Towards unlocking the mystery of adversarial fragility of neural networks

• URL: http://arxiv.org/abs/2406.16200v1
• Date: Sun, 23 Jun 2024 19:37:13 GMT
• Title: Towards unlocking the mystery of adversarial fragility of neural networks
• Authors: Jingchao Gao, Raghu Mudumbai, Xiaodong Wu, Jirong Yi, Catherine Xu, Hui Xie, Weiyu Xu,
• Abstract summary: We look at the smallest magnitude of possible additive perturbations that can change the output of a classification algorithm. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural network for classification.
• Score: 6.589200529058999
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper, we study the adversarial robustness of deep neural networks for classification tasks. We look at the smallest magnitude of possible additive perturbations that can change the output of a classification algorithm. We provide a matrix-theoretic explanation of the adversarial fragility of deep neural network for classification. 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 fragility of neural networks.

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