"Hey, that's not an ODE": faster ODE adjoints with 12 lines of code

Conference item

Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is accepted if its error, \emph{relative to some norm}, is sufficiently small; else it is rejected, the step is shrunk, and the process is repeated. Here, we demonstrate that the particular structure of the adjoint equations makes the usual choices of norm (such as 𝐿2) unnecessarily stringent. By replacing it with a more appropriate (semi)norm, fewer steps are unnecessarily rejected and the backpropagation is made faster. This requires only minor code modifications. Experiments on a wide range of tasks—including time series, generative modeling, and physical control—demonstrate a median improvement of 40% fewer function evaluations. On some problems we see as much as 62% fewer function evaluations, so that the overall training time is roughly halved.

Authors: Kidger, P; Chen, RTQ; Lyons, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Journal of Machine Learning Research
• Pages: 5443-5452
• Series: Proceedings of Machine Learning Research
• Series number: 139
• Publication date: 2021-07-01
• Acceptance date: 2021-05-08
• Event title: Thirty-eighth International Conference on Machine Learning (ICML 2021)
• Event location: Virtual event
• Event website: https://icml.cc/Conferences/2021
• Event start date: 2021-07-18
• Event end date: 2021-07-24
• ISSN: 2640-3498
• Language: English
• Keywords: FFR