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Neural Ordinary Differential Equations (NODEs) probed the usage of numericalsolvers to solve the differential equation characterized by a Neural Network(NN), therefore initiating a new paradigm of deep learning models with infinitedepth. NODEs were designed to tackle the irregular time series problem.However, NODEs have demonstrated robustness against various noises andadversarial attacks. This paper is about the natural robustness of NODEs andexamines the cause behind such surprising behaviour. We show that bycontrolling the Lipschitz constant of the ODE dynamics the robustness can besignificantly improved. We derive our approach from Grownwall's inequality.Further, we draw parallels between contractivity theory and Grownwall'sinequality. Experimentally we corroborate the enhanced robustness on numerousdatasets - MNIST, CIFAR-10, and CIFAR 100. We also present the impact ofadaptive and non-adaptive solvers on the robustness of NODEs.

Ortho-ODE: Enhancing Robustness and of Neural ODEs against Adversarial Attacks