A Conservation Law for Equilibrium Propagation and Coupled Learning
Joshua A. McGinnis, Adam G. Kline, Yoichiro Mori
math.OC cs.LG
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.
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.