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.

翻译：本文表明，在连续时间、小扰动极限下，物理学习方法（即耦合学习（coupled learning, CL）和平衡传播（equilibrium propagation, EP））在可训练参数中守恒一个类似质量的量。我们证明该守恒定律在广泛的物理相关场景中成立。进而论证该守恒律以特定方式约束训练动力学，使得线性电路在重要场景下的收敛具有可靠性。最后，我们讨论了该守恒定律的一些实际意义。