ASSO: Associative Memory

Abstract

This program implements an associative-memory network of the type advanced by Hopfield [Ho82] and Little [Li74]. In accordance with the discussion of Chap. 3 the network consists of a set of N units s _i which can take on the values ±1. A set of p patterns σ^μ _i each containing N bits of information is to be memorized. This storage is distributed over the set of (N × N) real-valued synaptic coefficients w _ij mutually connecting the neurons. Memory recall proceeds by initially clamping the neurons to a starting pattern s _i (0). Then the state of the network develops according to a relaxation dynamics in discrete time steps s _i (0) → s _i (1) → . . .. Whether a neuron flips its state depends on the strength of the ‘local field’

$$ {h_i}\left( t \right)\,\, = \,\,\sum\limits_{j\, = \,1}^N {{w_{ij}}{s_j}\left( t \right).} $$

(20.1)