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In recent years several adversarial attacks and defenses have been proposed.Often seemingly robust models turn out to be non-robust when more sophisticatedattacks are used. One way out of this dilemma are provable robustnessguarantees. While provably robust models for specific $l_p$-perturbation modelshave been developed, we show that they do not come with any guarantee againstother $l_q$-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 robustmodels wrt any $l_p$-norm for $p\geq 1$.

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