Detection of Iterative Adversarial Attacks via Counter Attack

Matthias Rottmann (), Kira Maag (), Mathis Peyron (), Hanno Gottschalk () and Nataša Krejić ()
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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

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 3, No 2, 892-929

Abstract: 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.

Keywords: Deep neural networks; Adversarial attacks; Counter attacks; Asymptotically perfect detection; 49J52; 62H35; 68T10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02273-6

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