The signal-to-noise analysis of the Little-Hopfield model revisited

Abstract

Using the generating functional analysis an exact recursion relation is derived for the time evolution of the effective local field of the fully connected Little-Hopfield model. It is shown that, by leaving out the feedback correlations arising from earlier times in this effective dynamics, one precisely finds the recursion relations usually employed in the signal-to-noise approach. The consequences of this approximation as well as the physics behind it are discussed. In particular, it is pointed out why it is hard to notice the effects, especially for model parameters corresponding to retrieval. Numerical simulations confirm these findings. The signal-to-noise analysis is then extended to include all correlations, making it a full theory for dynamics at the level of the generating functional analysis. The results are applied to the frequently employed extremely diluted (a)symmetric architectures and to sequence processing networks.

26 pages, 3 figures

References in corpus (4)

• Transient dynamics for sequence processing neural networks
• Dynamics of a spherical minority game
• Mean-field dynamics of sequence processing neural networks with finite connectivity
• The Blume-Emery-Griffiths neural network: dynamics for arbitrary temperature

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• Parallel dynamics of continuous Hopfield model revisited
• Transient dynamics for sequence processing neural networks: effect of degree distributions