Hopfield Network — Memory & Energy Landscape

A Hopfield network stores binary patterns as energy minima. Synaptic weights are set by Hebbian learning (W = (1/N)Σ ξᵘξᵘᵀ). Starting from a noisy or partial pattern, asynchronous updates descend the energy landscape to retrieve the stored memory — until the capacity limit α ≈ 0.14N is exceeded and spurious states appear.

Stored pattern
Current state

Controls

Energy:
Overlap m₁:
Capacity α:
Converged: