Energy Landscape
Overview
Framework for systems with many local minima. Hopfield (1982) introduced associative memory networks with energy functions. Landscape metaphor guides optimization and statistical mechanics.
Era: 1982
Proposed at: Pasadena, USA (Caltech)
Formal structure
Domain: State s ∈ {±1}^n (spins); coupling matrix W_ij
E(s) = -½ Σ_{i≠j} W_ij s_i s_j − Σ_i b_i s_i
Constraints: W symmetric; dynamics: s_i → sign(Σ_j W_ij s_j + b_i) (local min)
Objective: min E(s); associative memory; metastable states