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arXiv · 2606.15444

A Conservation Law for Equilibrium Propagation and Coupled Learning

Joshua A. McGinnis·Adam G. Kline·Yoichiro Mori
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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.

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Joshua A. McGinnis, Adam G. Kline, Yoichiro Mori. 2026-06-13. A Conservation Law for Equilibrium Propagation and Coupled Learning. https://arxiv.org/abs/2606.15444

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