Mean-field dynamics of sequence processing neural networks with finite connectivity

TL;DR

This paper extends a dynamic mean-field theory to analyze the behavior of sequence processing neural networks with finite connectivity, providing equations for dynamics and stationary states, and establishing equivalence with layered feed-forward networks.

Contribution

It introduces a new theoretical framework for finite connectivity neural networks, expanding previous models that focused on fully connected systems.

Findings

Derived equations for network dynamics and stationary states.

Established equivalence with layered feed-forward networks.

Extended mean-field theory to finite connectivity networks.

Abstract

A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity near saturation. Equations for the dynamics and the stationary states are obtained for the macroscopic observables and the precise equivalence is established with the single-pattern retrieval problem in a layered feed-forward network with finite connectivity.