. https://doi.org/10.1007/s11633-022-1328-1

Effective and Robust Detection of Adversarial Examples via Benford-Fourier Coefficients

doi: 10.1007/s11633-022-1328-1
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  • Author Bio:

    Cheng-Cheng Ma received the B. Sc. degree in automation from Northwestern Polytechnical University, China in 2017. Currently, he is a Ph. D. degree candidate of Institute of Automation, Chinese Academy of Sciences, China. His research interests include adversarial learning and machine learning. E-mail: machengcheng2017@ia.ac.cn ORCID iD: 0000-0002-0502-3960

    Bao-Yuan Wu received the Ph. D. degree in pattern recognition and intelligent systems from National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, China in 2014. From November 2016 to August 2020, he was a senior and principal researcher at AI Lab, Tencent Inc., China. Currently, he is an associate professor of School of Data Science, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), China. He is also the director of the Secure Computing Lab of Big Data, Shenzhen Research Institute of Big Data (SBRID), China. He has published more than 50 top-tier conference and journal papers, including TPAMI, IJCV, NeurIPS, CVPR, ICCV, ECCV, ICLR, AAAI, and one paper was selected as the Best Paper Finalist of CVPR 2019. He is currently serving as an Associate Editor of Neurocomputing, Area Chair of ICLR 2022, AAAI 2022 and ICIG 2021, Senior Program Committee Member of AAAI 2021 and IJCAI 2020/2021. His research interests include AI security and privacy, machine learning, computer vision and optimization. E-mail: wubaoyuan@cuhk.edu.cn (Corresponding author) ORCID iD: 0000-0003-2183-5990

    Yan-Bo Fan received the B. Sc. degree in computer science and technology from Hunan University, China in 2013, and the Ph. D. degree in pattern recognition and intelligent systems from Institute of Automation, Chinese Academy of Sciences, China in 2018, He is currently a senior researcher at AI Lab, Tencent Inc., China. His research interests include computer vision and machine learning. E-mail: fanyanbo0124@gmail.com ORCID iD: 0000-0002-8530-485X

    Yong Zhang received the Ph. D. degree in pattern recognition and intelligent systems from Institute of Automation, Chinese Academy of Sciences, China in 2018. From 2015 to 2017, he was a visiting scholar with the Rensselaer Polytechnic Institute, USA. He is currently with AI Lab, Tencent Inc., China. His research interests include computer vision and machine learning. E-mail: zhangyong201303@gmail.com ORCID iD: 0000-0003-0066-3448

    Zhi-Feng Li received the Ph. D. degree from The Chinese University of Hong Kong, China in 2006. After that, he was a postdoctoral fellow at The Chinese University of Hong Kong, China, and Michigan State University, USA for several years. He is currently a top-tier principal research scientist with Tencent, China. Before joining Tencent, he was a full professor with Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China. He was one of the 2020 Most Cited Chinese Researchers (Elsevier-Scopus) in computer science and technology. He is currently serving on the editorial boards of Neurocomputing, IEEE Transactions on Circuits and Systems for Video Technology, and Pattern Recognition. He is a Fellow of British Computer Society (FBCS). His research interests include deep learning, computer vision and pattern recognition, and face detection and recognition. E-mail: michaelzfli@tencent.com ORCID iD: 0000-0001-5902-5067

  • Corresponding author: Baoyuan Wu (wubaoyuan@cuhk.edu.cn)
  • Received Date: 2021-12-31
  • Accepted Date: 2022-03-24
  • Publish Online: 2022-04-25
  • Adversarial example has been well known as a serious threat to deep neural networks (DNNs). In this work, we study the detection of adversarial examples based on the assumption that the output and internal responses of one DNN model for both adversarial and benign examples follow the generalized Gaussian distribution (GGD) but with different parameters (i.e., shape factor, mean, and variance). GGD is a general distribution family that covers many popular distributions (e.g., Laplacian, Gaussian, or uniform). Therefore, it is more likely to approximate the intrinsic distributions of internal responses than any specific distribution. Besides, since the shape factor is more robust to different databases rather than the other two parameters, we propose to construct discriminative features via the shape factor for adversarial detection, employing the magnitude of Benford-Fourier (MBF) coefficients, which can be easily estimated using responses. Finally, a support vector machine is trained as an adversarial detector leveraging the MBF features. Extensive experiments in terms of image classification demonstrate that the proposed detector is much more effective and robust in detecting adversarial examples of different crafting methods and sources compared to state-of-the-art adversarial detection methods.

     

  • 1 The base number can be other numbers than 10. See Table 7 for ablation study on base number.
    2 https://pytorch.org/docs/robust/torchvision/models.html3 https://foolbox.readthedocs.io/en/v1.8.04 https://github.com/rfeinman/detecting-adversarial-samples5 https://github.com/pokaxpoka/deep_Mahalanobis_detector6 https://github.com/xingjunm/lid_adversarial_subspace_detection7https://www.mathworks.com/help/stats/fitcsvm.html
    https://foolbox.readthedocs.io/en/v1.8.0
    https://github.com/rfeinman/detecting-adversarial-samples
    https://github.com/pokaxpoka/deep_Mahalanobis_detector
    https://github.com/xingjunm/lid_adversarial_subspace_detection
    https://www.mathworks.com/help/stats/fitcsvm.html
    8 https://image.baidu.com9 https://www.facebook.com
    https://www.facebook.com
    10 https://github.com/kabkabm/defensegan
    11 https://github.com/s-huu/TurningWeaknessIntoStrength
    12 https://github.com/yk/icml19_public13 https://github.com/jayaram-r/adversarial-detection
    https://github.com/jayaram-r/adversarial-detection
    14 https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.ks_2samp.html
    †These authors contributed equally to this work.
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