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Adversarial Training is a Form of Data-dependent Operator Norm Regularization
Kevin Roth · Yannic Kilcher · Thomas Hofmann

Wed Dec 09 07:20 AM -- 07:30 AM (PST) @ Orals & Spotlights: Social/Adversarial Learning
in Orals & Spotlights Track 20: Social/Adversarial Learning »
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.
[ Paper ]

Author Information

Kevin Roth (ETH Zurich)
Yannic Kilcher (ETH Zurich)
Thomas Hofmann (ETH Zurich)

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