Stability-Informed Initialization of Neural Ordinary Differential Equations

Theodor Westny, Arman Mohammadi, Daniel Jung, Erik Frisk
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:52903-52914, 2024.

Abstract

This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver’s corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-westny24a, title = {Stability-Informed Initialization of Neural Ordinary Differential Equations}, author = {Westny, Theodor and Mohammadi, Arman and Jung, Daniel and Frisk, Erik}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {52903--52914}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/westny24a/westny24a.pdf}, url = {https://proceedings.mlr.press/v235/westny24a.html}, abstract = {This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver’s corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.} }
Endnote
%0 Conference Paper %T Stability-Informed Initialization of Neural Ordinary Differential Equations %A Theodor Westny %A Arman Mohammadi %A Daniel Jung %A Erik Frisk %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-westny24a %I PMLR %P 52903--52914 %U https://proceedings.mlr.press/v235/westny24a.html %V 235 %X This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver’s corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.
APA
Westny, T., Mohammadi, A., Jung, D. & Frisk, E.. (2024). Stability-Informed Initialization of Neural Ordinary Differential Equations. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:52903-52914 Available from https://proceedings.mlr.press/v235/westny24a.html.

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