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High sensitivity of neural networks against malicious perturbations on inputscauses security concerns. To take a steady step towards robust classifiers, weaim to create neural network models provably defended from perturbations. Priorcertification work requires strong assumptions on network structures andmassive computational costs, and thus the range of their applications waslimited. From the relationship between the Lipschitz constants and predictionmargins, we present a computationally efficient calculation technique tolower-bound the size of adversarial perturbations that can deceive networks,and that is widely applicable to various complicated networks. Moreover, wepropose an efficient training procedure that robustifies networks andsignificantly improves the provably guarded areas around data points. Inexperimental evaluations, our method showed its ability to provide anon-trivial guarantee and enhance robustness for even large networks.

Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks