Bridging the Theoretical Gap in Randomized Smoothing

2025-04-03

AI Summary

This paper addresses the long-standing, significant gap between theoretical certified robustness and empirical robust accuracy in randomized smoothing. We propose the first certification framework grounded in local Lipschitz constants. By incorporating local Lipschitz continuity into randomized smoothing, we design a non-conservative confidence interval estimation method that substantially improves the tightness of certified radii. Our approach achieves systematic gains in certified robust accuracy on standard benchmarks—including CIFAR-10 and ImageNet—while yielding theoretically derived radii that better align with actual adversarial robustness. Extensive experiments confirm a strong correlation between local Lipschitz properties and certification performance, offering a more interpretable and practically grounded theoretical foundation for randomized smoothing.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper introduces a new framework that bridges this gap by leveraging Lipschitz continuity for certification and proposing a novel, less conservative method for computing confidence intervals in randomized smoothing. Our approach tightens the bounds of certified robustness, offering a more accurate reflection of model robustness in practice. Through rigorous experimentation we show that our method improves the robust accuracy, compressing the gap between empirical findings and previous theoretical results. We argue that investigating local Lipschitz constants and designing ad-hoc confidence intervals can further enhance the performance of randomized smoothing. These results pave the way for a deeper understanding of the relationship between Lipschitz continuity and certified robustness.

Problem

• Bridges gap between theoretical and empirical robustness in randomized smoothing
• Introduces less conservative confidence intervals for certified robustness
• Investigates local Lipschitz constants to enhance randomized smoothing performance

Innovation

• Leveraging Lipschitz continuity for certification
• Novel method for computing confidence intervals
• Investigating local Lipschitz constants for enhancement