Transient dynamics for sequence processing neural networks: effect of degree distributions

TL;DR

This paper develops an analytical model for the transient dynamics of sequence processing neural networks, highlighting how degree distributions influence performance and identifying critical loading ratios.

Contribution

It introduces a new evolution equation accounting for degree distributions and validates predictions against numerical experiments across various network types.

Findings

Critical loading ratio $ ext{alpha}_c = N^{-1/2}$ for globally coupled networks

Theoretical predictions match numerical results for delta, binomial, and power-law distributions

Degree distribution significantly affects transient dynamics and retrieval capacity

Abstract

We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely retrieved critical loading ratio $\alpha_c = N ^{-1/2}$ is obtained, where $N$ is the network size. In the presence of random networks, our theoretical predictions agree quantitatively with the numerical experiments for delta, binomial, and power-law degree distributions.