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Detection of Iterative Adversarial Attacks via Counter Attack

Author

Listed:
  • Matthias Rottmann

    (University of Wuppertal)

  • Kira Maag

    (Ruhr University Bochum)

  • Mathis Peyron

    (Institut de Recherche en Informatique de Toulouse)

  • Hanno Gottschalk

    (Technical University of Berlin)

  • Nataša Krejić

    (University of Novi Sad)

Abstract

Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However, for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added to the input can be used to fool DNNs. Various attacks, hardening methods and detection methods have been introduced in recent years. Notoriously, Carlini–Wagner (CW)-type attacks computed by iterative minimization belong to those that are most difficult to detect. In this work we outline a mathematical proof that the CW attack can be used as a detector itself. That is, under certain assumptions and in the limit of attack iterations this detector provides asymptotically optimal separation of original and attacked images. In numerical experiments, we experimentally validate this statement and furthermore obtain AUROC values up to $$99.73\%$$ 99.73 % on CIFAR10 and ImageNet. This is in the upper part of the spectrum of current state-of-the-art detection rates for CW attacks.

Suggested Citation

  • Matthias Rottmann & Kira Maag & Mathis Peyron & Hanno Gottschalk & Nataša Krejić, 2023. "Detection of Iterative Adversarial Attacks via Counter Attack," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 892-929, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02273-6
    DOI: 10.1007/s10957-023-02273-6
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    References listed on IDEAS

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    1. M. V. Solodov & S. K. Zavriev, 1998. "Error Stability Properties of Generalized Gradient-Type Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 663-680, September.
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