How to train your neural ODE: the world of Jacobian and kinetic regularization
This work addresses the scalability issue for neural ODEs in large-scale applications, making them more practical, though it is incremental as it builds on existing regularization techniques.
The paper tackles the challenge of training neural ODEs on large datasets, which is hindered by slow convergence due to complex dynamics requiring many solver steps, and introduces a regularization method that simplifies dynamics to reduce training time without performance loss, achieving significant reductions in training time while matching the performance of unregularized models.
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.