Relation between firing statistics of spiking neuron with instantaneous feedback and without feedback

TL;DR

This paper derives mathematical relations connecting input and output interspike interval distributions for a broad class of spiking neuron models with and without instantaneous feedback, enabling easier analysis of neuronal firing statistics.

Contribution

It introduces a general framework to relate the firing statistics of neurons with and without feedback, applicable to various neuron models like leaky integrate-and-fire.

Findings

Derived explicit relations between input and output interspike interval pdfs.

Validated the relations using the binding neuron model.

Provided formulas for means and variances of interspike intervals.

Abstract

We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between the three probability density functions (pdf): (i) pdf of input interspike intervals, (ii) pdf of output interspike intervals of a neuron with instantaneous feedback and (iii) pdf for that same neuron without feedback is derived. This allows to calculate any of the three pdfs provided the another two are given. Similar relation between corresponding means and variances is derived. The relations are checked exactly for the binding neuron model.