Reliability entails input-selective contraction and regulation in excitable networks

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.

💡 Research Summary

The paper addresses a fundamental question in neuromorphic engineering: how can a system combine the digital reliability of spike timing with the analog efficiency of continuous dynamics? Using the FitzHugh‑Nagumo (FHN) model as a minimal representation of an excitable neuron, the authors develop a rigorous mathematical framework that links neuronal reliability to a property called “input‑selective contraction.”

First, the state space of the FHN system (membrane potential v and recovery variable w) is partitioned into three regions based on the value of v: a lower contraction region (v < −1), an upper contraction region (v > 1), and an intermediate expansion region (|v| ≤ 1). In the two contraction regions the system is shown to be contractive with respect to a weighted Euclidean metric d(x₁,x₂)=½