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

Abstract

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, we show that they do not come with any guarantee against 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 the first provably robust models wrt any $l_p$-norm for $p\ge 1$.

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Cited by in corpus (2)

• Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications
• Adversarial Examples and Metrics