# Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifiers

arXiv: https://arxiv.org/abs/2503.17172 · HTML: https://mlsanity.com/paper/2503.17172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 66 of its 80 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 30 of 66)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Adversarial Risk and the Dangers of Evaluating Against Weak Attacks](https://mlsanity.com/paper/1802.05666/) (2018)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Skip Connections Matter: On the Transferability of Adversarial Examples Generated with ResNets](https://mlsanity.com/paper/2002.05990/) (2020)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [To be Robust or to be Fair: Towards Fairness in Adversarial Training](https://mlsanity.com/paper/2010.06121/) (2020)
- [(Certified!!) Adversarial Robustness for Free!](https://mlsanity.com/paper/2206.10550/) (2022)
- [RAB: Provable Robustness Against Backdoor Attacks](https://mlsanity.com/paper/2003.08904/) (2020)

## Abstract (arXiv)

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.