◄ WORLD V · SONNY 5DART 095 · a helldive at the net

HOPFIELD NETWORK a memory that falls into place

Store patterns in a web of symmetric weights; show it a corrupted version and it settles — neuron by neuron, always downhill in energy — into the nearest stored pattern. An associative memory built from physics: it is the Ising model of a magnet, run as recall. It won Hopfield a share of the 2024 Nobel in Physics — though the idea had earlier owners.

THE TECHNIQUE recall = roll downhill in energy

Weights store patterns by a Hebbian outer product (Wᵢⱼ = Σ patternᵢ patternⱼ). To recall, repeatedly set each neuron to the sign of its weighted input; the energy E = −½ Σ Wᵢⱼ sᵢ sⱼ only ever decreases, so the state slides into a stored pattern. Corrupt a stored image and watch it heal. live demo

HISTORY & CREDIT a Nobel with older roots

“Hopfield invented the recurrent associative net in 1982” — he invented gave it an energy function and fame; the network existed a decade earlier. cited

1949 · Donald Hebb — “cells that fire together wire together,” the learning rule the weights use.
1972 / 1974 · Shun-ichi Amari and William Little describe recurrent associative-memory networks — before Hopfield.
1982 · John Hopfield adds the energy function (borrowed from spin-glass physics, the Ising model), proving recall converges — the framing that made it click, and revived neural nets.
2024 · Hopfield & Hinton share the Nobel Prize in Physics — for foundational work on artificial neural networks.

The physics was the insight: a memory is a landscape, and recall is a ball rolling to the bottom. Hopfield 1982, roots 1972

RECOMMEND FOR I-13 a weight matrix and a sign

State is a ±1 array, weights a flattened matrix; recall is a dot product then a sign — and it heals a corrupted pattern on the compiler:

$ i13 run hop.i13 # store (+1,+1,-1,+1), flip bit 1 field h1 = 3 -> sign +1 (bit heals) energy 0 -> -6 (global minimum)
Recommend: almost entirely runnable — state s is a 1-D ±1 f64 array; the weight matrix is symmetric, zero-diagonal, 2-D (PS-004) flattened to W[i*N+j]; store is an outer-product multiply-add, recall is a dot product, and the update sᵢ = sign(hᵢ) is a single comparison (verified h₁=3, energy 0→−6). No new primitive.
Note: the only structural want is the 2-D matrix (PS-004) — here index arithmetic — the same want a dozen darts now share.