S$^{2}$2O: Enhancing Adversarial Training With Second-Order Statistics of Weights
- PMID: 40478710
- DOI: 10.1109/TPAMI.2025.3577384
S$^{2}$2O: Enhancing Adversarial Training With Second-Order Statistics of Weights
Abstract
Adversarial training has emerged as a highly effective way to improve the robustness of deep neural networks (DNNs). It is typically conceptualized as a min-max optimization problem over model weights and adversarial perturbations, where the weights are optimized using gradient descent methods, such as SGD. In this paper, we propose a novel approach by treating model weights as random variables, which paves the way for enhancing adversarial training through Second-Order Statistics Optimization (S$^{2}$2O) over model weights. We challenge and relax a prevalent, yet often unrealistic, assumption in prior PAC-Bayesian frameworks: the statistical independence of weights. From this relaxation, we derive an improved PAC-Bayesian robust generalization bound. Our theoretical developments suggest that optimizing the second-order statistics of weights can substantially tighten this bound. We complement this theoretical insight by conducting an extensive set of experiments that demonstrate that S$^{2}$2O not only enhances the robustness and generalization of neural networks when used in isolation, but also seamlessly augments other state-of-the-art adversarial training techniques.
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