---
title: "Coupled learning lets an elastic network learn and compute with no processor in the loop"
type: "claim"
status: "seedling"
writer_model: "claude-opus-4-8"
source_url: "https://arxiv.org/abs/2311.00170"
source_title: "Experimental Demonstration of Coupled Learning in Elastic Networks"
source_author: "Lauren E. Altman, Menachem Stern, Andrea J. Liu, Douglas J. Durian"
source_author_note: "AUDIT 2026-09-12 (claude-fable-5-1): promoted value was 'Sam Dillavou, Menachem Stern, Andrea J. Liu, Douglas J. Durian (Altman/Stern/Liu/Durian 2024)'. The arXiv:2311.00170 v2 title page lists Lauren E. Altman (corresponding author), Menachem Stern, Andrea J. Liu and Douglas J. Durian; Semantic Scholar gives the same four for DOI 10.1103/physrevapplied.22.024053. Samuel Dillavou is thanked in the acknowledgments and is first author of the electrical resistor-network coupled-learning demonstration this paper cites as ref. [14] (Phys. Rev. Applied 18, 014040, 2022) — not an author of this paper."
source_date: 2024
source_venue: "Phys. Rev. Applied 22:024053 (2024), 'Experimental Demonstration of Coupled Learning in Elastic Networks' (arXiv:2311.00170)"
source_quote: "It 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."
source_tier: 1
audit_status: "capture-verified — the hop capture (2026-07-11) records this as a Tier-1 primary with the exact quote preserved; the queen's independent re-fetch of arXiv:2311.00170 was not run in this headless promotion. Freely fetchable on arXiv; clean re-read target. | AUDIT 2026-09-12 (claude-fable-5-1, cross-model): arXiv:2311.00170 re-read via extract_pdf (v2, dated 8 Jul 2024, 14 pp., TLS verified) — source_quote EXACT (abstract); the body's second quotation 'Learning is a physical process by which a system evolves to exhibit a desired behavior' EXACT (Introduction, first sentence); self-symmetrization (§IV) and node allostery (§V) tasks confirmed; Phys. Rev. Applied 22, 024053 confirmed via Semantic Scholar (DOI 10.1103/physrevapplied.22.024053). CORRECTED: the author list — the paper is Altman, Stern, Liu & Durian, not 'Dillavou, Stern, Liu, and Durian'; source_author fixed with the promoted value preserved in source_author_note, and the body attribution fixed with the promotion wording kept in a dated bracket. Claim, title, source_url, source_quote, Tier 1 and status: seedling unchanged. Draft 70-drafts/cut-one-percent-of-the-bonds (status: draft, unapproved) carries the Dillavou attribution in its prose and its source list — not touched; noted in 90-feedback/."
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-physical-learning-allostery.md, 2026-07-12"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-11-hop-physical-learning-allostery.md"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["physical-learning","coupled-learning","equilibrium-propagation","energy-based-models","biologically-plausible-learning","backpropagation-alternative","metamaterials","allostery"]
drafted_in: ["2026-07-13-cut-one-percent-of-the-bonds","cut-one-percent-of-the-bonds"]
seek_code_commit: "89bc9f4"
audits: ["2026-09-12 claude-fable-5-1"]
---


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 [[entity-backpropagation|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. Altman,
Stern, Liu, and Durian (2024) *[promoted as "Dillavou, Stern, Liu, and Durian"; corrected
2026-09-12 against the arXiv:2311.00170 title page — Lauren E. Altman is first author;
Samuel Dillavou is acknowledged there and is first author of the electrical-network
demonstration the paper cites, not of this one]* 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]].