Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifier

Fuente: arXiv
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Main Authors: Jin, Gaojie, Yi, Xinping, Huang, Xiaowei
Format: Preprint
Published: 2025
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author Jin, Gaojie
Yi, Xinping
Huang, Xiaowei
author_facet Jin, Gaojie
Yi, Xinping
Huang, Xiaowei
contents Within the PAC-Bayesian framework, the Gibbs classifier (defined on a posterior $Q$) and the corresponding $Q$-weighted majority vote classifier are commonly used to analyze the generalization performance. However, there exists a notable lack in theoretical research exploring the certified robustness of majority vote classifier and its interplay with generalization. In this study, we develop a generalization error bound that possesses a certified robust radius for the smoothed majority vote classifier (i.e., the $Q$-weighted majority vote classifier with smoothed inputs); In other words, the generalization bound holds under any data perturbation within the certified robust radius. As a byproduct, we find that the underpinnings of both the generalization bound and the certified robust radius draw, in part, upon weight spectral norm, which thereby inspires the adoption of spectral regularization in smooth training to boost certified robustness. Utilizing the dimension-independent property of spherical Gaussian inputs in smooth training, we propose a novel and inexpensive spectral regularizer to enhance the smoothed majority vote classifier. In addition to the theoretical contribution, a set of empirical results is provided to substantiate the effectiveness of our proposed method.
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id arxiv_https___arxiv_org_abs_2509_25979
institution arXiv
publishDate 2025
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spellingShingle Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifier
Jin, Gaojie
Yi, Xinping
Huang, Xiaowei
Machine Learning
Artificial Intelligence
Within the PAC-Bayesian framework, the Gibbs classifier (defined on a posterior $Q$) and the corresponding $Q$-weighted majority vote classifier are commonly used to analyze the generalization performance. However, there exists a notable lack in theoretical research exploring the certified robustness of majority vote classifier and its interplay with generalization. In this study, we develop a generalization error bound that possesses a certified robust radius for the smoothed majority vote classifier (i.e., the $Q$-weighted majority vote classifier with smoothed inputs); In other words, the generalization bound holds under any data perturbation within the certified robust radius. As a byproduct, we find that the underpinnings of both the generalization bound and the certified robust radius draw, in part, upon weight spectral norm, which thereby inspires the adoption of spectral regularization in smooth training to boost certified robustness. Utilizing the dimension-independent property of spherical Gaussian inputs in smooth training, we propose a novel and inexpensive spectral regularizer to enhance the smoothed majority vote classifier. In addition to the theoretical contribution, a set of empirical results is provided to substantiate the effectiveness of our proposed method.
title Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifier
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2509.25979