@incollection{icml2020_2933,
abstract = {A robustness certificate against adversarial examples is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For \lbrace \textbackslash it any\rbrace perturbation of the input with a magnitude smaller than the certificate value, the classification output will provably remain unchanged. Computing exact robustness certificates for neural networks is difficult in general since it requires solving a non-convex optimization. In this paper, we provide computationally-efficient robustness certificates for neural networks with differentiable activation functions in two steps. First, we show that if the eigenvalues of the Hessian of the network (curvatures of the network) are bounded (globally or locally), we can compute a robustness certificate in the \textdollar l\_2\textdollar norm efficiently using convex optimization. Second, we derive a computationally-efficient differentiable upper bound on the curvature of a deep network. We also use the curvature bound as a regularization term during the training of the network to boost its certified robustness. Putting these results together leads to our proposed \lbrace \textbackslash bf C\rbrace urvature-based \lbrace \textbackslash bf R\rbrace obustness \lbrace \textbackslash bf C\rbrace ertificate (CRC) and \lbrace \textbackslash bf C\rbrace urvature-based \lbrace \textbackslash bf R\rbrace obust \lbrace \textbackslash bf T\rbrace raining (CRT). Our numerical results show that CRT leads to significantly higher certified robust accuracy compared to interval-bound propagation based training.},
author = {Singla, Sahil and Feizi, Soheil},
booktitle = {Proceedings of Machine Learning and Systems 2020},
pages = {5283--5293},
title = {Second-Order Provable Defenses against Adversarial Attacks},
year = {2020}
}