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

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.

PDF Abstract ICML 2020 PDF

Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Density Estimation CelebA-HQ 256x256 RNODE Log-likelihood 1.04 # 1
Image Generation CelebA-HQ 256x256 RNODE bits/dimension 1.04 # 1
Image Generation CIFAR-10 RNODE bits/dimension 3.38 # 50
Density Estimation CIFAR-10 RNODE Log-likelihood 3.38 # 3
Density Estimation ImageNet 64x64 RNODE Log-likelihood 3.83 # 1
Image Generation MNIST RNODE bits/dimension 0.97 # 2
Density Estimation MNIST RNODE NLL 0.97 # 1


No methods listed for this paper. Add relevant methods here