Response of Spiking Neurons to Correlated Inputs

TL;DR

This paper investigates how correlated synaptic inputs influence the firing rate of leaky integrate-and-fire neurons, providing analytical and simulation results across different correlation time scales.

Contribution

It offers a comprehensive analysis of the neuron's response to correlated inputs using Fokker-Planck formalism and simulations, covering all correlation time scales.

Findings

Analytical expressions for output firing rate across correlation time scales.

Validation of analytical results with simulations.

Insights into neuron response to rapid changes in input correlation.

Abstract

The effect of a temporally correlated afferent current on the firing rate of a leaky integrate-and-fire (LIF) neuron is studied. This current is characterized in terms of rates, auto and cross-correlations, and correlation time scale $\tau_c$ of excitatory and inhibitory inputs. The output rate $\nu_{out}$ is calculated in the Fokker-Planck (FP) formalism in the limit of both small and large $\tau_c$ compared to the membrane time constant $\tau$ of the neuron. By simulations we check the analytical results, provide an interpolation valid for all $\tau_c$ and study the neuron's response to rapid changes in the correlation magnitude.