# Practical Approximation Method for Firing Rate Models of Coupled Neural Networks with Correlated Inputs

## TL;DR

This paper introduces a fast approximation method for analyzing firing rate models of large, coupled neural networks with correlated inputs, reducing computational costs compared to traditional simulation methods.

## Contribution

The authors develop a novel approximation technique for Wilson-Cowan type neural networks that efficiently estimates activity and firing statistics with high accuracy, even in complex, heterogeneous systems.

## Key findings

- Method is faster than Monte Carlo simulations.
- Accurately predicts neural activity with moderate coupling.
- Works well with heterogeneity in network parameters.

## Abstract

Rapid experimental advances now enable simultaneous electrophysiological recording of neural activity at single-cell resolution across large regions of the nervous system. Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and the challenge of analyzing them. Here we present a novel method to approximate the activity and firing statistics of a general firing rate network model (of Wilson-Cowan type) subject to noisy correlated background inputs. The method requires solving a system of transcendental equations and is fast compared to Monte Carlo simulations of coupled stochastic differential equations. We implement the method with several examples of coupled neural networks and show that the results are quantitatively accurate even with moderate coupling strengths and an appreciable amount of heterogeneity in many parameters. This work should be useful for investigating how various neural attributes qualitatively effect the spiking statistics of coupled neural networks. Matlab code implementing the method is freely available at GitHub (\url{http://github.com/chengly70/FiringRateModReduction}).