Adversarial Examples Exist in Two-Layer ReLU Networks for Low Dimensional Linear Subspaces

Odelia Melamed · Gilad Yehudai · Gal Vardi

Great Hall & Hall B1+B2 (level 1) #829
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Tue 12 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples.In this work we focus on two-layer neural networks trained using data which lie on a low dimensional linear subspace.We show that standard gradient methods lead to non-robust neural networks, namely, networks which have large gradients in directions orthogonal to the data subspace, and are susceptible to small adversarial $L_2$-perturbations in these directions.Moreover, we show that decreasing the initialization scale of the training algorithm, or adding $L_2$ regularization, can make the trained network more robust to adversarial perturbations orthogonal to the data.

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