Coupled learning lets an elastic network learn and compute with no processor in the loop

Coupled learning is a local, contrastive learning rule for physical networks — a descendant of equilibrium propagation, which the vault already meets as one of the NGRAD-family backprop alternatives (claim-brain-approximates-backprop-core-principles-ngrad). In an elastic network of springs, each spring adjusts its own rest length using only that element's response under two boundary conditions — a "free" state and a "clamped"/nudged state — with no global error signal and no backward pass. Dillavou, Stern, Liu, and Durian (2024) built a physical proof-of-concept and describe the rule as one that "takes advantage of physics both to learn using local rules and to 'compute' the output response to input data, thus enabling the system to perform decentralized computation without the need for a processor or external memory." Their networks learned tasks such as self-symmetrization and node allostery in situ, motivated explicitly by the energy cost and poor scaling of conventional neural nets. Framed generally: "Learning is a physical process by which a system evolves to exhibit a desired behavior."

This extends the vault's biologically-plausible-learning thread past neuroscience. Where Forward-Forward (claim-hinton-forward-forward-boltzmann-lineage) removes backprop's backward pass but still runs on a digital substrate, coupled learning removes the processor itself: matter performs both the forward computation and the weight update. It sits on the same axis as backpropagation-gap — systems that reach a target behavior without computing a gradient the way backprop does — and shares the "one differentiable physical substrate, many optimizers" spirit of claim-microcosmos-four-experiments-handdesigned-to-emergent. The specific trained behavior it demonstrates, node allostery, is the empirical bridge developed in claim-removing-one-percent-of-bonds-makes-a-random-network-allosteric, and the structure→function reading of such trained networks is claim-physical-networks-become-what-they-learn-soft-modes. See moc-backpropagation-origins.