MATLAB Simulation of Hopfield Neural Network

Hopfield Neural Network is a classic fully-connected recurrent neural network proposed by John Hopfield in 1982. Its key features include associative memory and optimization capabilities, which can be efficiently implemented in MATLAB using matrix operations for core logic computation.

Core Principles Network Architecture: Consists of N fully-connected neurons with symmetric weight matrix and zero diagonal elements (no self-connections). Energy Function: Network state changes always drive the energy function to decrease monotonically, eventually converging to stable states. Update Rules: Supports both synchronous (all neurons update simultaneously) and asynchronous (random sequential update) modes.

MATLAB Implementation Key Aspects Weight Calculation: Stores preset patterns using Hebbian learning rule, where weight matrix is determined by outer product sum of input vectors. State Initialization: Input noisy or corrupted patterns as initial neuron states for pattern recall. Iteration Process: Determines neuron activation states through sign function until energy function stabilizes.

Application Scenarios Image Restoration: Recovering original images from partially damaged binary images Pattern Recognition: Rapid matching of noisy input patterns Combinatorial Optimization: Approximate solutions for NP-hard problems like TSP

Important Considerations Network Capacity Limit: Maximum storable patterns approximately 15% of neuron count Spurious State Risk: Possible convergence to unintended local minima Matrix operations in MATLAB significantly enhance simulation efficiency for large-scale networks