Hebbian Learning — Hopfield Attractor Network

10×10 Hopfield network stores 3 patterns; noisy inputs converge to nearest memory

Current state (click to flip bits):
Energy: 0 Overlap P1: 0.00 Overlap P2: 0.00 Overlap P3: 0.00
Stored patterns:
Pattern 1 (checkerboard)
Pattern 2 (stripes)
Pattern 3 (diagonal)
Energy over updates:
About: A Hopfield network (1982) stores patterns via Hebbian learning: W_ij = (1/N)Σ_μ ξᵢ^μ ξⱼ^μ. Starting from a noisy version of a stored pattern, synchronous updates s_i ← sign(Σ_j W_ij s_j) decrease the Lyapunov energy E = −½ΣW_ij s_i s_j, converging to the nearest attractor. Capacity is ~0.14N patterns (McEliece et al 1987).