Untrainable elements determine what physical learning remembers

The paper investigates how two independent inductive biases—one from the circuit’s invariance under conductance rescaling and one from the learning rule’s conservation of a mass quantity—affect what a physical learning system remembers. By separating these effects, the authors show that when every element is trainable, the initialization scale has negligible influence on the learned function, whereas a single untrainable element can cause the function to shift significantly with initialization. They further demonstrate that the conservation law does not protect memory but instead influences solution quality, with adjoint coupled learning (AL) generally performing worse than equilibrium propagation (EP) and coupled learning (CL) in small circuits. whyItMatters":"The study clarifies that only the circuit’s structural bias, not the rule’s conservation property, determines memory retention in physical learning systems."

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