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

TL;DR

This paper introduces a regularization method combining optimal transport and stability principles to simplify neural ODE dynamics, enabling faster training on large datasets without sacrificing performance.

Contribution

It proposes a theoretically grounded regularization technique that encourages simpler neural ODE dynamics, reducing training time and improving scalability.

Findings

Faster convergence and reduced training time for neural ODEs.

Achieved comparable performance to unregularized models on large datasets.

Significant decrease in solver discretizations and wall-clock time.

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.