Despite recent success, state-of-the-art learning-based models remain highly vulnerable to input changes such as adversarial examples. In order to obtain certifiable robustness against such perturbations, recent work considers Lipschitz-based regularizers or constraints while at the same time increasing prediction margin. Unfortunately, this comes at the cost of significantly decreased accuracy. In this paper, we propose a Calibrated Lipschitz-Margin Loss (CLL) that addresses this issue and improves certified robustness by tackling two problems: Firstly, commonly used margin losses do not adjust the penalties to the shrinking output distribution; caused by minimizing the Lipschitz constant $K$. Secondly, and most importantly, we observe that minimization of $K$ can lead to overly smooth decision functions. This limits the model's complexity and thus reduces accuracy. Our CLL addresses these issues by explicitly calibrating the loss w.r.t. margin and Lipschitz constant, thereby establishing full control over slack and improving robustness certificates even with larger Lipschitz constants. On CIFAR-10, CIFAR-100 and Tiny-ImageNet, our models consistently outperform losses that leave the constant unattended. On CIFAR-100 and Tiny-ImageNet, CLL improves upon state-of-the-art deterministic $L_2$ robust accuracies. In contrast to current trends, we unlock potential of much smaller models without $K=1$ constraints.

通过校准的利普希茨边界-边际损失（CLL）方法，本论文针对对抗性样本、利普希茨边界和预测边际进行研究，提出了改进的鲁棒性证明，通过解决输出分布缩减、决策函数平滑和模型复杂度方面的问题，得到更好的鲁棒性。

具有弹性控制和较大利普希茨常数的认证鲁棒模型