Provable robustness against all adversarial $l_p$-perturbations for $p\geq 1$

Francesco Croce, Matthias Hein

Published 2019-05-27Version 1

In recent years several adversarial attacks and defenses have been proposed. Often seemingly robust models turn out to be non-robust when more sophisticated attacks are used. One way out of this dilemma are provable robustness guarantees. While provably robust models for specific $l_p$-perturbation models have been developed, they are still vulnerable to other $l_q$-perturbations. We propose a new regularization scheme, MMR-Universal, for ReLU networks which enforces robustness wrt $l_1$- and $l_\infty$-perturbations and show how that leads to provably robust models wrt any $l_p$-norm for $p\geq 1$.