Towards unlocking the mystery of adversarial fragility of neural networks
Keywords: deep learning, adversarial attack, adversarial robustness
Abstract: In this paper, we study the adversarial robustness of deep neural networks for classification tasks. The adversarial robustness of a classification algorithm is defined as the smallest magnitude of possible additive perturbations that can change the output of the classification algorithm. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural network. In particular, our theoretical results show that neural network's adversarial robustness can degrade as the input dimension $d$ increases. Analytically we show that neural networks' adversarial robustness can be only $1/\sqrt{d}$ of the best possible adversarial robustness. Our matrix-theoretic explanation is consistent with an earlier information-theoretic feature-compression-based explanation for the adversarial robustness of neural networks.
Primary Area: learning theory
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Submission Number: 7956
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