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This research establishes a fundamental conservation law governing the training dynamics of Equilibrium Propagation and Coupled Learning, ensuring reliable convergence in linear circuit architectures through continuous-time analysis. By proving that these physical learning methods preserve a mass-like quantity across broad settings, the work provides theoretical guarantees for next-generation energy-efficient AI hardware designs. The findings bridge optimization theory with neural engineering principles to constrain parameter evolution without explicit regularization mechanisms.
A Conservation Law for Equilibrium Propagation and Coupled Learning
arXiv:2606.15444v1 Announce Type: cross Abstract: In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit. We prove that this conservation holds in a broad range of physically relevant settings. We then show that the conservation law constrains the training dynamics in a way that makes convergence reliable in important settings for linear circuits. We conclude by discussing some practical implications of this conservation law.
Abstract:In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit. We prove that this conservation holds in a broad range of physically relevant settings. We then show that the conservation law constrains the training dynamics in a way that makes convergence reliable in important settings for linear circuits. We conclude by discussing some practical implications of this conservation law.
Optimization and Control (math.OC); Machine Learning (cs.LG)
arXiv:2606.15444 [math.OC]
(or arXiv:2606.15444v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2606.15444 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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