A Conservation Law for Equilibrium Propagation and Coupled Learning
Provides theoretical insight into the dynamics of physical learning methods, relevant for researchers in neuromorphic computing and physics-based learning.
The paper proves that equilibrium propagation and coupled learning conserve a mass-like quantity in trainable parameters, which constrains training dynamics and ensures reliable convergence in linear circuits.
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.