A discrete time neural network model with spiking neurons II. Dynamics with noise

TL;DR

This paper rigorously analyzes the spike train statistics in a discrete-time noisy neural network model, establishing the existence of a unique Gibbs measure and connecting Markovian approximations to experimental data analysis.

Contribution

It provides exact mathematical characterization of spike train statistics in a discrete-time noisy neural network, including existence and uniqueness of an invariant measure.

Findings

Existence and uniqueness of a Gibbs-type invariant measure.

Connection between Markovian approximations and experimental spike train analysis.

Rigorous mathematical framework for spike train statistics in noisy neural networks.

Abstract

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.