Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifiers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913750318055424 |
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| author | Jin, Gaojie Huang, Tianjin Mu, Ronghui Huang, Xiaowei |
| author_facet | Jin, Gaojie Huang, Tianjin Mu, Ronghui Huang, Xiaowei |
| contents | Recent studies have identified a critical challenge in deep neural networks (DNNs) known as ``robust fairness", where models exhibit significant disparities in robust accuracy across different classes. While prior work has attempted to address this issue in adversarial robustness, the study of worst-class certified robustness for smoothed classifiers remains unexplored. Our work bridges this gap by developing a PAC-Bayesian bound for the worst-class error of smoothed classifiers. Through theoretical analysis, we demonstrate that the largest eigenvalue of the smoothed confusion matrix fundamentally influences the worst-class error of smoothed classifiers. Based on this insight, we introduce a regularization method that optimizes the largest eigenvalue of smoothed confusion matrix to enhance worst-class accuracy of the smoothed classifier and further improve its worst-class certified robustness. We provide extensive experimental validation across multiple datasets and model architectures to demonstrate the effectiveness of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifiers Jin, Gaojie Huang, Tianjin Mu, Ronghui Huang, Xiaowei Machine Learning Recent studies have identified a critical challenge in deep neural networks (DNNs) known as ``robust fairness", where models exhibit significant disparities in robust accuracy across different classes. While prior work has attempted to address this issue in adversarial robustness, the study of worst-class certified robustness for smoothed classifiers remains unexplored. Our work bridges this gap by developing a PAC-Bayesian bound for the worst-class error of smoothed classifiers. Through theoretical analysis, we demonstrate that the largest eigenvalue of the smoothed confusion matrix fundamentally influences the worst-class error of smoothed classifiers. Based on this insight, we introduce a regularization method that optimizes the largest eigenvalue of smoothed confusion matrix to enhance worst-class accuracy of the smoothed classifier and further improve its worst-class certified robustness. We provide extensive experimental validation across multiple datasets and model architectures to demonstrate the effectiveness of our approach. |
| title | Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifiers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.17172 |