Understanding Adversarially Robust Generalization via Weight-Curvature Index

Despite numerous efforts, achieving adversarial robustness in deep learning remains a critical challenge. Recent studies have discovered that adversarial training, a widely adopted method for improving model robustness against adversarial perturbations, prevalently suffers from robust overfitting. To better characterize the robust generalization of adversarially trained models, we introduce the Weight-Curvature Index (WCI), a novel metric that captures the Frobenius norm of layer-wise weight matrices and the trace of the Hessian matrix with respect to the adversarial loss function. In particular, we establish a theoretical connection between WCI and robust generalization gap under a PAC-Bayesian framework. By analyzing the dynamics of these factors, WCI offers a nuanced understanding of why robust overfitting happens during adversarial training. Experimental results demonstrate a strong correlation between WCI and traditional robustness measures, suggesting the effectiveness of WCI in capturing the learning dynamics of adversarial training.