通过优化混淆矩阵最大特征值，提升平滑分类器最差类别的鲁棒性。
Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifiers
- 基于最大特征值设计正则化方法，改善平滑分类器的最差类别表现。
- 理论证明最大特征值直接影响最差类别错误率，实验证明其有效性。
- 适合关注模型公平性和鲁棒性均衡的研究者与应用开发者。
近期研究揭示了深度神经网络中一个关键挑战——‘鲁棒不公平’现象，即模型在不同类别间的鲁棒准确率存在显著差异。尽管已有工作尝试缓解对抗鲁棒性中的不公，但平滑分类器的最差类别认证鲁棒性研究仍属空白。本文通过构建平滑分类器最差类别误差的PAC-Bayesian界，理论分析表明：平滑混淆矩阵的最大特征值从根本上影响最差类别误差。基于此，我们提出一种正则化方法，优化平滑混淆矩阵的最大特征值，以提升平滑分类器的最差类别准确率，并进一步增强其最差类别认证鲁棒性。我们在多个数据集和模型架构上进行了广泛实验，验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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