Statistical Neurodynamics for sequence processing neural networks with finite dilution

TL;DR

This paper extends statistical neurodynamics to analyze the transient behavior of sequence processing neural networks with finite dilution, confirming theoretical predictions with numerical simulations and validating the Gaussian nature of crosstalk noise.

Contribution

It introduces a novel extension of statistical neurodynamics for finite dilution networks and demonstrates the equivalence to the Generating Functional Method, confirming the Gaussian assumption of crosstalk noise.

Findings

Order parameter equations match those of the Generating Functional Method.

Crosstalk noise is normally distributed even during retrieval failure.

Numerical cumulants confirm the Gaussian nature of crosstalk noise.

Abstract

We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results is supported by the extensive numerical simulations. It is found that the order parameter equations are completely equivalent to those of the Generating Functional Method, which means that crosstalk noise is normal distribution even in the case of failure in retrieval process. In order to verify the gaussian assumption of crosstalk noise, we numerically obtain the cumulants of crosstalk noise, and third- and fourth-order cumulants are found to be indeed zero even in non-retrieval case.