On the Role of Image Statistics and Gradient Learning in the Adversarial Vulnerability of Neural Networks

Hadar Yosef, Yair Weiss

Keywords: Adversarial Examples, Image Statistics, Gradient Learning

TL;DR: Adversarial examples arise due to the use of gradient learning and random initial conditions. This means they can be alleviated using a simple postprocessing.

Abstract:

Perhaps the most surprising failure of classifiers learned by modern neural networks is that they can be fooled by tiny, imperceptible, perturbations to the input.
In this paper, we present theoretical and empirical results which
suggest that this failure is related to the use of randomly-initialized gradient-based learning together with the statistics of natural images. Our results are based on the previously reported 'PC-bias' of gradient-based learning: projections of the classifier in directions with large variance are learned much faster than directions with small variance. We prove that when the PC-bias is combined with the rapidly decreasing eigenspectrum of natural images, then gradient learning will provably learn a classifier that is highly vulnerable to small perturbations and we show experimentally that this behavior occurs when training deep, nonlinear neural networks. We use our analysis to suggest a simple post-processing of a learned classifier which can significantly improve its robust accuracy.

Primary Area: learning theory

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Submission Number: 2635