Joint Statistics of Strongly Correlated Neurons via Dimensional Reduction

TL;DR

This paper introduces a non-perturbative method to analyze strong correlations in spike trains of two neurons with shared input, providing accurate theoretical predictions for correlation functions in non-linear neuron models.

Contribution

It presents a novel non-perturbative approach to compute correlations in strongly coupled neurons, extending analysis beyond weak-input approximations.

Findings

Theoretical predictions match simulated spike train correlations accurately.

Method captures asymmetric correlations due to neuron heterogeneity.

Applicable to non-linear neuron models with strong shared input.

Abstract

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train correlations are an inevitable consequence of two neurons being part of the same network and sharing some synaptic input. For non-linear neuron models, however, explicit correlation functions are difficult to compute analytically, and perturbative methods work only for weak shared input. In order to treat strong correlations, we suggest here an alternative non-perturbative method. Specifically, we study the case of two leaky integrate-and-fire neurons with strong shared input. Correlation functions derived from simulated spike trains fit our theoretical predictions very accurately. Using our method, we computed the non-linear correlation transfer as well as correlation functions that are asymmetric due to inhomogeneous intrinsic parameters or unequal input.