A dynamical memory with only one spiking neuron

TL;DR

This paper demonstrates that a single recursive spiking neuron can implement a robust dynamical memory, challenging the common belief that multiple neurons and recurrence are necessary.

Contribution

It introduces a minimal model of dynamical memory using only one spiking neuron, both in software and hardware implementations.

Findings

Single neuron can realize dynamical memory.

Bistability explained via self-consistent geometric model.

Hardware implementation with memristive spiking neuron.

Abstract

Common wisdom indicates that to implement a Dynamical Memory with spiking neurons two ingredients are necessary: recurrence and a neuron population. Here we shall show that the second requirement is not needed. We shall demonstrate that under very general assumptions a single recursive spiking neuron can realize a robust model of a dynamical memory. We demonstrate the implementation of a dynamical memory in both, software and hardware. In the former case, we introduce trivial extensions of the popular aQIF and AdEx models. In the latter, we show traces obtained in a circuit model with a recently proposed memristive spiking neuron. We show that the bistability of the theoretical models can be understood in terms of a self-consistent problem that can be represented geometrically. Our minimal dynamical memory model provides a simplest implementation of an important neuro-computational primitive, which can be useful in navigation system models based on purely spiking dynamics. A one neuron dynamical memory may also provides a natural explanation to the surprising recent observation that the excitation bump in Drosophila's ellipsoidal body is made by just a handful of neurons.