Input-output consistency in integrate and fire interconnected neurons

Petr Lansky; Federico Polito; Laura Sacerdote

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arXiv · 2206.12324

Input-output consistency in integrate and fire interconnected neurons

Petr Lansky·Federico Polito·Laura Sacerdote

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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.

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Petr Lansky, Federico Polito, Laura Sacerdote. 2022-06-24. Input-output consistency in integrate and fire interconnected neurons. https://arxiv.org/abs/2206.12324

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