Plasticity and Learning Memory and Synaptic Weight Storage
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10NeuromorphicNetworksofSpikingNeurons
GiacomoIndiveriRodneyDouglas
10.1Neuromorphicvs.ConventionalUseofVLSITechnology...........................................10-1
10.2Simulationvs.Emulation..............................10-3
10.3ActionPotentialsandtheAddress-EventRepresentation........................................10-3
10.4SiliconNeurons.......................................10-4
10.5SiliconSynapses.......................................10-6
PlasticityandLearning•MemoryandSynapticWeightStorage10.6Multi-ChipNeuralNetworks..........................10-8
10.7Acknowledgments....................................10-9
References...................................................10-9
Recentadvancesinneurosciencearerevealingtheprinciplesofneuralcomputationusedbythemammalianbrain[7],whilemodelingstudiesshowhowneuralarchitecturescomposedofdiversifiedandunreliablecomputingelements(neuronsandsynapses)cansupportrobustandreliablecomputationusingcompu-tationalprimitivesofbothanaloganddigitalnature[10].Itisnowclearthattheprinciplesofcomputationusedbynervoussystemsareradicallydifferentfromthosegenerallyusedincurrentcomputers.Unlikecomputers,neuronalnetworksprocessinformationusingenergy-efficientasynchronous,event-driven,methods.Theyareself-constructingandrepairing,self-programming,andtheyareabletoflexiblycom-posecomplexbehaviorsfromsimplerelements.Thesebiologicalabilitiesofferanattractivealternativetoconventionalcomputingtechnology,andcouldhaveenormousconsequencesforfuturegenerationsofartificialinformationprocessingandbehavingsystems.Thequesttodesignandfabricateelectronicneuralsystemscomposedof,forexample,retinas,cochles,andneuronalnetworkswhosearchitectureanddesignprinciplesarebasedonthoseofbiologicalnervoussystemsisknownasneuromorphicengineering[4,18].Inthischapter,wedescribesomegeneralpropertiesofneuromorphicsystems,andalsohowneuronsandsynapsescanbeimplementedintheCMOS(com-plimentarymetal-oxidesemiconductor)electronicmediumusinghybridanalog/digitalVLSI(verylargescaleintegrated)technology.
10.1Neuromorphicvs.ConventionalUseofVLSITechnologyTheprimaryfeatureofthevastmajorityofconventionalVLSIcircuitsisthattheyarepurelydigital:Theyusetransistorsason-offswitches,andtheyrepresentnumbersascollectionsofbinarydigits.Becausethesecircuitsuseonlyabinaryencoding,itispossibletoreducetheperformanceoftheircomponenttransistorstotheextentthattheyonlyreliablydetermineasinglebit.Thesesimplebitscanthenbecombinedto
10-1
© 2007 by Taylor & Francis Group, LLC10-2NanoandMolecularElectronicsHandbookencodevariablesofarbitraryhighprecision.Itisthesetwofeatures—simplicityandreliability—combinedwiththeTuringMachineconceptofhowtoencodeanalgorithmonsimplesymbols,thathasenabledthelongandhugelysuccessfulgrowthofdigitalelectronics.ThissuccesshaspropelledadramaticdevelopmentofVLSIfabricationtechnology.However,thisindustryhasfocusedalmostexclusivelyonproducingcircuitsconsistentwiththedigital—Turing—vonNeumannmethod,withtheresultthatmoderncomputerprocessorsnowcontainmillionsoftransis-torsorganizedintostereotypedprocessor,communication,andmemoryarchitecturesthatmanipulatelargefixedlengthvariablesviaserialalgorithms.Asaconsequence,presentcomputersareobligedtousedeterministic,veryhighprecisionmethodstodealevenwithreal-worldtaskswhosenaturalcharacteristicsareusuallyasynchronous,stochastic,parallel,andhaveverylowprecisionthatcouldbeencodedwithafewbits.Formanysuchproblems,particularlythoseinwhichtheinputdataareill-conditionedandthecomputationcanbespecifiedinarelativemanner,biologicalsolutionsaremanyordersofmagnitudemoreeffectivethanthoseusingdigitalmethods.Becausedigitalcomputationrequiresthatmanybinarynodesbecombinedtoencodeonevariable,theoperationofthenodesofanyonevariableaswellasitsinteractionswithothervariables,mustbecarefullysynchronized.This,together,withtheneedforserialimplementationofalgorithmsmeansthatdigitalsystemsrequireglobalcoordinationsupportedbypreciseglobalclocking.Unlikethesedigitalcircuits,thecontinuousvariablesofanalogcircuitsinteractwithoneconcurrently,andinreal-time.So,iftheirtimeconstantsaresetappropriately,theirprocessingisinherentlysynchronizedwithreal-worldevents.Digitalvariableshavenomeaninginandofthemselves.Inordertoexpressafunction,thebinarycomponentsofdigitalvariablesmustbesetaccordingtoanexternallyimposedencodingscheme,andthencombinedalgorithmicallytoobtainarequiredresult,whichisthendecodedaccordingtothesamescheme.Forexample,tocomputeanexponentialrequiresthatthevalueofanargumentbeloadedintoaregister.Then,manysuccessivebinaryshiftsandadditionsmustbeappliedtomultibitvariablesusingcircuitsthatinvolvehundredsoftransistors.Finally,theresultmustbereadfromtheoutputregister.Bycontrast,analogprocessingismorecompactthanitsdigitalcounterpart:Asingleanalogvariableiscontinuousandthusabletorepresentmanybitsofinformation;andcomputationalprimitivesareexpresseddirectlyintermsofthephysicalpropertiesoftheanalogdevices.Forexample,usingtheanalogapproach,anexponentialcanbegeneratedbyjustasingleproperlyconfiguredtransistoroperatinginitssub-thresholdanalogdomain[15].Thetransistorgeneratesadraincurrentthatisexponentialinitsgatevoltage.Moreover,thisdraincurrentdoesnotencodetheexponentialresult,itistheresultitself;availabledirectlyasameasurable,physicalquantity.Notallfunctionscanbecomputedsoefficientlybyanalogcircuits.However,byexploitingthephysicsofsilicon,itisratherstraightforwardtoperformoperationssuchasinvert,add,differentiate,integrate,andcorrelate;andtogenerateexponentials,logarithms,tanh,andthelike.Indeed,theseareexactlythekindofoperationsandfunctionsrequiredforemulatingtheelectrophysiologicalbehaviorofneurons.Althoughstraightforwardinprinciple,analogcomputingisdifficulttoimplementinpractice,becausethephysicalpropertiesofthematerialusedtoconstructthemachineplaysanimportantroleinthesolutionoftheproblem.Biologyissuccessfulinimplementinganalogcomputationbecauseitisabletodirectlygrowadaptivestructures.Butwearestillobligedtousefeed-forwardmanufacturingproceduresforconstructingVLSIcircuits.Usingthisapproach,itisdifficulttocontrolthephysicalpropertiesofmicron-sizeddevicessotheiranalogcharacteristicsarewellmatched.TheadaptivetechniquesusedinneuromorphicVLSIdesign,inspiredbybiology,playakeyroleincompensatingfortheeffectsofdevicemismatchduetocomponentdifferences.Theseadaptationtechniques,usedatthebasiccircuitlevel,leadnaturallytothedesignofsystemsthat,atafundamentallevel,canlearnabouttheirenvironment.Adaptationmayalsobecomerelevantforconventionaltechnology,becauseasVLSItechnologypro-gressesandtransistorsbecomesmaller,theindividualprocessingcomponentsconsumeproportionatelymorepower,andbecomelessreliable.Reliabilityisaseriousproblemforadvanceddigitalcomputingsystemswhosecomponentcountsareeverincreasing,becauseifevenonlyasingletransistorisdefective,thefunctionalityofthewholelargecircuitiscompromised.Mostneuromorphiccircuitsaredesignedtoemulatepopulationsofspikingneuronsandsocomprisemassivelyparallelarraysofsiliconsynapsesand