Towards Bridging the gap between Empirical and Certified Robustness against Adversarial Examples

Abstract

The current state-of-the-art defense methods against adversarial examples typically focus on improving either empirical or certified robustness. Among them, adversarially trained (AT) models produce empirical state-of-the-art defense against adversarial examples without providing any robustness guarantees for large classifiers or higher-dimensional inputs. In contrast, existing randomized smoothing based models achieve state-of-the-art certified robustness while significantly degrading the empirical robustness against adversarial examples. In this paper, we propose a novel method, called \emph{Certification through Adaptation}, that transforms an AT model into a randomized smoothing classifier during inference to provide certified robustness for $\ell_2$ norm without affecting their empirical robustness against adversarial attacks. We also propose \emph{Auto-Noise} technique that efficiently approximates the appropriate noise levels to flexibly certify the test examples using randomized smoothing technique. Our proposed \emph{Certification through Adaptation} with \emph{Auto-Noise} technique achieves an \textit{average certified radius (ACR) scores} up to $1.102$ and $1.148$ respectively for CIFAR-10 and ImageNet datasets using AT models without affecting their empirical robustness or benign accuracy. Therefore, our paper is a step towards bridging the gap between the empirical and certified robustness against adversarial examples by achieving both using the same classifier.