Gradient Methods Provably Converge to Non-Robust Networks

Gal Vardi; Gilad Yehudai; Ohad Shamir

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arXiv · 2202.04347

Gradient Methods Provably Converge to Non-Robust Networks

Gal Vardi·Gilad Yehudai·Ohad Shamir

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Abstract

Despite a great deal of research, it is still unclear why neural networks are so susceptible to adversarial examples. In this work, we identify natural settings where depth-$2$ ReLU networks trained with gradient flow are provably non-robust (susceptible to small adversarial $\ell_2$-perturbations), even when robust networks that classify the training dataset correctly exist. Perhaps surprisingly, we show that the well-known implicit bias towards margin maximization induces bias towards non-robust networks, by proving that every network which satisfies the KKT conditions of the max-margin problem is non-robust.

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Gal Vardi, Gilad Yehudai, Ohad Shamir. 2022-02-09. Gradient Methods Provably Converge to Non-Robust Networks. https://arxiv.org/abs/2202.04347

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