Recurrent Interactions in Spiking Networks with Arbitrary Topology

TL;DR

This paper uses linear response theory to analyze how detailed network structures and neuron characteristics influence correlations and dynamics in recurrent spiking networks, revealing conditions for transitions to highly correlated states.

Contribution

It introduces a framework linking network topology and neuron properties to spike train correlations, providing new tools for analyzing complex neural networks.

Findings

Pairwise correlations relate to the matrix of linear interactions.

Reset mechanisms influence autocorrelation and correlation levels.

Erdős-Rényi networks exhibit a transition to high correlation states at instability.

Abstract

The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations emerges in sparsely connected networks. We apply linear response theory to evaluate the influence of detailed network structure on neuron dynamics. It turns out that pairwise correlations induced by direct and indirect network connections can be related to the matrix of direct linear interactions. Furthermore, we study the influence of characteristics of the neuron model. Interpreting the reset as self-inhibition we examine its influence, via the spectrum of single neuron activity, on network autocorrelation functions and the overall correlation level. The neuron model also affects the form of interaction kernels and consequently the time-dependent correlation functions. We finally find that a linear instability of networks with Erd\H{o}s-R\'{e}nyi topology coincides with a global transition to a highly correlated network state. Our work shows that recurrent interactions have a profound impact on spike train statistics and provides tools to study effects of specific network topologies.