An event-driven framework for the simulation of networks of(2)

Abstract. We propose an event-driven framework dedicated to the design and the simulation of networks of spiking neurons. It consists of an abstract model of spiking neurons and an efficient event-driven simulation engine so as to achieve good performance

Previousresearchhasproventhatsuchanevent-drivenapproachiswellsuitedtothesimulationoflargenetworksofspikingneurons,sinceitleadstofastsimulationswhilehandlingthedi culttaskofdealingwiththehighpreci-sionrequiredinthecomputationofspiketimes[7].However,theevent-drivensoftwaresimulatorsthathavebeendevelopedsofararespeci ctoparticularmodelsofneuronsornetworks.Forexample,theevent-drivensimulatorsin

[11,4,8,7]areratherdedicatedtointegrate-and- reneurons,theonein[1]isdedicatedtoneuronssimilartoautomatawitha nitenumberofstates.

Incontrast,weproposeinthispaperanevent-drivenframeworkinwhichtheneuronmodelsareonlylimitedbythefactthattheycanbeimplementedinanevent-drivenfashion.Thisencompassesalargeclassofspikingneuronsrang-ingfromusualleakyintegrate-and- reneuronstomoreabstractneurons,e.g.de nedascomplex nitestatemachines.Asaresult,theproposedframeworkfeaturesahighlevelof exibilitythatallowsthesimulationoflargenetworkscomposedofuniqueordi erenttypesofneurons.

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2.1SpikingneuronmodelsAbstractneuronmodel

We rstneedtode neanabstractmodelofneuronstobeusedwithinourevent-drivenframework.Accordingtothebasicalgorithmdescribedabove,thefollowingrequirementsmustbeful lledbysuchaneuron:wemustknowhowitsinternalstateisa ectedbythereceptionofaspike,howitsinternalstateismodi edwhenemittingaspike,andwhenitsnext ringwilloccur. i},Wethereforede neanabstractmodelofneuronsasaset{xi,ri,si,twith

xi∈XisthestatevariableoftheneuronandXisagivenstatespace.Thisvariablecanchangeonlyatthetimesofsomeeventsoccuringinthesystem.

ri:X×S×R→Xisthefunctionthatdescribesthechangeofthestatevariabledrivenbythereceptionofapulsefromasynapses∈S,whereSisthesetofallsynapses,attimetr∈R.Wewillbemorespeci caboutthesynapsesinsection2.2.

si:X→Xcaracterizesthechangeofstatevariablecausedbythe ringoftheneuron(resetfunction).

i:X→R+∪{+∞}givesthetimeofthenext ring,giventhepresent t

statevariable,withtheadditionalhypothesisthatnoevent-drivenchangeofstatevariablewilloccuruntilthen.Weneedtoprovidethespecialvalue+∞asawaytosignifythatno ringcanoccurwithoutfurtherevents.

i’sto ndthenext ringeventpending.Thesimulationengineusesthet

This,togetherwithamethodtotakecareof(possiblydelayed)receptionevents