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1、LETTERCommunicatedbyRichardZemelBayesianFilteringinSpikingNeuralNetworks:Noise,Adaptation,andMultisensoryIntegrationOmerBobrowskibober@tx.technion.ac.ilRonMeirrmeir@ee.technion.ac.ilYoninaC.Eldaryonina@ee.technion.ac.ilDepartmentofElectricalEngineering,Techni
2、on,Haifa32000,IsraelAkeyrequirementfacingorganismsactinginuncertaindynamicenvi-ronmentsisthereal-timeestimationandpredictionofenvironmentalstates,basedonwhicheffectiveactionscanbeselected.Whileitisbe-comingevidentthatorganismsemployexactorapproximateBayesians
3、tatisticalcalculationsforthesepurposes,itisfarlessclearhowtheseputativecomputationsareimplementedbyneuralnetworksinastrictlydynamicsetting.Inthiswork,wemakeuseofrigorousmathematicalresultsfromthetheoryofcontinuoustimepointprocessfilteringandshowhowoptimalreal-
4、timestateestimationandpredictionmaybeim-plementedinageneralsettingusingsimplerecurrentneuralnetworks.Theframeworkisapplicabletomanysituationsofcommoninterest,includingnoisyobservations,non-Poissonspiketrains(incorporatingadaptation),multisensoryintegration,an
5、dstateprediction.Theoptimalnetworkpropertiesareshowntorelatetothestatisticalstructureoftheenvironment,andthebenefitsofadaptationarestudiedandexplicitlydemonstrated.Finally,werecoverseveralexistingresultsasappropriatelimitsofourgeneralsetting.1IntroductionThese
6、lectionofappropriateactionsinthefaceofuncertaintyisaformidabletaskfacedbyanyorganismattemptingtosurviveinahostiledynamicen-vironment.Thistaskisexacerbatedbythefactthattheorganismdoesnothavedirectaccesstotheenvironment(ortoitsinternalbodystate),butmustassessth
7、esestatesthroughnoisysensors,oftenrepresentingtheworldviarandomspiketrains.Itisbecomingincreasinglyevidentthatinmanycases,organismsemployexactorapproximateBayesianstatisticalcalculations(Averbeck,Latham,&Pouget,2006;Deneve,Latham,&Pouget,2001;Ma,Beck,Latham,&
8、Pouget,2006;Pouget,Deneve,&Duhamel,2002;Doya,Ishii,Pouget,&Rao,2007;Knill&Pouget,2004)inordertocontinuouslyNeuralComputation21,1277–1320(2009)C2008MassachusettsInstituteofTechnology1278O
