A Conservation Law for Equilibrium Propagation and Coupled Learning
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.
| Authors | Joshua A. McGinnis, Adam G. Kline, Yoichiro Mori |
|---|---|
| Primary category | math.OC |
| Published | 13 June 2026 |
| Last updated at source | 13 June 2026 |
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