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Deep neural networks have achieved state-of-the-art performance in a varietyof fields. Recent works observe that a class of widely used neural networks canbe viewed as the Euler method of numerical discretization. From the numericaldiscretization perspective, Strong Stability Preserving (SSP) methods are moreadvanced techniques than the explicit Euler method that produce both accurateand stable solutions. Motivated by the SSP property and a generalizedRunge-Kutta method, we propose Strong Stability Preserving networks (SSPnetworks) which improve robustness against adversarial attacks. We empiricallydemonstrate that the proposed networks improve the robustness againstadversarial examples without any defensive methods. Further, the SSP networksare complementary with a state-of-the-art adversarial training scheme. Lastly,our experiments show that SSP networks suppress the blow-up of adversarialperturbations. Our results open up a way to study robust architectures ofneural networks leveraging rich knowledge from numerical discretizationliterature.

Robust Neural Networks inspired by Strong Stability Preserving Runge-Kutta methods