ANCER: Anisotropic Certification via Sample-wise Volume Maximization

Abstract

Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic ℓp certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via ℓp-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, i.e., it cannot reason about other “close”, potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing ℓ1 and ℓ2 certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a practical framework for obtaining anisotropic certificates for a given test set sample via volume maximization. Our empirical results demonstrate that ANCER achieves state-of-the-art ℓ1 and ℓ2 certified accuracy on both CIFAR-10 and ImageNet at multiple radii, while certifying substantially larger regions in terms of volume, thus highlighting the benefits of moving away from isotropic analysis.

Publication
In arxiv
Motasem Alfarra
Motasem Alfarra
PhD Candidate - Electrical and Computer Engineering

I am a Ph.D. candidate at KAUST in Saudi Arabia. I am part of the Image and Video Understanding Lab (IVUL) advised by Prof. Bernard Ghanem. I obtained my M.Sc degree in Electrical Engineering from KAUST, and my undergraduate degree in Electrical Engineering from Kuwait University. I am interested in building robust neural networks and leveraging robust models for different applications.