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arXiv 1705.09554cs.CVcs.AIcs.LGstat.ML
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Robustness of classifiers to universal perturbations: a geometric perspective

École Polytechnique Fédérale de Lausanne(洛桑联邦理工学院);University of California, Los Angeles(加利福尼亚大学洛杉矶分校);ENS de Lyon(里昂高等师范学校);CNRS(法国国家科学研究中心);UCBL(里昂第一大学);INRIA(法国国家信息与自动化研究所);Université de Lyon(里昂大学)

Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, Omar Fawzi, Pascal Frossard, Stefano Soatto

英文摘要:

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturbations, and draw a formal link between the robustness to universal perturbations, and the geometry of the decision boundary. Specifically, we establish theoretical bounds on the robustness of classifiers under two decision boundary models (flat and curved models). We show in particular that the robustness of deep networks to universal perturbations is driven by a key property of their curvature: there exists shared directions along which the decision boundary of deep networks is systematically positively curved. Under such conditions, we prove the existence of small universal perturbations. Our analysis further provides a novel geometric method for computing universal perturbations, in addition to explaining their properties.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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