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LyaNet: A Lyapunov Framework for Training Neural ODEs

Jimenez Rodriguez, Ivan Dario and Ames, Aaron D. and Yue, Yisong (2022) LyaNet: A Lyapunov Framework for Training Neural ODEs. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220224-200943137

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Abstract

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2202.02526arXivDiscussion Paper
https://github.com/ivandariojr/LyapunovLearningRelated ItemCode
ORCID:
AuthorORCID
Jimenez Rodriguez, Ivan Dario0000-0001-9065-5227
Ames, Aaron D.0000-0003-0848-3177
Yue, Yisong0000-0001-9127-1989
Record Number:CaltechAUTHORS:20220224-200943137
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220224-200943137
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113606
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Feb 2022 00:25
Last Modified:25 Feb 2022 00:25

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