Extending the Functional Subnetwork Approach to a Generalized Linear Integrate-and-Fire Neuron Model.

Alexander J Hunt,Roger D Quinn,Nicholas S Szczecinski

doi:10.3389/fnbot.2020.577804

Alexander J Hunt, Roger D Quinn + Show 1 more

Open Access

https://doi.org/10.3389/fnbot.2020.577804

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Abstract

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the “Functional subnetwork approach” (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network's intended function, without the use of global optimization or machine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuron model have fundamental similarities to those of a non-spiking leaky integrator neuron model. We derive analytical expressions that show functional parallels between: (1) A spiking neuron's steady-state spiking frequency and a non-spiking neuron's steady-state voltage in response to an applied current; (2) a spiking neuron's transient spiking frequency and a non-spiking neuron's transient voltage in response to an applied current; and (3) a spiking synapse's average conductance during steady spiking and a non-spiking synapse's conductance. The models become more similar as additional spiking neurons are added to each population “node” in the network. We apply the FSA to model a neuromuscular reflex pathway two different ways: Via non-spiking components and then via spiking components. These results provide a concrete example of how a single non-spiking neuron may model the average spiking frequency of a population of spiking neurons. The resulting model also demonstrates that by using the FSA, models can be constructed that incorporate both spiking and non-spiking units. This work facilitates the construction of large networks of spiking neurons and synapses that perform specific functions, for example, those implemented with neuromorphic computing hardware, by providing an analytical method for directly tuning their parameters without time-consuming optimization or learning.

Highlights

We have developed methods for applying our functional subnetwork approach (FSA) for designing non-spiking recurrent neural networks (Szczecinski et al, 2017b) to the specific generalized integrate-and-fire (GLIF) model used by Intel’s Loihi chip (Mihalas and Niebur, 2009; Davies et al, 2018)
Where Uis the non-spiking neuron voltage above its rest potential, Cmem is the capacitance of the cell membrane, Gmem is the leak conductance, Gs,i is the instantaneous conductance of the ith incoming non-spiking synapse, Es,i is the reversal potential of the ith incoming
The analysis and numerical results in this manuscript show how continuous, non-spiking leaky-integrator neural dynamics can approximate the dynamics of a population of identical GLIF spiking neurons with randomized interconnections

Summary

Introduction

Neuromorphic computing hardware is becoming more widely available (Khan et al, 2008; Pfeil et al, 2013; Benjamin et al, 2014; Gehlhaar, 2014; Merolla et al, 2014; Ionica and Gregg, 2015; Davies et al, 2018) Such chips have non-traditional architecture, with highly-parallel processing and specialized circuits that mimic neural and synaptic dynamics. The details of this comparison are listed at the end of the Introduction

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