Hopfield Network Attractor Memory

Content-addressable memory via Hebbian learning and energy minimization

Energy Landscape

Network Parameters

Convergence

Energy E:—
Overlap m₁:—
Iteration:0
Capacity αc:—

Hopfield Network (1982)

Store P binary patterns {ξᵢᵘ} via Hebbian rule: W_ij = (1/N)Σ_μ ξᵢᵘξⱼᵘ

Retrieval: asynchronous updates σᵢ ← sign(Σⱼ W_ij σⱼ) until convergence. Energy E = −(1/2)ΣW_ij σᵢσⱼ decreases monotonically.

Hopfield capacity: αc = P/N ≈ 0.138. Above this, spurious attractors proliferate and memory fails.