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

Understand

We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks.

• Specifically, we prove that $\ell_p$-norm constrained projected gradient ascent based adversarial training with an $\ell_q$-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.