  We study adversarial robustness of neural networks from a margin maximization
perspective, where margins are defined as the distances from inputs to a
classifier's decision boundary. Our study shows that maximizing margins can be
achieved by minimizing the adversarial loss on the decision boundary at the
"shortest successful perturbation", demonstrating a close connection between
adversarial losses and the margins. We propose Max-Margin Adversarial (MMA)
training to directly maximize the margins to achieve adversarial robustness.
Instead of adversarial training with a fixed $\epsilon$, MMA offers an
improvement by enabling adaptive selection of the "correct" $\epsilon$ as the
margin individually for each datapoint. In addition, we rigorously analyze
adversarial training with the perspective of margin maximization, and provide
an alternative interpretation for adversarial training, maximizing either a
lower or an upper bound of the margins. Our experiments empirically confirm our
theory and demonstrate MMA training's efficacy on the MNIST and CIFAR10
datasets w.r.t. $\ell_\infty$ and $\ell_2$ robustness. Code and models are
available at https://github.com/BorealisAI/mma_training.
