Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons

A modelforalarge network of"neurons" withagraded response (orsigmoid input-output relation) is studied. Thisdeterministic system hascollective properties in veryclose correspondence withtheearlier stochastic model based onMcCulloch-Pitts neurons. Thecontent-addressable memoryandother emergent collective properties oftheorigi- nalmodelalso arepresent inthegraded response model. The idea that suchcollective properties areusedinbiological sys- temsisgiven addedcredence bythecontinued presence ofsuch properties formorenearly biological "neurons." Collective analog electrical circuits ofthekinddescribed will certainly function. Thecollective states ofthetwomodels haveasimple correspondence. Theoriginal modelwill continue tobeuseful forsimulations, because its connection tograded response sys- temsisestablished. Equations that include theeffect ofaction potentials inthegraded response system arealsodeveloped. Recent papers (1-3) haveexplored theability ofasystem of highly interconnected "neurons" tohaveuseful collective computational properties. Theseproperties emergesponta- neously inasystem having alarge numberofelementary "neurons." Content-addressable memory(CAM)isoneof thesimplest collective properties ofsucha system. The mathematical modeling hasbeenbasedon"neurons" that aredifferent bothfromreal biological neurons andfromthe realistic functioning ofsimple electronic circuits. Someof these differences aremajor enough thatneurobiologists and circuit engineers alike havequestioned whether real neural orelectrical circuits wouldactually exhibit thekindofbe- haviors foundinthemodelsystem evenifthe"neurons" wereconnected inthefashion envisioned. Twomajor divergences between themodelandbiological orphysical systems stand out.Realneurons (andreal physi- caldevices suchasoperational amplifiers that might mimic them) havecontinuous input-output relations. (Action po- tentials areomitted until Discussion.) Theoriginal modeling usedtwo-state McCulloch-Pitts (4)threshold devices having outputs of0or1only. Realneurons andreal physical circuits haveintegrative timedelays duetocapacitance, andthetime evolution ofthestate ofsuchsystems should berepresented byadifferential equation (perhaps withaddednoise). The original modeling usedastochastic algorithm involving sud- den0-1or1-0changes ofstates ofneurons atrandom times. Thispaper showsthat theimportant properties oftheorigi- nalmodelremain intact whenthese twosimplifications of themodeling areeliminated. Although itisuncertain wheth- ertheproperties ofthese newcontinuous "neurons" areyet close enough totheessential properties ofrealneurons (and/or their dendritic arborization) tobedirectly applicable toneurobiology, amajor conceptual obstacle hasbeenelimi- nated. Itiscertain that aCAM constructed onthebasic ideas