Adversarial Training is a Form of Data-dependent Operator Norm Regularization

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Kevin Roth, Yannic Kilcher, Thomas Hofmann


We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks. Specifically, we prove that $l_p$-norm constrained projected gradient ascent based adversarial training with an $l_q$-norm loss on the logits of clean and perturbed inputs is equivalent to data-dependent (p, q) operator norm regularization. This fundamental connection confirms the long-standing argument that a network’s sensitivity to adversarial examples is tied to its spectral properties and hints at novel ways to robustify and defend against adversarial attacks. We provide extensive empirical evidence on state-of-the-art network architectures to support our theoretical results.