General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothing

Dmitrii Korzh, Mikhail Pautov, Olga Tsymboi, Ivan V. Oseledets

Abstract: Randomized smoothing is the state-of-the-art approach to constructing image classifiers that are provably robust against additive adversarial perturbations of bounded magnitude. However, it is more complicated to compute reasonable certificates against semantic transformations (e.g., image blurring, translation, gamma correction) and their compositions. In this work, we propose General Lipschitz (GL), a new flexible framework to certify neural networks against resolvable semantic transformations. Within the framework, we analyze transformation-dependent Lipschitz-continuity of smoothed classifiers w.r.t. transformation parameters and derive corresponding robustness certificates. To assess the effectiveness of the proposed approach, we evaluate it on different image classification datasets against several state-of-the-art certification methods.