Boosting Adversarial Training via Fisher-Rao Norm-based Regularization

Abstract

Adversarial training is extensively utilized to improve the adversarial robustness of deep neural networks. Yet, mitigating the degradation of standard generalization performance in adversarial-trained models remains an open problem. This paper attempts to resolve this issue through the lens of model complexity. First, We leverage the Fisher-Rao norm, a geometrically invariant metric for model complexity, to establish the non-trivial bounds of the Cross-Entropy Loss-based Rademacher complexity for a ReLU-activated Multi-Layer Perceptron. Then we generalize a complexity-related variable, which is sensitive to the changes in model width and the trade-off factors in adversarial training. Moreover, intensive empirical evidence validates that this variable highly correlates with the generalization gap of Cross-Entropy loss between adversarial-trained and standard-trained models, especially during the initial and final phases of the training process. Building upon this observation, we propose a novel regularization framework, called Logit-Oriented Adversarial Training (LOAT), which can mitigate the trade-off between robustness and accuracy while imposing only a negligible increase in computational overhead. Our extensive experiments demonstrate that the proposed regularization strategy can boost the performance of the prevalent adversarial training algorithms, including PGD-AT, TRADES, TRADES (LSE), MART, and DM-AT, across various network architectures. Our code will be available at https://github.com/TrustAI/LOAT.