2022/06/27 by Kenji Kawaguchi, Zhun Deng, Kawaguchi, Kenji +5 · 2 citations
Computer Science · #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2206.13497
openalex publication_date 2022/06/27 · openalex created_date 2022/06/30 · openalex updated_date 2026/07/28
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds in two directions, to solve an open problem that has seen little development since 2010. The first is to reduce the dependence on the covering number. The second is to remove the dependence on the hypothesis space. We present several examples, including ones for lasso and deep learning, in which our bounds are provably preferable. The experiments on real-world data and theoretical models demonstrate near-exponential improvements in various situations. To achieve these improvements, we do not require additional assumptions on the unknown distribution; instead, we only incorporate an observable and computable property of the training samples. A key technical innovation is an improved concentration bound for multinomial random variables that is of independent interest beyond robustness and generalization.