UniCR: Universally Approximated Certified Robustness via Randomized Smoothing

TL;DR

UniCR introduces a universal framework for certifying the robustness of classifiers against any adversarial perturbations using randomized smoothing, offering automatic, tight, and optimal robustness guarantees.

Contribution

UniCR is the first framework to universally approximate certified robustness for any classifier, perturbation, and noise distribution, advancing robustness certification methods.

Findings

Outperforms existing certified defenses in robustness validation.

Provides automatic and case-free robustness certification.

Validates the tightness and optimality of noise distributions.

Abstract

We study certified robustness of machine learning classifiers against adversarial perturbations. In particular, we propose the first universally approximated certified robustness (UniCR) framework, which can approximate the robustness certification of any input on any classifier against any $\ell_p$ perturbations with noise generated by any continuous probability distribution. Compared with the state-of-the-art certified defenses, UniCR provides many significant benefits: (1) the first universal robustness certification framework for the above 4 'any's; (2) automatic robustness certification that avoids case-by-case analysis, (3) tightness validation of certified robustness, and (4) optimality validation of noise distributions used by randomized smoothing. We conduct extensive experiments to validate the above benefits of UniCR and the advantages of UniCR over state-of-the-art certified defenses against $\ell_p$ perturbations.