Ortho-ODE: Enhancing Robustness and of Neural ODEs against Adversarial
  Attacks
Vishal Purohit
Neural Ordinary Differential Equations (NODEs) probed the usage of numerical
solvers to solve the differential equation characterized by a Neural Network
(NN), therefore initiating a new paradigm of deep learning models with infinite
depth. NODEs were designed to tackle the irregular time series problem.
However, NODEs have demonstrated robustness against various noises and
adversarial attacks. This paper is about the natural robustness of NODEs and
examines the cause behind such surprising behaviour. We show that by
controlling the Lipschitz constant of the ODE dynamics the robustness can be
significantly improved. We derive our approach from Grownwall's inequality.
Further, we draw parallels between contractivity theory and Grownwall's
inequality. Experimentally we corroborate the enhanced robustness on numerous
datasets - MNIST, CIFAR-10, and CIFAR 100. We also present the impact of
adaptive and non-adaptive solvers on the robustness of NODEs.