Input-output consistency in integrate and fire interconnected neurons

TL;DR

This paper investigates how to mathematically define input-output consistency in interconnected stochastic integrate-and-fire neuron models, focusing on the preservation of interspike interval tail behavior.

Contribution

It introduces a framework for input-output consistency using regularly-varying vectors in stochastic neuron networks, with necessary technical conditions.

Findings

Regularly-varying vectors ensure input-output tail behavior consistency.

Necessary technical hypotheses are identified for the model.

The approach formalizes how neuronal signals can be reliably transmitted.

Abstract

Interspike intervals describe the output of neurons. Signal transmission in a neuronal network implies that the output of some neurons becomes the input of others. The output should reproduce the main features of the input to avoid a distortion when it becomes the input of other neurons, that is input and output should exhibit some sort of consistency. In this paper, we consider the question: how should we mathematically characterize the input in order to get a consistent output? Here we interpret the consistency by requiring the reproducibility of the input tail behaviour of the interspike intervals distributions in the output. Our answer refers to a system of interconnected neurons with stochastic perfect integrate and fire units. In particular, we show that the class of regularly-varying vectors is a possible choice to obtain such consistency. Some further necessary technical hypotheses are added.