
extrinsicallyevokedactivityhasbeenstudiedexperimentallybycomparingactivity patternsacrosscorticalmaps (Arielietal.,1995&1996) .Wedeveloptechniques forperformingsuchcomparisonsincaseswherethereisnoapparentsensorymap. Inadditiontorevealinghowthetemporalandspatialstructureofspontaneous activityaffectsevokedresponses,thesemethodscanbeusedtoinferinput selectivity.Historically,selectivitywasfirstmeasuredbystudyingstimulus-driven responses (HubelandWiesel,1962) ,andonlylaterweresimilarselectivitypatterns observedinspontaneousactivityacrossthecorticalsurface (Arielietal.,1995& 1996 .Wearguethatitispossibletoworkinthereverseorder.Havinglittleinitial knowledgeofsensorymapsinournetworks,weshowhowtheirspontaneous activitycaninformusabouttheselectivityofevokedresponsestoinputfeatures. Throughoutthisstudy,werestrictourselvestoquantitiesthatcanbemeasured experimentally,suchasresponsecorrelations,soouranalysismethodscanbe appliedequallytotheoreticalmodelsandexperimentaldata.

Webeginbydescribingthenetworkmodelandillustratingthetypesofactivityit produces,usingcomputersimulations.Inparticular,weillustrateanddiscussa transitionbetweentwotypesofresponses;oneinwhichintrinsicandstimulusevokedactivitycoexist,andtheotherinwhichintrinsicactivityiscompletely suppressed.Next,weexplorehowthespatialpatternsofspontaneousandevoked responsesarerelated.Byspatialpattern,wemeanthewaythatactivityis distributedacrossthedifferentneuronsofthenetwork.Spontaneousactivityisa usefulindicatorofrecurrenteffects,becauseitiscompletelydeterminedbynetwork feedback.Therefore,westudytheimpactofnetworkconnectivityonthespatial patternofinput-drivenresponsesbycomparingthespatialstructureofevokedand spontaneousactivity.Finally,weshowhowthestimulusselectivityofthenetwork canbeinferredfromananalysisofitsspontaneousactivity. TheModel Neuronsinthemodelweconsideraredescribedbyfiring-rates,theydonotfire individualactionpotentials.Suchfiring-ratenetworksareattractivebecausethey areeasiertosimulatethanspikingnetworkmodelsandareamenabletomore detailedmathematicalanalyses.Ingeneral,aslongasthereisnolarge-scale synchronizationofactionpotentials,firing-ratemodelsdescribenetworkactivity adequately (Shriki,HanselandSompolinsky,2003; WongandWang,2006 (vanVreeswijkandSompolinsky, 1996&1998; RajanandAbbott,2006) . Theparametergcontrolsthestrengthofthesynapticconnectionsinthemodel, butbecausethesestrengthsarechosenfromadistributionwithzeromeanand nonzerovariance,gactuallycontrolsthesizeofthestandarddeviationofthe synapticstrengths(seeDiscussion).Withoutanyinput(I i =0foralli)andforlarge networks(largeN),twospontaneouspatternsofactivityareseen.Ifg<1,the networkisinatrivialstateinwhichx i =0andr i =R 0 forallneurons(alli).Thecase g>1ismoreinterestinginthatthespontaneousactivityofthenetworkischaotic, meaningthatitisirregular,non-repeatingandhighlysensitivetoinitialconditions (Sompolinsky,Crisanti,andSommers,1988; vanVreeswijkandSompolinsky,1996 Intheabsenceofastimulusinput,thefiringratesofindividualneuronsfluctuate irregularly,asseeninFigure2(Figure4a-i),andthepowerspectrumacross networkneuronsiscontinuousanddecaysexponentiallyasafunctionoffrequency (Figure4b-i),acharacteristicfeaturesofthechaoticstateofthisnetwork (Sompolinsky,Crisanti,andSommers,1988 Wehaveusedamean-fieldapproachsimilartothatdevelopedbySompolinsky, Crisanti,andSommers(1988)toanalyzepropertiesofthetransitionbetween chaoticaperiodicresponsestoaperiodicstimulus (Rajan,AbbottandSompolinsky, 2009) .Thisextendspreviousworkontheeffectofinputonchaoticnetworkactivity (Molgedey,SchuchhardtandSchuster,1992; BertchingerandNatschläger,2004) to continuoustimemodelsandperiodicinputs.Wefindthatthereisacriticalinput intensity(acriticalvalueofI)thatdependsonfandg,belowwhichnetworkactivity ischaoticthoughdrivenbytheinput(asinFigures4a-ii&4b-ii)andabovewhichit isperiodic(asinFigures4a-iii&4b-iii).Asurprisingfeatureofthiscritical amplitudeisthatitisanon-monotonicfunctionofthefrequencyfoftheinput.Asa result,thereisa"best"frequencyatwhichitiseasiesttoentrainthenetworkand suppresschaos.Fortheparametersweuse,the"best"frequencyisaround5Hz,a frequencyweremanysensorysystemstendtooperate,andtherearesomeinitial experimentalindicationsthatthisisindeedtheoptimalfrequencyforsuppressing backgroundactivitybyvisualstimulation (WhiteandFiser,2008 

{'paper_id': '25358975', 'title': 'Interactions between Intrinsic and Stimulus-Evoked Activity in Recurrent Neural Networks', 's2_url': 'https://api.semanticscholar.org/CorpusID:25358975', 'source': 'S2ORC'}