使用Python实现人工智能

Lecture11:UsingPythonforArtificialIntelligence

CS5001/CS5003:

IntensiveFoundationsofComputerScience

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Lecture11:UsingPythonforArtificialIntelligence

Today'stopics:IntroductiontoArtificialIntelligence

IntroductiontoArtificialNeuralNetworksExamplesofsomebasicneuralnetworksUsingPythonforArtificialIntelligenceExample:PyTorch

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Lecture11:IntroductiontoArtificialIntelligence

VideoIntroduction

1950:

AlanTuring

:

TuringTest

1951:FirstAIprogram1965:

Eliza

(firstchatbot)

1974:Firstautonomousvehicle

1997:

DeepBluebeatsGaryKasimov

atChess2004:FirstAutonomousVehiclechallenge2011:

IBMWatsonbeatsJeopardywinners

2016:

DeepMindbeatsGochampion

2017:

AlphaGoZerobeatsDeepMind

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

NNslearnrelationshipbetweencauseandeffectororganizelargevolumesofdataintoorderlyandinformativepatterns.

Slidesmodifiedfrom

PPT

byMohammedShbier

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

ANeuralNetworkisabiologicallyinspiredinformationprocessingidea,modeledafterourbrain.

Aneuralnetworkisalargenumberofhighlyinterconnectedprocessingelements(neurons)workingtogether

Likepeople,theylearnfromexperience(byexample)

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

NeuralnetworkstaketheirinspirationfromneurobiologyThisdiagramisthehumanneuron:

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Abiologicalneuronhasthreetypesofmaincomponents;dendrites,soma(orcellbody)andaxonDendritesreceivessignalsfromotherneurons

Thesoma,sumstheincomingsignals.Whensufficientinputisreceived,thecellfires;thatisittransmitasignaloveritsaxontoothercells.

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Anartificialneuralnetwork(ANN)isaninformationprocessingsystemthathascertainperformancecharacteristicsincommonwithbiologicalnets.

SeveralkeyfeaturesoftheprocessingelementsofANNaresuggestedbythepropertiesofbiologicalneurons:

Theprocessingelementreceivesmanysignals.

Signalsmaybemodifiedbyaweightatthereceivingsynapse.

Theprocessingelementsumstheweightedinputs.

Underappropriatecircumstances(sufficientinput),theneurontransmitsasingleoutput.

Theoutputfromaparticularneuronmaygotomanyotherneurons.

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Fromexperience:examples/trainingdata

Strengthofconnectionbetweentheneuronsisstoredasaweight-valueforthespecificconnection.

Learningthesolutiontoaproblem=changingtheconnectionweights

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

ANNshavebeendevelopedasgeneralizationsofmathematicalmodelsofneuralbiology,basedontheassumptionsthat:

Informationprocessingoccursatmanysimpleelementscalledneurons.

Signalsarepassedbetweenneuronsoverconnectionlinks.

Eachconnectionlinkhasanassociatedweight,which,intypicalneuralnet,multipliesthesignaltransmitted.

Eachneuronappliesanactivationfunctiontoitsnetinputtodetermineitsoutputsignal.

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Modelofaneuron

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Aneuralnetconsistsofalargenumberofsimpleprocessingelementscalledneurons,units,cellsornodes.

Eachneuronisconnectedtootherneuronsbymeansofdirectedcommunicationlinks,eachwithassociatedweight.

Theweightrepresentinformationbeingusedbythenettosolveaproblem.

Eachneuronhasaninternalstate,calleditsactivationoractivitylevel,whichisafunctionoftheinputsithasreceived.Typically,aneuronsendsitsactivationasasignaltoseveralotherneurons.

Itisimportanttonotethataneuroncansendonlyonesignalatatime,althoughthatsignalisbroadcasttoseveralotherneurons.

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Neuralnetworksareconfiguredforaspecificapplication,suchaspatternrecognitionordataclassification,throughalearningprocess

Inabiologicalsystem,learninginvolvesadjustmentstothesynapticconnectionsbetweenneurons

Thisisthesameforartificialneuralnetworks(ANNs)!

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Aneuronreceivesinput,determinesthestrengthortheweightoftheinput,calculatesthetotalweightedinput,andcomparesthetotalweightedwithavalue(threshold)Thevalueisintherangeof0and1

Ifthetotalweightedinputgreaterthanorequalthethresholdvalue,theneuronwillproducetheoutput,andifthetotalweightedinputlessthanthethresholdvalue,nooutputwillbeproduced

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Let'smodelaslightlymorecomplicatedneuralnetwork:

Ifwetouchsomethingcoldweperceiveheat

Ifwekeeptouchingsomethingcoldwewillperceivecold

Ifwetouchsomethinghotwewillperceiveheat

WewillassumethatwecanonlychangethingsondiscretetimestepsIfcoldisappliedforonetimestepthenheatwillbeperceived

Ifacoldstimulusisappliedfortwotimestepsthencoldwillbeperceived

Ifheatisappliedatatimestep,thenweshouldperceiveheat

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SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Ittakestimeforthestimulus(appliedatX1andX2)tomakeitswaytoY1and

Y2whereweperceiveeitherheatorcold

Att(0),weapplyastimulustoX1andX2Att(1)wecanupdateZ1,Z2andY1

Att(2)wecanperceiveastimulusatY2

Att(2+n)thenetworkisfullyfunctional

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SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Wewantthesystemtoperceivecoldifacoldstimulusisappliedfortwotimesteps

Y2(t)=X2(t–2)ANDX2(t–1)

X2(t–2)

X2(t–1)

Y2(t)

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SlidesmodifiedfromGrahamKendall'sIntroductiontoArtificialIntelligence

Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Wewantthesystemtoperceiveheatifeitherahotstimulusisappliedoracoldstimulusisapplied(foronetimestep)andthenremoved

Y1(t)=[X1(t–1)]OR[X2(t–3)ANDNOTX2(t–2)]

X2(t–3)

X2(t–2)

ANDNOT

X1(t–1)

OR

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Lecture11:IntroductiontoArtificialNeuralNetworks(ANNs)

Thenetworkshows

Y1(t)=X1(t–1)ORZ1(t–1)

Z1(t–1)=Z2(t–2)ANDNOTX2(t–2)Z2(t–2)=X2(t–3)

Substituting,weget

Y1(t)=[X1(t–1)]OR[X2(t–3)ANDNOTX2(t–2)]

whichisthesameasouroriginalrequirements

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Lecture11:UsingPythonforArtificialIntelligence

Thisisgreat...buthowdoyoubuildanetworkthatlearns?Wehavetouseinputtopredictoutput

Wecandothisusingamathematicalalgorithmcalledbackpropogation,whichmeasuresstatisticsfrominputvaluesandoutputvalues.

Backpropogationusesatrainingset

Wearegoingtousethefollowingtrainingset:

Canyoufigureoutwhatthequestionmarkshouldbe?

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

Thisisgreat...buthowdoyoubuildanetworkthatlearns?Wehavetouseinputtopredictoutput

Wecandothisusingamathematicalalgorithmcalledbackpropogation,whichmeasuresstatisticsfrominputvaluesandoutputvalues.

Backpropogationusesatrainingset

Wearegoingtousethefollowingtrainingset:

Canyoufigureoutwhatthequestionmarkshouldbe?

Theoutputisalwaysequaltothevalueoftheleftmostinputcolumn.Thereforetheansweristhe

‘?’shouldbe1.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

Westartbygivingeachinputaweight,whichwillbeapositiveornegativenumber.

Largenumbers(positiveornegative)willhavealargeeffectontheneuron'soutput.

Westartbysettingeachweighttoarandomnumber,andthenwetrain:

Taketheinputsfromatrainingsetexample,adjustthembytheweights,andpassthemthroughaspecialformulatocalculatetheneuron’soutput.

Calculatetheerror,whichisthedifferencebetweentheneuron’soutputandthedesiredoutputinthetrainingsetexample.

Dependingonthedirectionoftheerror,adjusttheweightsslightly.

Repeatthisprocess10,000times.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

Eventuallytheweightsoftheneuronwillreachanoptimumforthetrainingset.Ifweallowtheneurontothinkaboutanewsituation,thatfollowsthesamepattern,itshouldmakeagoodprediction.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

Whatisthisspecialformulathatwe'regoingtousetocalculatetheneuron'soutput?

First,wetaketheweightedsumoftheneuron'sinputs:

∑weighti

×inputi

=weight1×input1+weight2×input2+weight3×input3

Nextwenormalizethis,sotheresultisbetween0and1.Forthis,weuseamathematicallyconvenientfunction,calledtheSigmoidfunction:

1 1+e−x

TheSigmoidfunctionlookslikethiswhenplotted:Noticethecharacteristic"S"

shape,andthatitisboundedby1and0.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

WecansubstitutethefirstfunctionintotheSigmoid:

1 1+e−(∑weighti×inputi)

Duringthetraining,wehavetoadjusttheweights.Tocalculatethis,weusetheErrorWeightedDerivativeformula:

error×input×SigmoidCurvedGradient(output)

What'sgoingonwiththisformula?

Wewanttomakeanadjustmentproportionaltothesizeoftheerror

Wemultiplybytheinput,whichiseither1or0

Wemultiplybythe

gradient(steepness)oftheSigmoidcurve

.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

What'sgoingonwiththisformula?

Wewanttomakeanadjustmentproportionaltothesizeoftheerror

Wemultiplybytheinput,whichiseither1or0

Wemultiplybythe

gradient(steepness)oftheSigmoidcurve

.

WhythegradientoftheSigmoid?

WeusedtheSigmoidcurvetocalculatetheoutputoftheneuron.

Iftheoutputisalargepositiveornegativenumber,itsignifiestheneuronwasquiteconfidentonewayoranother.

Fromthediagram,wecanseethatatlargenumbers,theSigmoidcurvehasashallowgradient.

Iftheneuronisconfidentthattheexistingweightiscorrect,itdoesn’twanttoadjustitverymuch.MultiplyingbytheSigmoidcurvegradientachievesthis.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

ThegradientoftheSigmoidcurve,canbefoundbytakingthederivative(remembercalculus?)

SigmoidCurvedGradient(output)=output×(1−output)

Sobysubstitutingthesecondequationintothefirstequation(fromtwoslidesago),thefinalformulaforadjustingtheweightsis:

error×input×output×(1−output)

Thereareother,moreadvancedformulas,butthisoneisprettysimple.

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

Finally,Python!

Wewillusethenumpymodule,whichisamathematicslibraryforPython.Wewanttousefourmethods:

exp—thenaturalexponential

array—createsamatrix

dot—multipliesmatrices

random—givesusrandomnumbers

array()createslist-likearraysthatarefasterthanregularlists.E.g.,forthetrainingsetwesawearlier:

1training_set_inputs=array([[0,0,1],[1,1,1],[1,0,1],[0,1,1]])

2training_set_outputs=array([[0,1,1,0]]).T

The‘.T’function,transposesthematrixfromhorizontaltovertical.Sothe

0 0

⎡

⎢1 1

1⎤⎡0⎤

1⎥⎢1⎥

⎣

computerisstoringthenumberslikethis: 1

0

0 1⎥⎢1⎥

1 1⎦⎣0⎦

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Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

Lecture11:UsingPythonforArtificialIntelligence

In10linesofPythoncode:

fromnumpyimportexp,array,random,dot

training_set_inputs=array([[0,0,1],[1,1,1],[1,0,1],[0,1,1]])

training_set_outputs=array([[0,1,1,0]]).T

random.seed(1)

synaptic_weights=2*random.random((3,1))-1

foriterationinrange(10000):

output=1/(1+exp(-(dot(training_set_inputs,synaptic_weights))))

synaptic_weights+=dot(training_set_inputs.T,(training_set_outputs-output)

*output*(1-output))

print1/(1+exp(-(dot(array([1,0,0]),synaptic_weights))))

35

Exampleborrowedfrom:

Howtobuildasimpleneuralnetworkin9linesofPythoncode

1fromnumpyimportexp,array,random,dot

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definit(self):

#Seedtherandomnumbergenerator,soitgeneratesthesamenumbers#everytimetheprogramruns.

random.seed(1)

#Wemodelasingleneuron,with3inputconnectionsand1outputconnection.

#Weassignrandomweightstoa3x1matrix,withvaluesintherange-1to1#andmean0.

self.synaptic_weights=2*random.random((3,1))-1

#TheSigmoidfunction,whichdescribesanSshapedcurve.

#Wepasstheweightedsumoftheinputsthroughthisfunctionto#normalisethembetween0and1.

defsigmoid(self,x):return1/(1+exp(-x))

#ThederivativeoftheSigmoidfunction.

#ThisisthegradientoftheSigmoidcurve.

#Itindicateshowconfidentweareabouttheexistingweight.defsigmoid_derivative(self,x):

returnx*(1-x)

#Wetraintheneuralnetworkthroughaprocessoftrialanderror.#Adjustingthesynapticweightseachtime.

deftrain(self,training_set_inputs,training_set_outputs,number_of_training_iterations):foriterationinrange(number_of_training_iterations):

#Passthetrainingsetthroughourneuralnetwork(asingleneuron).output=self.think(training_set_inputs)

#Calculatetheerror(Thedifferencebetweenthedesiredoutput#andthepredictedoutput).

error=training_set_outputs-output

#MultiplytheerrorbytheinputandagainbythegradientoftheSigmoidcurve.#Thismeanslessconfidentweightsareadjustedmore.

#Thismeansinputs,whicharezero,donotcausechangestotheweights.adjustment=dot(training_set_inputs.T,error*self.sigmoid_derivative(output))

#Adjusttheweights.self.synaptic_weights+=adjustment

#Theneuralnetworkthinks.defthink(self,inputs):

#Passinputsthroughourneuralnetwork(oursingleneuron).returnself.sigmoid(dot(inputs,self.synaptic_weights))

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#Intialiseasingleneuronneuralnetwork.

neural_network=NeuralNetwork()

print("Randomstartingsynapticweights:")

print(neural_network.synaptic_weights)

#Thetrainingset.Wehave4examples,eachconsistingof3inputvalues#and1outputvalue.

training_set_inputs=array([[0,0,1],[1,1,1],[1,0,1],[0,1,1]])

training_set_outputs=array([[0,1,1,0]]).T

#Traintheneuralnetworkusingatrainingset.

#Doit10,000timesa