Networks that learn without a computer reproduce protein allostery — learning as a physical process

Chasing biologically-plausible alternatives to backprop past Hinton's Forward-Forward leads out of neuroscience entirely and into soft-matter physics — where a disordered spring or resistor network is trained by physics itself, no processor in the loop, and where the trained result turns out to be the same trick evolution uses in proteins.

1. A physical network can learn and "compute" with no processor. Coupled learning (a local, contrastive descendant of equilibrium propagation) tunes each spring's rest length using only that element's own response to two boundary conditions. "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." (Altman/Stern/Liu/Durian 2024, arXiv:2311.00170, Tier 1). Framing: "Learning is a physical process by which a system evolves to exhibit a desired behavior."

2. Tuning ~1% of bonds turns a random network allosteric. "With nearly complete success, we are able to produce a strain between any pair of target nodes... by removing only ∼1% of the bonds... This targeted behavior is reminiscent of the long-range coupled conformational changes that often occur during allostery in proteins." (Rocks et al. 2016/17, arXiv:1607.08562, Tier 1).

3. The bridge closes into biology. The ease of engineering long-range response "may give insight into why allostery is a common means for the regulation of activity in biological molecules" (same source) — the trained artifact and the evolved protein occupy the same soft-mode geometry.

Why this was hop-worthy

It answers "what would biologically-plausible learning look like if it left biology?" — and the road home is that a protein is already a physical learning machine, and both are energy-based models like the Boltzmann lineage at the seed.

Further leads

• "Physical networks become what they learn" (arXiv:2406.09689): a trained net's function is readable from its physical Hessian's soft modes, tying conserved protein regions to slow collective modes.
• Direct Coupling Analysis of epistasis in allosteric materials (arXiv:1811.10480) — bridges to protein-sequence coevolution / statistical genetics.
• Vault neighbor "Cable bacteria conduct electricity over centimeters" — a latent cluster on unconventional long-range physical signalling.

Hop chain

Seed: 30-notes/claim-hinton-forward-forward-boltzmann-lineage.md — Forward-Forward as an energy-based, backprop-free learning rule descended from Boltzmann machines. Hops leave FF's own topic toward the substrate of energy-based learning.

Hop 1 — "Equilibrium Propagation: Bridging Energy-Based Models and Backpropagation" (Scellier & Bengio; via WebSearch, PMC5415673)

• Hook type: Mechanism question (zoom-out to the field)
• Hook: EP trains energy-based nets with two relaxation phases and local rules — no backward pass, and studied on "nonlinear resistor networks, elastic networks, Kuramoto oscillators."
• Why followed: mid-band novelty (0.678) with the most topic-diverse neighbors (SIREN, Microcosmos, Faggin) — a bridge signal; leaves the FF/Boltzmann topic cleanly.
• Key findings: EP needs only one circuit and one unit type, enabling energy-efficient physical implementations; the "physical" neighbors were the real lead.

Hop 2 — "Experimental Demonstration of Coupled Learning in Elastic Networks" (Altman/Stern/Liu/Durian 2024, arXiv:2311.00170)

• Hook type: Surprising claim / mechanism (zoom-in)
• Hook: a mechanical network that learns tasks by locally tuning spring rest lengths, "without the need for a processor or external memory."
• Why followed: bridge candidate (novelty 0.70) sitting beside Microcosmos's elastic filaments — decentralized learning in matter.
• Key findings: proof-of-concept networks learn self-symmetrization and node allostery in-situ; motivated explicitly by neural nets' energy cost and poor scaling.

Hop 3 — "Physical networks become what they learn" (arXiv:2406.09689)

• Hook type: Surprising claim (zoom-out to structure-function principle)
• Hook: you can reverse-engineer a trained network's function from its physical Hessian, without knowing the task.
• Why followed: reframes learning as literal structural reorganization and points at proteins/neural circuits.
• Key findings: task-critical edges become measurable soft modes; "conserved regions in proteins were associated with slow collective modes."

Hop 4 — "Designing allostery-inspired response in mechanical networks" (Rocks/Pashine/Bischofberger/Goodrich/Liu/Nagel, arXiv:1607.08562, PNAS 2017)

• Hook type: Cross-domain bridge (physics ↔ protein biology)
• Hook: removing ~1% of bonds in a random elastic network produces allostery-like long-range response.
• Why followed: highest-priority hook type; novelty 0.668 lands beside "Cable bacteria" and Microcosmos — the vault's physical-computation cluster.
• Key findings: allosteric response is generic and cheap to engineer in disordered networks, suggesting why evolution reuses it.

Surprise: expected biologically-plausible-learning alternatives to stay inside neuroscience/neuromorphics — found the most vivid ones are in soft-matter physics, where matter learns with no processor at all. Surprise: expected engineered "allostery" to be a loose metaphor — found it is quantitatively the same soft-mode geometry, tunable by deleting ~1% of bonds, and offered as an explanation for why real proteins use allostery.

Saved hooks not followed:

• Direct Coupling Analysis of epistasis in allosteric materials (arXiv:1811.10480) — bridges physical learning to protein-sequence coevolution / statistical genetics; a new thread, not this chain.
• Kuramoto-oscillator implementations of equilibrium propagation — mechanism zoom-in kept for a hardware-focused chain.
• "Physical networks become what they learn" full formalism (physical Hessian ↔ cost Hessian) — deserves its own claim-note.

post-worthy: yes — a clean cross-domain arc from Hinton's backprop-free learning to matter that learns to protein allostery, all one energy-based-model family, with Tier 1 grounding.