🤖 AI Summary
This study investigates the training dynamics of coupled learning (CL) and equilibrium propagation (EP) in the continuous-time, small-perturbation limit, revealing a parameter conservation law in physically realizable systems that parallels mass conservation. By leveraging continuous-time dynamical systems analysis and perturbation theory, the work establishes— for the first time—that this conservation law holds universally across a broad range of physical settings. Furthermore, it elucidates how this constraint governs the convergence behavior of learning in linear circuits. The findings not only enhance the reliability of CL and EP training but also provide a rigorous theoretical foundation and practical guidance for achieving efficient and stable learning in neuromorphic hardware implementations.
📝 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.