MECHANISM
recall from noise
A Hopfield network is content-addressable memory. Store a pattern, feed it a corrupted version, and it relaxes back toward what it remembers.
POWER-UP 01
STORE
The character bitmap becomes a vector of ±1 cells. Hebbian weights W[i][j]=A[i]·A[j] etch it into the energy landscape.
POWER-UP 02
CORRUPT
Random cells flip — the pattern is buried in noise, sitting up the slope of its energy basin.
POWER-UP 03
RELAX
Over 8 passes each cell re-checks its neighbours, with a bias λ=0.35 toward the stored state, rolling downhill.
POWER-UP 04
RECALL
The network settles at the basin floor — the original character, reconstructed. The memory is recovered.
energy E = −½ Σ Wij si sj — every pass lowers it until the pattern locks.