Output stream of binding neuron with delayed feedback

TL;DR

This paper analyzes how delayed feedback in a binding neuron affects its output spike train, deriving exact and numerical ISI distributions, revealing significant changes in firing statistics due to feedback delay.

Contribution

It provides the first exact mathematical expression for the ISI distribution of a binding neuron with threshold 2 and delayed feedback, and explores effects for higher thresholds.

Findings

Delayed feedback radically alters firing statistics.

Exact ISI distribution derived for threshold 2 neuron.

Distributions exhibit discontinuities and Dirac delta singularities.

Abstract

A binding neuron (BN) whith delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity $\lambda$. The neuron's output spikes are fed into its input with time delay $\Delta$. The resulting output stream of the BN is not Poissonian, and we look for its interspike intervals (ISI) distribution. For BN with threshold 2 an exact mathematical expression as function of $\lambda$, $\Delta$ and BN's internal memory, $\tau$ is derived for the ISI distribution, and for higher thresholds it is found numerically. The distributions found are characterized with discontinuities of jump type, and include singularity of Dirac's $\delta$-function type. It is concluded that delayed feedback presence can radically alter neuronal output firing statistics.