AUTHOR=Zhang Wenjia , Zhang Yikai , Hu Xiaoling , Yao Yi , Goswami Mayank , Chen Chao , Metaxas Dimitris TITLE=Manifold-driven decomposition for adversarial robustness JOURNAL=Frontiers in Computer Science VOLUME=5 YEAR=2024 URL=https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2023.1274695 DOI=10.3389/fcomp.2023.1274695 ISSN=2624-9898 ABSTRACT=

The adversarial risk of a machine learning model has been widely studied. Most previous studies assume that the data lie in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lie 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 a surprisingly pessimistic case that the standard adversarial risk can be non-zero even when both normal and in-manifold adversarial risks are zero. We finalize the study with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier without sacrificing model accuracy, by only focusing on the normal adversarial risk.