Neuro-Fuzzy Hardware: Design, Development and Performance

Neuro-FuzzyHardware:Design,DevelopmentandPerformanceL.M.ReyneriDipartimento di Elettronica, Politecnico di Torino,C.soDuca degli Abruzzi 24, 10129 TORINO,ITALYAbstract| Thispap erintro duceshardwareimplementa-tions of Arti cial Neural Networks and Fuzzy Systems.Sev-eralimplementation metho dologiesaredescrib ed,rangingfrom fully digital to fully analog ones.Advantages and draw-backsare outlinedandp erformance of existing implemen-tationsarepresented.Thepap eralsoanalyzeshardwp erformance parameters and tradeo s, and the b ottlenecksintrinsic in several implementation metho dologies. The con-straints p osed by hardware technologies onto algorithms andp erformance are also clearly describ ed.I.INTRODUCTIONArti cial Neural Networks [1] (NNs), Fuzzy Systems [2](FSs)andWaveletNetworks[3]WNaregainingwidespreadacceptanceinalargevarietyofapplication elds,rangingfromengineeringtoeconomics,fore-casting to control.Literature describ es an incredibly largeamount of di erent algorithms, architectures and learningrules.Unfortunately,manypracticalapplicationsrequirealarge computational p ower to cop e with complexity or real-timeconstraints.Oftensuchpowerisnotavailablefromtraditionalcomputers,oritisto oexp ensiveandcannotalways b e a orded.One solution to this problem is the use of ad-ho c hard-ware systems, purp osely designed and manufactured to im-plement NNs, FSs or WNs.Dedicated hardware implemen-tations(mostlysilicon chips) can often o er very high com-putational p ower at a limited price.The ma jor drawbackisthat they must often b e designed and manufactured ad-ho c,therefore their use can b e justi ed only for either very largequantities or when very high p erformance are required.Thispap erintro duceshardwareimplementationsofneuro-fuzzy systems, describ es the technologies commonlyused in designing and manufacturing them and outlines theproblemsandadvantagesofmanyimplementationtech-niques.A.Neuro-Fuzzy Uni cationUntil a few years ago, NNs, FSs and WNs were consid-ered very di erent and incompatible paradigms.As a con-sequence, manufacturers were pro ducing interesting piecesof hardware (devices and/or b oards; see table I I) targetedsp eci cally for just one prede ned paradigm, selected apri-ori according to manufacturer's taste or exp erience.Asaconsequence,NN(resp ectively,FS)hadtoberun on a dedicated NN (resp ectively, FS) hardware, whilea FS could not b e run on a NNhardware and vice-versa.Furthermore, WNs had no dedicated hardware asso ciatedwiththem,thereforetheycouldonlybeimplementedongeneral-purp ose computers at a limited sp eed.More recently, NNs, FSs, WNs and a few otherSoft Com-putingparadigms have b een uni ed together [4] and can atpresentbeconsideredasthedi erensidesofsame\coin".Thisisaveryimp ortantasp ecttobediscussedb efore intro ducing the various hardware implementations.Neuro-fuzzy uni cation [4] (see U-neurons, in sect. I-C)allowstomixtogetherthevariousparadigmswithinsamepro jectorsystem.Finstance,p eoplecaneasilytrain a NN or a WN by means of a set ofexamples(namely,thetrainingset)andthenrunitonaFShardware.Or,forinstance,takealinguistic(namely,fuzzy)descriptionofa systemor a controller andrun iton ahardwareimplementation, etc.This augments signi cantly exibility and re-usabilityofhardwaredevicesandsystems,reducesthehumanusers'\training"costs,asusersneedtolearnonlyonehard-ware system (for instance, NN) on which several di erentparadigms can b e implemented, leaving the user to cho osethe preferred (or the optimal) paradigms to use.B.Neuro-Fuzzy ParadigmsThe most widely used neuron paradigms which are easilyimplemented in hardware are the following [4]:CorrelationBasedneurons(orP-neur),whichinclude,amongothers,(Multi-Layer)Perceptrons(MLPs) [5], [6], [7],Hop eld Networks,(Bidirectional)Associative Memories,Linear Networks, etc.Neuronshave the following paradigm:yj=F!Xixiwi(1)wherexiandwjiare, resp ectively, the input of thei-thsynapse and the asso ciated weight in thej-th neuron,whileF(z) is a (p ossibly) non-linear transfer function(eithersigmoid,orhyperbolictangenthard thresh-old,orlinear).Distance Based neurons(orR-neur), which include,amongothers,RadialBasisFunctions(RBFs),Ko-honen Maps[8], someFuzzy Rules[9],uzzy Clusters,etc.Neurons have the following paradigm:yj=G!Xi(xici)2(2)wherexiandcjiare, resp ectiv, the input of thei-thsynapse and the asso ciated center in thej-th neuron,whileF(z) is a (p ossibly) non-linear transfer function(eitherGaussian,orexponentiallinear).Uni edneurons(orU-neur),whichinclude,amongothers,WeightedRadialBasisFunctions