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1、Brain,neuralnetworks,andcomputationJ.J.HopfieldDepartmentofMolecularBiology,PrincetonUniversity,Princeton,NewJersey08544[S0034-6861(99)04102-1]I.INTRODUCTIONtheactuatorsofarobotforadesiredmotionisaprob-leminclassicalmechanicsthatcanbesolvedonacom-Themethodbywhichbrainproducesmindhasforputer.While
2、wemaynotknowhowtowriteef®cientcenturiesbeendiscussedintermsofthemostcomplexalgorithmsforthesetasks,suchexamplesdoillustrateengineeringandsciencemetaphorsoftheday.Descartesthatwhatthenervoussystemdoesmightbedescribedasdescribedmindintermsofinteractingvortices.Psy-computation.chologistshavemetapho
3、rizedmemoryintermsofpathsForpresentpurposes,acomputercanbeviewedasanortracesworninalandscape,ageologicalrecordofourinput-outputdevice,withinputandoutputsignalsthatexperiences.ToMcCullochandPitts(1943)andvonareinthesameformat(Hop®eld,1994).ThusinaveryNeumann(1958),theappropriatemetaphorwasthesimp
4、ledigitalcomputer,theinputisastringofbits(indigitalcomputer,theninitsinfancy.The®eldof``neuraltime),andtheoutputisanotherstringofbits.Amillionnetworks''isthestudyofthecomputationalpropertiesaxonscarryelectrochemicalpulsesfromtheeyetotheandbehaviorofnetworksof``neuronlike''elements.Itbrain.Simila
5、rsignalingpulsesareusedtodrivetheliessomewherebetweenamodelofneurobiologyandamusclesofthevocaltract.Whenwelookatapersonmetaphorforhowthebraincomputes.Itisinspiredbyandsay,``Hello,Jessica,''ourbrainisproducingacom-twogoals:tounderstandhowneurobiologyworks,andplicatedtransformationfromone(parallel
6、)inputpulsetounderstandhowtosolveproblemswhichneurobiol-sequencecomingfromtheeyetoanother(parallel)out-ogysolvesrapidlyandeffortlesslyandwhichareveryputpulsesequencewhichresultsinsoundwavesbeinghardonpresentdigitalmachines.generated.TheideaofcompositionisimportantinthisMostphysicistswill®nditobv
7、iousthatunderstandingde®nition.Theoutputofonecomputercanbeusedasbiologymighthelpinengineering.Theobversetheinputforanothercomputerofthesamegeneralengineering-toward-biologicallinkcanbemadebytest-type,fortheyarecompatiblesign
