From Basic Network Principles to Neural Architecture: Emergence of Spatial-Opponent CellsRalph Linsker doi:10.1073/pnas.83.19.7508 1986;83;7508-7512 PNAS This information is current as of December 2006. www.pnas.org#otherarticlesThis article has been cited by other articles: E-mail Alerts. click heretop right corner of the article orReceive free email alerts when new articles cite this article - sign up in the box at the Rights & Permissions www.pnas.org/misc/rightperm.shtmlTo reproduce this article in part (figures, tables) or in entirety, see: Reprints www.pnas.org/misc/reprints.shtmlTo order reprints, see: Notes:Proc.Nati.Acad.Sci.USAVol.83,pp.7508-7512,October1986NeurobiologyFrombasicnetworkprinciplestoneuralarchitecture:Emergenceofspatial-opponentcells(modularself-adaptivenetworks/visualsystem/feature-analyzingcells)RALPHLINSKERIBMThomasJ.WatsonResearchCenter,YorktownHeights,NY10598CommunicatedbyRichardL.Garwin,June3,1986ABSTRACTThefunctionalarchitectureofmammalianvisualcortexhasbeenelucidatedinimpressivedetailbyexperimentalworkofthepast20-25years.Theoriginofmanyofthesalientfeaturesofthisarchitecture,however,hasremainedunexplained.Thispaperisthefirstofthree(theotherswillappearinsubsequentissuesoftheseProceedings)thataddresstheoriginandorganizationoffeature-analyzing(spatial-opponentandorientation-selective)cellsinsimplesystemsgovernedbybiologicallyplausibledevelopmentrules.Ianalyzetheprogressivematurationofasystemcomposedofafewlayersofcells,withconnectionsthatdevelopaccordingtoasimplesetofrules(includingHebb-typemodification).Tounderstandtheprenataloriginoforientation-selectivecellsincertainprimates,Iconsiderthecaseinwhichthereisnoexternalinput,withthefirstlayerexhibitingrandomsponta-neouselectricalactivity.Noorientationpreferenceisspecifiedtothesystematanystage,andnoneofthebasicdevelopmentalrulesisspecifictovisualprocessing.HereIintroducethetheoryof"modularself-adaptivenetworks,"ofwhichthissystemisanexample,andexplicitlydemonstratetheemergenceofalayerofspatial-opponentcells.Thissetsthestagefortheemergence,insucceedinglayers,ofanorientation-selectivecellpopulation.Acomplexfunctionalarchitectureformammalianprimaryvisualcortex(andprecorticalstructures)hasbeenexperi-mentallyelucidatedoverthepast20-25years,spearheadedbytheworkofHubelandWiesel(1,2).Howcomplexdotherulesthatspecifythedevelopmentofthisarchitectureneedtobe,andwhataretheorganizingprinciplesforthisspeci-fication?Ihavefoundthatasurprisinglysimplesetofphysiologi-callyandanatomicallyplausiblerulessufficestogeneratemanyofthesalientfeaturesofthisfunctionalarchitecture.Thestartingpointisanetworkcomprisingseveraltwo-dimensionallayersofcells,withconnectionsofunspecifiedstrengthtoeachcellofonelayerfromaneighborhoodofcellsoftheprecedinglayer,andwithagivenruleforupdatingconnectionstrength.Thesynapticconnectionstrengthsreachtheirmaturevaluesundertheinfluenceofthisrule,whichinthepresentworkisofHebbtype(3).Thisisaparticularexampleoftheclassofsystemsthatweshallcall"modularself-adaptivenetworks."Thismeansthatthenetworkarrangementisspecifiedatthemodule(inthiscase,layer)level(e.g.,"layerAprovidesinputtolayerB")andthatasmallamountofstatisticalinformationaboutthecell-to-cellconnectionsisprovided(e.g.,theinitialratioofthenumbersofexcitatoryandinhibitorysynapses)butthatthedetailedconnectionsandtheirstrengthsareunspecifiedandallowedtoemergeduringthedevelopmentofthesystem.Thispapershowshow,andunderwhatconditions,spatial-opponentcells(withcentralexcitatoryandperipheralinhib-itoryinputsatmaturity,orwiththereverse)emergeduringthedevelopmentofsuchalayerednetwork,evenintheabsenceofvisualexperience.Thenextpaperinthisserieswillshowhoworientation-selectivecells(4)(whichrespondmaximallytobarsoredgesofparticularorientation)emergeinsucceedinglayersofthesamesystem.Iemphasizethatthesepapersdealwiththeemergenceofnetworkstructureanddifferentiatedcelltypes,startingwithrulesgoverningconnectionformationandmodification.Theydonotaddressthebiochemicalandothermechanismsbywhichtheselower-levelrulesmaybeimplemented.Wearethusconcernedwiththefollowingquestions.Givensomesimple,biologicallyplausiblerulesforsynapticmodi-ficationandforthebasicstructureofanetwork,andgivenonlyspontaneouselectricalactivity(noenvironmentalin-put),doanybiologicallyinterestingnetworkstructuresemerge?Iftheydo,howconstrainedistheclassofstructuresthatcanarise?Iffeature-analyzingcellsofvarioustypes(e.g.,opponentcellsandorientation-selectivecells)emerge,istheirformationrobust,orisitdependentuponprecisechoicesofinitialconditionsandofmodificationrules?Weconsiderhereasystemhavingasimplegrossarchi-tectureanddevelopmentrule.Thisisinordertolaybarethemechanismsbywhichcertainfeature-analyzingfunctionsobservedinthevisualsystememergeeveninasimplyspecifiedexampleofamodularself-adaptivenetwork.Morecomplicatedassumptions-whichmaybeappropriateifone'sgoalisadetailedmodelofaretinocorticalpathway-maybeanalyzedusingthesameprinciplesas
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