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arXiv 1802.08686cs.LGcs.CRcs.CVstat.ML

Adversarial vulnerability for any classifier

Univ Lyon(里昂大学);ENS de Lyon(里昂高等师范学院);CNRS(法国国家科学研究中心);UCBL(里昂第一大学);DeepMind(深度思维);University of Cambridge(剑桥大学)

Alhussein Fawzi, Hamza Fawzi, Omar Fawzi

英文摘要:

Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the data is generated with a smooth generative model. We derive fundamental upper bounds on the robustness to perturbations of any classification function, and prove the existence of adversarial perturbations that transfer well across different classifiers with small risk. Our analysis of the robustness also provides insights onto key properties of generative models, such as their smoothness and dimensionality of latent space. We conclude with numerical experimental results showing that our bounds provide informative baselines to the maximal achievable robustness on several datasets.

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