  In this paper, we address the adversarial training of neural ODEs from a
robust control perspective. This is an alternative to the classical training
via empirical risk minimization, and it is widely used to enforce reliable
outcomes for input perturbations. Neural ODEs allow the interpretation of deep
neural networks as discretizations of control systems, unlocking powerful tools
from control theory for the development and the understanding of machine
learning. In this specific case, we formulate the adversarial training with
perturbed data as a minimax optimal control problem, for which we derive first
order optimality conditions in the form of Pontryagin's Maximum Principle. We
provide a novel interpretation of robust training leading to an alternative
weighted technique, which we test on a low-dimensional classification task.
