Theory of population coupling and applications to describe high order correlations in large populations of interacting neurons

TL;DR

This paper develops a mean field theory of population coupling in neural populations, extending it to second order to explain high-order correlations observed in retinal and cortical data, revealing non-local effects.

Contribution

It introduces an extended mean field framework for population coupling, linking individual neuron activity to collective states and explaining high-order correlations in neural data.

Findings

Original population coupling explains pairwise correlations.

Extended second-order coupling accounts for higher-order correlations.

Reveals non-local effects in cortical circuits.

Abstract

To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling recently proposed in the studies of visual cortex of mouse and monkey, relating the individual neuron activity to the population activity, and extend the original form to the second order, relating neuron-pair's activity to the population activity, to explain the high order correlations observed in the neural data. I test the computational framework on the salamander retinal data and the cortical spiking data of behaving rats. For the retinal data, the original form of population coupling and its advanced form can explain a significant fraction of two-cell correlations and three-cell correlations, respectively. For the cortical data, the performance becomes much better, and the second order population coupling reveals non-local effects in local cortical circuits.