How to train your neural ODE: the world of Jacobian and kinetic regularization

TLDR

Training neural ODEs on large datasets is infeasible because adaptive solvers must use very small step sizes, yielding dynamics equivalent to hundreds or thousands of layers. The study introduces a theoretically grounded combination of optimal transport and stability regularizations to encourage neural ODEs to adopt simpler dynamics that still solve the task. By promoting simpler dynamics, the method achieves faster convergence and fewer solver discretizations, cutting training time without sacrificing performance. The approach trains neural ODE generative models to match unregularized performance while substantially reducing training time, making neural ODEs more practical for large-scale use.

Abstract

Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE-based generative models to the same performance as the unregularized dynamics, with significant reductions in training time. This brings neural ODEs closer to practical relevance in large-scale applications.