Certified Training: Small Boxes are All You Need

Mark Niklas Mueller, Franziska Eckert, Marc Fischer, Martin Vechev

Keywords: Certified Training, Certified Robustness, Adversarial Robustness, Robustness Verification

TL;DR: We propose a novel certified training method based on propagating small input regions, establishing a new state of the art for certified accuracy.

Abstract: To obtain, deterministic guarantees of adversarial robustness, specialized training methods are used. We propose, SABR, a novel such certified training method, based on the key insight that propagating interval bounds for a small but carefully selected subset of the adversarial input region is sufficient to approximate the worst-case loss over the whole region while significantly reducing approximation errors. We show in an extensive empirical evaluation that SABR outperforms existing certified defenses in terms of both standard and certifiable accuracies across perturbation magnitudes and datasets, pointing to a new class of certified training methods promising to alleviate the robustness-accuracy trade-off.

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Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.04871/code)