Stability of stochastic finite-size spiking-neuron networks: Comparing mean-field, 1-loop correction and quasi-renewal approximations

TL;DR

This paper compares mean-field, 1-loop correction, and quasi-renewal approximations for analyzing the stability of stochastic finite-size spiking-neuron networks, highlighting the superior predictive performance of a quasi-renewal variant.

Contribution

It extends existing theoretical approximations to include auto-history effects and multivariate networks, improving stability prediction accuracy.

Findings

Quasi-renewal approximation outperforms other methods in predicting network stability.

Incorporating auto-history effects enhances the accuracy of stability analysis.

The extended models better match simulated neuronal network behaviors.

Abstract

We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate nonlinear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history effects. In particular, we adapt previous theoretical approximations based on mean field and mean field plus 1-loop correction to incorporate absolute refractory periods and other auto-history effects. Furthermore, we extend previous quasi-renewal approximations to the multivariate case, i.e. neuronal networks. The best sensitivity and specificity performance, in terms of predicting stability and divergence to nonphysiologically high firing rates in the examined simulations, was obtained by a variant of the quasi-renewal approximation.