S2O: Enhancing Adversarial Training with Second-Order Statistics of Weights
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914361613746176 |
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| author | Jin, Gaojie Yi, Xinping Huang, Wei Schewe, Sven Huang, Xiaowei |
| author_facet | Jin, Gaojie Yi, Xinping Huang, Wei Schewe, Sven Huang, Xiaowei |
| contents | 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 \textbf{S}econd-Order \textbf{S}tatistics \textbf{O}ptimization (S$^2$O) 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$^2$O 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. The code is available at https://github.com/Alexkael/S2O. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | S2O: Enhancing Adversarial Training with Second-Order Statistics of Weights Jin, Gaojie Yi, Xinping Huang, Wei Schewe, Sven Huang, Xiaowei Machine Learning 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 \textbf{S}econd-Order \textbf{S}tatistics \textbf{O}ptimization (S$^2$O) 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$^2$O 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. The code is available at https://github.com/Alexkael/S2O. |
| title | S2O: Enhancing Adversarial Training with Second-Order Statistics of Weights |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.01264 |