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Despite recent success, state-of-the-art learning-based models remain highlyvulnerable to input changes such as adversarial examples. In order to obtaincertifiable robustness against such perturbations, recent work considersLipschitz-based regularizers or constraints while at the same time increasingprediction margin. Unfortunately, this comes at the cost of significantlydecreased accuracy. In this paper, we propose a Calibrated Lipschitz-MarginLoss (CLL) that addresses this issue and improves certified robustness bytackling two problems: Firstly, commonly used margin losses do not adjust thepenalties to the shrinking output distribution; caused by minimizing theLipschitz constant $K$. Secondly, and most importantly, we observe thatminimization of $K$ can lead to overly smooth decision functions. This limitsthe model's complexity and thus reduces accuracy. Our CLL addresses theseissues by explicitly calibrating the loss w.r.t. margin and Lipschitz constant,thereby establishing full control over slack and improving robustnesscertificates even with larger Lipschitz constants. On CIFAR-10, CIFAR-100 andTiny-ImageNet, our models consistently outperform losses that leave theconstant unattended. On CIFAR-100 and Tiny-ImageNet, CLL improves uponstate-of-the-art deterministic $L_2$ robust accuracies. In contrast to currenttrends, we unlock potential of much smaller models without $K=1$ constraints.

Certified Robust Models with Slack Control and Large Lipschitz Constants