Adaptive Randomized Smoothing: Certified Adversarial Robustness for Multi-Step Defences

Abstract

We propose Adaptive Randomized Smoothing (ARS) to certify the predictions of our test-time adaptive models against adversarial examples. ARS extends the analysis of randomized smoothing using f-Differential Privacy to certify the adaptive composition of multiple steps. For the first time, our theory covers the sound adaptive composition of general and high-dimensional functions of noisy inputs. We instantiate ARS on deep image classification to certify predictions against adversarial examples of bounded norm. In the L-infinity threat model, ARS enables flexible adaptation through high-dimensional input-dependent masking. We design adaptivity benchmarks, based on CIFAR-10 and CelebA, and show that ARS improves standard test accuracy by 1 to 15% points. On ImageNet, ARS improves certified test accuracy by up to 1.6% points over standard RS without adaptivity.