Papers › How to train your neural ODE: the world of Jacobian and kinetic regularization
How to train your neural ODE: the world of Jacobian and kinetic regularization
Chris Finlay, Jörn-Henrik Jacobsen, Levon Nurbekyan, Adam M. Oberman
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.
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Code
Syntology Ran 4 of 15 code samples harvested from 2 repositories linked to this paper; 11 have no recorded run. Of those that ran: 1 ran · honoured contract; 2 ran · our draft was wrong; 1 ran with no contract checked.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Density Estimation | CIFAR-10 | RNODE | NLL (bits/dim) | 3.38 | #11 of 15 | Archive leaderboard | report |
| Density Estimation | CelebA-HQ 256x256 | RNODE | Log-likelihood | 1.04 | #1 of 1 | Archive leaderboard | report |
| Density Estimation | ImageNet 64x64 | RNODE | Log-likelihood | 3.83 | #1 of 1 | Archive leaderboard | report |
| Density Estimation | MNIST | RNODE | NLL (bits/dim) | 0.97 | #2 of 6 | Archive leaderboard | report |
| Image Generation | CelebA-HQ 256x256 | RNODE | bits/dimension | 1.04 | #18 of 19 | Archive leaderboard | report |
| Image Generation | MNIST | RNODE | bits/dimension | 0.97 | #3 of 15 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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