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Independent researcher
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示平衡传播等物理学习规则的守恒结构决定其初始化记忆、训练速度与泛化性，耗散规则泛化性更差但训练更快，守恒性可作为物理学习机器的设计参数。
AI 中文摘要
平衡传播（EP）、耦合学习（CL）、伴随耦合学习（AL）等物理学习规则通过局部测量训练阻性网络。在小扰动极限下，EP和CL严格守恒电导质量K=(1/2)∑_e κ_e²，该特性可稳定训练过程。研究表明，守恒性同样决定这些规则的归纳偏置：对于单输出情况，证明EP和CL轨迹等价，因此单输出实验无法区分两者的学习结果；AL不守恒该质量，而是以恰好两倍于自身损失的速率耗散它。在线性电路中，守恒质量无功能影响：三个向量场均与电导齐次，因此选定的解与初始化尺度无关；固定非线性元件会破坏这种保护，在二极管电路中，学习到的输入输出函数与初始化尺度的依赖关系可达约40%，线性对照中无此效应，保守规则会永久保留该记忆，而耗散规则会部分擦除它。在匹配训练损失时，耗散规则通常比保守规则泛化性更差，但能更快达到低训练损失；该损失与途中耗散的质量相关，且在大型电路中会消失，因为大型电路中耗散的质量极少。因此，局部学习规则的守恒结构决定了其初始化记忆、训练速度，以及耗散显著时的泛化性能，应将其视为物理学习机器的设计参数。
英文摘要
Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements. The learned function is decided by where on the solution manifold training lands. Two properties could decide it, and they have not been separated: the circuit's invariance under rescaling every conductance, and the rule's conservation of the mass K = (1/2) sum_e kappa_e^2. We separate them. When every element is trainable, all three vector fields are homogeneous in the conductances, so the initialization scale is provably inert. An element the rule does not adjust breaks that homogeneity whatever its constitutive law. Across twenty topologies the learned function moves with the initialization scale by a median of twelve percent with fixed rectifiers and eight with fixed linear resistors, against 3e-8 when every element is trainable; a single fixed rectifier produces the whole effect. The conservation law is not what protects the function: AL, which we prove dissipates the mass at exactly twice its own loss, remembers its initialization as strongly as the rules that conserve it, and the memory survives in runs where K is conserved to 1e-4. Raising the fixed-element count from one to eight multiplies the conservation drift by five thousand and leaves the memory unchanged, while the all-trainable circuit under AL drifts comparably and remembers nothing. What the rule's conservation structure does control is solution quality: at matched training loss AL is worse than EP and CL in four of six small circuits, by a median of three to seven percent, though the ordering is not stable across checkpoints and does not reproduce at fifty nodes. Physical learning therefore carries two independent inductive biases, one belonging to the circuit and one to the rule, and only the first is a memory of how the device was built.
Comments8 pages, 3 figures, 3 tables
