Hopfield Network — Pattern Completion
Associative memory: store patterns as attractors, retrieve from noisy/partial inputs
Current state (click to toggle)
Hopfield network: N=64 neurons (8×8). Weights W=Σ_μ ξ_μ ξ_μᵀ/N (Hebb rule, diagonal=0).
Asynchronous update: sᵢ ← sign(Σⱼ Wᵢⱼ sⱼ). Energy: E=−½ sᵀWs (decreases monotonically).
Capacity ≈ 0.14N patterns before spurious attractors dominate.
Spurious attractors = mixtures of stored patterns (±1 spin glass states).