Artificial Intelligence · 20.08.2026, 06:46 UTC
Untrainable elements determine what physical learning remembers
| Schweregrad | info |
|---|---|
| Kategorie | Artificial Intelligence |
| Quelle | arXiv cs.LG ↗ |
| Veröffentlicht | 20.08.2026 UTC |
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arXiv:2608.00097v2 Announce Type: replace-cross Abstract: 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 …