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We study adversarial robustness of neural networks from a margin maximizationperspective, where margins are defined as the distances from inputs to aclassifier's decision boundary. Our study shows that maximizing margins can beachieved by minimizing the adversarial loss on the decision boundary at the"shortest successful perturbation", demonstrating a close connection betweenadversarial 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 animprovement by enabling adaptive selection of the "correct" $\epsilon$ as themargin individually for each datapoint. In addition, we rigorously analyzeadversarial training with the perspective of margin maximization, and providean alternative interpretation for adversarial training, maximizing either alower or an upper bound of the margins. Our experiments empirically confirm ourtheory and demonstrate MMA training's efficacy on the MNIST and CIFAR10datasets w.r.t. $\ell_\infty$ and $\ell_2$ robustness. Code and models areavailable at https://github.com/BorealisAI/mma_training.

MMA Training: Direct Input Space Margin Maximization through Adversarial Training