Bridging the Theoretical Gap in Randomized Smoothing

Blaise Delattre, Paul Caillon, Quentin Barthélemy, Erwan Fagnou, Alexandre Allauzen

TL;DR: We bridge the gap between certified and empirical robustness in randomized smoothing by leveraging Lipschitz continuity and improved confidence intervals, enhancing robust accuracy without sacrificing performance.

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.

Submission Number: 1512