A Manifold View of Adversarial Risk

• URL: http://arxiv.org/abs/2203.13277v1
• Date: Thu, 24 Mar 2022 18:11:21 GMT
• Title: A Manifold View of Adversarial Risk
• Authors: Wenjia Zhang, Yikai Zhang, Xiaolin Hu, Mayank Goswami, Chao Chen, Dimitris Metaxas
• Abstract summary: We investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction, and the in-manifold adversarial risk due to perturbation within the manifold. We show with a surprisingly pessimistic case that the standard adversarial risk can be nonzero even when both normal and in-manifold risks are zero.
• Score: 23.011667845523267
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The adversarial risk of a machine learning model has been widely studied. Most previous works assume that the data lies in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lies in a manifold, we investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction, and the in-manifold adversarial risk due to perturbation within the manifold. We prove that the classic adversarial risk can be bounded from both sides using the normal and in-manifold adversarial risks. We also show with a surprisingly pessimistic case that the standard adversarial risk can be nonzero even when both normal and in-manifold risks are zero. We finalize the paper with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier by only focusing on the normal adversarial risk.

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