Reliability entails input-selective contraction and regulation in excitable networks

TL;DR

This paper investigates how reliability, contraction, and regulation in excitable networks like neurons can enable robust analog computation, using the FitzHugh-Nagumo model to formalize these concepts.

Contribution

It introduces a formal connection between reliability and trajectory contraction in excitable systems, highlighting regulation as a mechanism for stable, robust analog computation.

Findings

Reliability corresponds to an average trajectory contraction property.

Regulation in excitable networks enables stable steady states.

Stability enhances robustness of the computational model.

Abstract

The animal nervous system offers a model of computation combining digital reliability and analog efficiency. Understanding how this sweet spot can be realized is a core question of neuromorphic engineering. To this aim, this paper explores the connection between reliability, contraction, and regulation in excitable systems. Using the FitzHugh-Nagumo model of excitable behavior as a proof-of-concept, it is shown that neuronal reliability can be formalized as an average trajectory contraction property induced by the input. In excitable networks, reliability is shown to enable regulation of the network to a robustly stable steady state. It is thus posited that regulation provides a notion of dynamical analog computation, and that stability makes such a computation model robust.