Journal of Statistical Physics

, Volume 71, Issue 3–4, pp 705–717 | Cite as

Theory of the dynamics of the Hopfield model of associative memory

  • Prabodh Shukla
Articles

Abstract

We present an analysis of the parallel dynamics of the Hopfield model of the associative memory of a neural network without recourse to the replica formalism. A probabilistic method based on the signal-to-noise ratio is employed to obtain a simple recursion relation for the zero temperature as well as the finite temperature dynamics of the network. The fixed points of the recursion relation and their basins of attraction are found to be in fairly satisfactory agreement with the numerical simulations of the model. We also present some new numerical results which support our recursion relation and throw light on the nature of the ensemble of the network states which are optimized with respect to single spin flips.

Key words

Hopfield model parallel dynamics probabilistic method signal-to-noise ratio 

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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Prabodh Shukla
    • 1
  1. 1.Department of PhysicsNorth Eastern Hill UniversityShillongIndia

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