脉冲神经网络

Brain-inspiredPatternClassificationwithMemristiveNeuralNetworkUsingtheHodgkin-HuxleyNeuronAmiraliAmirsoleimani,MajidAhmadiandArashAhmadiResearchCenterforIntegratedMicrosystemsUniversityofWindsorWindsor,Ontario,CanadaEmail:{amirsol,ahmadi,aahmadi}@uwindsor.caMounirBoukadoumMicroelectronicsPrototypingResearchLab.UniversityofQuebecatMontreal(UQAM)Montreal,Quebec,CanadaEmail:[e-mail]—Recentfindingsaboutusingmemristordevicestomimicbiologicalsynapsesinneuromorphicsystemsopenanewvisioninneuroscience.Ultra-denselearningarchitecturescanbeimplementedthroughtheSpike-Timing-Dependent-Plasticity(STDP)mechanismbyexploitingthesenanoscalenonvolatiledevices.Inthispaper,aSpikingNeuralNetwork(SNN)thatusesbiologicallyplausiblemechanismsisimplemented.TheproposedSNNreliesonHodgkin-Huxleyneuronsandmemristor-basedsynapsestoimplementabio-inspiredneuromorphicplatform.ThebehavioroftheproposedSNNanditslearningmechanismarediscussed,andtestresultsareprovidedtoshowtheeffective-nessoftheproposeddesignforpatternclassificationapplications.Keywords—Memristor,HudgkinHuxley,Spike-Timing-Dependent-Plasticity(STDP),SpikingNeuralNetwork(SNN).I.INTRODUCTIONSpikingSpikingNeuralNetworks(SNNs)haveapplicationpotentialinawiderangeofareas,includingpatternrecog-nition,clusteringandcomputations.TheemergingmemristordevicescanhelpimplementefficientSNNSastheiranalogmemorypropertymakesthemsuitabletomodelbiologicalsynapses.Thesetwo-terminaldeviceshavetriggeredresearchinmanyareassuchasmemory[1],logic[2][3][4],neuralnetworks[5]andneuromorphiccomputing[6][7].In[8],itwasshownthattheadaptivebehaviorofmemristordevicesallowsthemtoreproduceSpike-Timing-Dependent-Plasticity(STDP),themainlearningmechanismfoundinSNNs.SeveralworkshavebeenpublishedonimplementingSNNswithSTDPlearning.MostoftheseworksrelyontheLeakyIntegrateandFire(LIF)neuronmodelforsimplicity[6][7].However,usingamorebiologicallyplausibleneuronmodelcangivebetterinsightofbrainactivity.TheclassicHodgkin-Huxleyneuronmodel[9]isagoodcandidateforthis,sinceithasalreadybeenusedwithsuccesstorepresenttheionicmechanismsunderlyingtheinitiationandpropagationofactionpotentialsinbiologicalorganisms.Inthispaper,anSNNisimplementedwithHodgkin-Huxleyneuronsasneuronsandthecurrent-controlledmemris-tordevicesassynapses.Then,basicpatternrecognitiontasksareappliedtotheobtainedSNNtotestitsfunctionality.Therestofthispaperisorganizedasfollows:InsectionII,theHodgkin-Huxleyneuronisdefined,andinSectionIII,STDPlearningwiththememristorsynapseisexplained.The9,&0*/(/(1D(.,.,1D*1D*.,/3RWDVVLXP&KDQQHO6RGLXP&KDQQHOFig.1.EquivalentmemristivecircuitschematicfortheHodgkin-Huxleyneuronmodel(top).MemristorI-Vcurvestomodelthesodiumandpotassiumchannels(bottomrightandleft)proposedSNNstructureanditsbehavioraredescribedinSectionIV,andthepatternclassificationresultsarepresentedinsectionV.Finally,sectionVIprovidesasummaryandconclusion.II.HUDGKINHUXLEYNEURONTheconductance-basedHodgkin-Huxleymodel[9]isoneofthefirstaccurateneuronmodelsforexplainingthebiologicalmechanismsofneuronbehavior.Thecurrentacrosstheneuralmembraneisdividedintwomajorparts.Oneisassociatedwiththemembranecapacitanceandtheotheristhecurrentgeneratedbytheflowofionsthroughresistivechannels.ThefundamentalequationoftheHodgkin-Huxleymodelis[9]:I=CMdVdt+Iionic.(1)whereI,VandCMarethetotalmembranecurrent,themembranepotentialandthemembranecapacitance,respec-tively,andIionicisthetotalioniccurrentfromSodium,Potassiumandleakagechannels.Itisdefinedasfollows:Iionic=INa+IK+IL,(2)whereINa=gNa(V−ENa),(3)withgNa=¯gNam3h,(4)‹,(((WLPHPV9ROWDJHP9ííWLPHPV&XUUHQWX$,1$,.íí9ROWDJHP9&XUUHQWX$,1D,.9ROWDJHP96WDWHYDULDEOHPQKEFGDFig.2.(a)Hodgkin-Huxleymembranevoltagefora15μA/cm2stimuluscurrent.(b)Sodiumandpotassiumchannelcurrents,withparameterstakenfrom[9].(c)Sodiumandpotassiumchannelcurrentsversusmembranevoltage.(d)Hodgkin-Huxleyneuronstatevariablesbehavior.IK=gK(V−EK),(5)withgK=¯gKn4,(6)andIL=gL(V−EL),(7)Inthepreviousequations,INa,IKandILarethecurrentsthroughtheSodium,PotassiumandLeakagechannels,respec-tively,gNa,gKandgLarethecorrespondingconductances,andENa,EKandELarethecorrespondingequilibriumvoltages.¯gNaand¯gKareconstantsthataresetexperimentallytofitthebiophysicalpropertiesofrealneuralactionpotentials.Finally,m,nandharestatevariablesthatcontroltheconductanceoftheSodiumandPotassiumchannels.Theirsvaluesvarybetween0and1andaredeterminedby:dndt=an(1−n)−bnn,(8)an=0.01V+10e(V+1010−1),(9)bn=0.125e(V80),(10)dmdt=am(1−m)−bmm,(11)am=0.1V+25e(V+2510−1),(12)bm=4e(V18),(13)dhdt=ah(1−h)−bhh,(14)ah=0.07e(V20),(15)bh=(e(V+3010)+1)−1,(16)ThememristivecircuitequivalenttotheHodgkin-HuxleyneuronmodelwasdefinedbyLeonChuain[10].Heshowedthatthecurrentsinthesodiumandpotassiumchannelsaresimilartocurrentspassingthroughmemristordevices.Fig.,,,,,,,,,,,,,,,,,,,,WƌĞͲEĞƵƌŽŶWŽƐƚͲEĞƵƌŽŶƌŽƐƐďĂƌEĞƚǁŽƌŬ/ŶƉƵƚ,ƵĚŐŬŝŶ,ƵdžůĞLJEĞƵƌŽŶƐKƵƚƉƵƚ,ƵĚŐŬŝŶ,ƵdžůĞLJEĞƵƌŽŶƐWWGWWƌĞͲƐƉŝŬĞWŽƐƚͲƐƉŝŬĞDĞŵƌŝƐƚŽƌ^LJŶĂƉƐĞ/ŶƉƵƚ^ŝŐŶ