Analytic Investigation for Spatio-temporal Patterns Propagation in Spiking Neural Networks

TL;DR

This paper develops an analytical framework using Gaussian random fields to understand how spatio-temporal spike patterns propagate in neural networks, revealing conditions for synchronization and stable synfire chains.

Contribution

It introduces a moment closure-based analytical method to characterize spike propagation and synchronization in spiking neural networks, highlighting the role of excitation-inhibition balance.

Findings

Balanced networks are necessary for synfire chain formation.

Critical packet size influences invasion and annihilation of spike packets.

Analytic conditions for synchronization support stable pattern propagation.

Abstract

Based upon the moment closure approach, a Gaussian random field is constructed to quantitatively and analytically characterize the dynamics of a random point field. The approach provides us with a theoretical tool to investigate synchronized spike propagation in a feedforward or recurrent spiking neural network. We show that the balance between the excitation and inhibition postsynaptic potentials is required for the occurrence of synfire chains. In particular, with a balanced network, the critical packet size of invasion and annihilation is observed. We also derive a sufficient analytic condition for the synchronization propagation in an asynchronous environment, which further allows us to disclose the possibility of spatial synaptic structure to sustain a stable synfire chain. Our findings are in good agreement with simulations and help us understand the propagation of spatio-temporal patterns in a random point flied.