Papers › MMA Training: Direct Input Space Margin Maximization through Adversarial Training
MMA Training: Direct Input Space Margin Maximization through Adversarial Training
Gavin Weiguang Ding, Yash Sharma, Kry Yik Chau Lui, Ruitong Huang
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 ϵ, MMA offers an improvement by enabling adaptive selection of the "correct" ϵ 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. ℓ_∞ and ℓ₂ robustness. Code and models are available at https://github.com/BorealisAI/mma_training.
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