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Training certifiable neural networks enables one to obtain models withrobustness guarantees against adversarial attacks. In this work, we introduce aframework to bound the adversary-free region in the neighborhood of the inputdata by a polyhedral envelope, which yields finer-grained certified robustness.We further introduce polyhedral envelope regularization (PER) to encouragelarger polyhedral envelopes and thus improve the provable robustness of themodels. We demonstrate the flexibility and effectiveness of our framework onstandard benchmarks; it applies to networks of different architectures andgeneral activation functions. Compared with the state-of-the-art methods, PERhas very little computational overhead and better robustness guarantees withoutover-regularizing the model.

Training Provably Robust Models by Polyhedral Envelope Regularization