深度学习及其应用 课件4

QuantummachinelearningDeeplearninganditsapplicationsQuantumMachineLearningQMLisanovelsubjectcombinedboththestrengthofquantumcomputing(QC)anduniversalityofmachinelearning(ML).Fourdifferenttypesofresearch:WhatisQML?BenefitofQMLExtractsomeatypicalpatternsHavlíčekV,CórcolesAD,TemmeK,etal.Nature,2019.LiuY,ArunachalamS,TemmeK.NaturePhysics,2021.LearningefficiencyimprovementZhaoZ,FitzsimonsJK,etal.Phys.Rev.A,2019.KerenidisI,LandmanJ.Phys.Rev.A,2021.BusinessesandOrganizationsQuantumexperimentsHuangHL,DuY,etal.Phys.Rev.Appl.,2021.RobertA,BarkoutsosPK,etal.npjQuantumInf.,2021.ImagegenerationProteinfoldingTypicaldevelopmentofQMLCategoryMethodQuantumBasicLinearAlgebraSubroutines-basedQuantumprincipalcomponentanalysisLloyd,S.,Mohseni,M.&Rebentrost,P.Nat.Phys,2014.QuantumsupportvectormachineRebentrost,P.,Mohseni,M.&Lloyd,S.Phys.Rev.Lett.,2014.QuantumclusteringLloydS,MohseniM,Rebentrost.arXiv:1307.0411,2013.Quantumk-meansKerenidisI,LandmanJ,LuongoA,etal.

NeurIPS,2019.Quantumkernel-basedQuantum-enhancedfeaturespacelearningHavlíčekV,CórcolesAD,TemmeK,etal.Nature,

2019.ProjectedquantumkernelHuang,HY.,Broughton,M.,Mohseni,M.etal.Nat.

Comm.,2021.QuantumDeepLearningQuantumrecurrentneuralnetworkBauschJ.

NeurIPS,2020.QuantumdeepneuralnetworkBeerK,BondarenkoD,FarrellyT,etal.Nat.

Comm.,2020.Quantumcomputing4SJTUDeepLearningLecture.QuantumComputingharnessesthelawsofquantummechanicstosolveproblemstoocomplexforclassicalcomputers.QuantumSuperpositionQuantumEntanglementQuantumDevicesFastprogressofquantumdevicesDifferenttechnologiesSuperconducting,Trappedion,Neutralatom,Photonics,etc.5SJTUDeepLearningLecture.IBM

127QubitGoogle

53QubitsIonQ

32+Qubits6SJTUDeepLearningLecture.QuantumComputerRoadmapQuantumComputerRoadmapThenumberofqubitsincreasesexponentiallyovertimeThecomputingpowerincreasesexponentiallywiththenumberofqubits7SJTUDeepLearningLecture.IBMQuantumQuantumComputinginNISQEra8SJTUDeepLearningLecture.IBMQuantumNoisyIntermediate-ScaleQuantum(NISQ)Limitednumberofqubits:tenstohundredsofqubitsNoisy:qubitsaresensitivetoenvironment;quantumgatesareunreliableLimitedconnectivity:noall-to-allconnections/IBMQGateErrorRateGoogleSycamore53QIBMWashington127Q//articles/s41586-019-1666-59SJTUDeepLearningLecture.UniversalQuantumComputation（NISQ）where

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chemistryOptimizationMachine

learning10SJTUDeepLearningLecture.QuantumAlgorithms’Progression1992~1994指数级加速的量子算法(Deutsch-Jozsa,Shor因子分解，离散对数算法)2007HHL算法

解线性方程

2008量子支持向量机、量子主成分分析2013变分量子线路（VQE）2016量子近似优化算法（QAOA）2019量子卷积神经网络（QCNN）…requirebig,perfectquantumcomputers.Hybridquantum/classicalalgorithms,noise-robust.QuantumMachineLearningQuantumLinearAlgebraFault-tolerantvsNear-termVariationalquantumAlgorithm2019QuantumConvolutionNeuralNetwork(QCNN)

Quantumcomputing11SJTUDeepLearningLecture.QuantumSuperpositionQuantumEntanglementJohnvonNeumann.MathematicalFoundationsofQuantumMechanics(1932)

QuantumBit12SJTUDeepLearningLecture.QuantumBit(Qubit)

Anarbitraryquantumstates:QuantumBit13SJTUDeepLearningLecture.

QuantumGates14SJTUDeepLearningLecture.Qubitgates:operationsononequbitormultiplequbitsThequbitgatescanberepresentedwithmatrixformatwithdimensionAllgatematricesareunitarymatrices:theconjugatetransposeisthesameasitsinverseSinglequbitgates:

Pauligate(xyz):QuantumCircuit15SJTUDeepLearningLecture.Measurement:ameasurementcollapsesaqubit'sstatetooneofitsbasisstates:|0⟩or|1⟩

QBLAS-basedQML

16SJTUDeepLearningLecture.BiamonteJ,WittekP,PancottiN,etal.Quantummachinelearning[J].Nature,2017.QBLAS-basedQML

17SJTUDeepLearningLecture.inputqubitsunitaryoperationsmeasurementsmultiplytraceQBLAS-basedQML

18SJTUDeepLearningLecture.Theintuitionbehindquantumspeedups

ClassicalbitsQuantumbits(qubits)QBLAS-basedQML19SJTUDeepLearningLecture.QuantumparallelismInquantumcomputers,theresultsforallpossibleinputdataarecomputedinparallel.SequentialcomputationInputdata001010101101010100001010101101010100OutputdataClassicaldataprocessingQuantumdataprocessingQBLAS-basedQMLEncodeinputdata(vectors/matrices)asquantumstates;UseQBLAStocomputeanalgebraicexpressionoftheinput;Theadvantageofquantumalgorithms,isthathigh-dimensionalvectorscanberepresentedusingonlyafewqubits,suchthatweonlyneedtodealwiththeproblemthathasthelogarithmicsizeoftheoriginaldata.Extractinformationfromtheoutput(i.e.anestimatorofadesiredvalue)20SJTUDeepLearningLecture.AtypicalapplicationofQBLAStomachinelearningInputdataMorelinearalgebraclassicalalgorithmquantumalgorithm①②③somelinearalgebra21SJTUDeepLearningLecture.QBLAS-basedQMLLandscape:quantumspeedupsinquantummachinelearningTaskPublicationTaskPublicationPrincipalcomponentanalysisNat.Phys.2014SparselinearprogrammingPRL2009Semidefiniteprogramming2016DatafittingPRL2012Low-rankmatrixdecompositionPRA2018TopologydataanalysisNat.Comm.2016SupportvectormachinePRL2014GaussianprocessregressionPRA2019K-meansNIPS2019SupervisedclusteringPRL2001BayesianinferencePRA2014Recommendationsystems2016VariationalQuantumMachineLearningN-bodyProblemsCombinatorialOptimizationProblemsImageClassificationTasks…SJTUDeepLearningLecture.HybridLearningParadigmSJTUDeepLearningLecture.ClassicalSystemStatePreparationCalculatinglossCalculatingGradientOptimize/UpdateParametersQuantumSystemExecutethePQCMeasuretheoutputstateParameterizedQuantumCircuitSingle-qubitParameterizedRotationGates(includingparameterizedRx,Ry,Rzandphasegates)UsingTwo-qubitgatestoentangledifferentqubitsandenlargetheHilbertspaceUsingrotationangleastheparametersSJTUDeepLearningLecture.GradientApproximation

SJTUDeepLearningLecture.QuantumApproximateOptimizationAlgorithmCombinatorialOptimizationProblemsQAOAfocusesonquandtricunconstrianedbinaryoptimizationproblemthatinvolvesfinding"optimal"bitstringscomposedof0'sand1'samongafinitesetofbitstringsMax-CutProblemItinvolvespartitioningnodesofagraphintotwosets,suchthatthenumberofedgesbetweenthesetsismaximized.QAOAAnsatzSJTUDeepLearningLecture.QuantummachinelearningDeeplearninganditsapplicationsQuantumMachineLearningQMLisanovelsubjectcombinedboththestrengthofquantumcomputing(QC)anduniversalityofmachinelearning(ML).Fourdifferenttypesofresearch:WhatisQML?BenefitofQMLExtractsomeatypicalpatternsHavlíčekV,CórcolesAD,TemmeK,etal.Nature,2019.LiuY,ArunachalamS,TemmeK.NaturePhysics,2021.LearningefficiencyimprovementZhaoZ,FitzsimonsJK,etal.Phys.Rev.A,2019.KerenidisI,LandmanJ.Phys.Rev.A,2021.BusinessesandOrganizationsQuantumexperimentsHuangHL,DuY,etal.Phys.Rev.Appl.,2021.RobertA,BarkoutsosPK,etal.npjQuantumInf.,2021.ImagegenerationProteinfoldingTypicaldevelopmentofQMLCategoryMethodQuantumBasicLinearAlgebraSubroutines-basedQuantumprincipalcomponentanalysisLloyd,S.,Mohseni,M.&Rebentrost,P.Nat.Phys,2014.QuantumsupportvectormachineRebentrost,P.,Mohseni,M.&Lloyd,S.Phys.Rev.Lett.,2014.QuantumclusteringLloydS,MohseniM,Rebentrost.arXiv:1307.0411,2013.Quantumk-meansKerenidisI,LandmanJ,LuongoA,etal.

NeurIPS,2019.Quantumkernel-basedQuantum-enhancedfeaturespacelearningHavlíčekV,CórcolesAD,TemmeK,etal.Nature,

2019.ProjectedquantumkernelHuang,HY.,Broughton,M.,Mohseni,M.etal.Nat.

Comm.,2021.QuantumDeepLearningQuantumrecurrentneuralnetworkBauschJ.

NeurIPS,2020.QuantumdeepneuralnetworkBeerK,BondarenkoD,FarrellyT,etal.Nat.

Comm.,2020.VariationalQuantumMachineLearningN-bodyProblemsCombinatorialOptimizationProblemsImageClassificationTasks…SJTUDeepLearningLecture.HybridLearningParadigmSJTUDeepLearningLecture.ClassicalSystemStatePreparationCalculatinglossCalculatingGradientOptimize/UpdateParametersQuantumSystemExecutethePQCMeasuretheoutputstateParameterizedQuantumCircuitSingle-qubitParameterizedRotationGates(includingparameterizedRx,Ry,Rzandphasegates)UsingTwo-qubitgatestoentangledifferentqubitsandenlargetheHilbertspaceUsingrotationangleastheparametersSJTUDeepLearningLecture.GradientApproximation

SJTUDeepLearningLecture.QuantumApproximateOptimizationAlgorithmCombinatorialOptimizationProblemsQAOAfocusesonquandtricunconstrianedbinaryoptimizationproblemthatinvolvesfinding"optimal"bitstringscomposedof0'sand1'samongafinitesetofbitstringsMax-CutProblemItinvolvespartitioningnodesofagraphintotwosets,suchthatthenumberofedgesbetweenthesetsismaximized.QAOAAnsatzSJTUDeepLearningLecture.QuantumApproximateOptimizationAlgorithmHybridLearningParadigmOutputQuantumStateSJTUDeepLearningLecture.VariationalQuantumEigensolver

SJTUDeepLearningLecture.QuantumNeuralNetworksQNNimitatingclassicalneuralnetworksQuantumConvolutionalNeuralNetwork(QCNN)QuantumRecurrentNeuralNetwork(QRNN)QuantumGenerativeAdversarialNetwork(QGAN)QuantumGraphNeuralNetwork(QGNN)SJTUDeepLearningLecture.QCNNSimilarlayerconstruction-ConvolutionallayerandPoolinglayer.EncodingonepixelasonequbitUsingquantummeasurementinthepoolinglayertoreducethenumberofqubits.ExperimentsonMNISTwithcomparableresultstoCNNCong,Iris,SoonwonChoi,andMikhailD.Lukin."Quantumconvolutionalneuralnetworks."NaturePhysics15.12(2019):1273-1278.QRNNSequentialinputateachcell.Non-linearneuronNforeachrotationparameter.AdditionalI/OlanestoassistthetrainablequbitsBausch,Johannes."Recurrentquantumneuralnetworks."Advancesinneuralinformationprocessingsystems33(2020):1368-1379.QGANTestedonsuperconductingquantumcomputerZuchongzhi.HardwareEfficientAnsatz(simplenetworkstructure)forbothgeneratoranddiscriminator.Angleencodingtoreducethestatepreparationcost.Huang,He-Liang,etal."Experimentalquantumgenerativeadversarialnetworksforimagegeneration."PhysicalReviewApplied16.2(2021):024051.QGNNEncodinggraphfeaturetoquantumstates.Learningfromsubgraphswhichgreatlyreducethenumberofqubitsweneed.Quantumstateastheembeddingforfurtherdownstreamtasks(i.e.graphclassification).Ai,Xing,etal."Decompositionalquantumgraphneuralnetwork."arXivpreprintarXiv:2201.05158(2022).DeepLearningAdvancedGenerativeadversarialNetsWassersteindistance

v.s.JS

divergenceSJTUDeepLearningLecture.43Whyvanishinggradient?JSDorKLD—Allthedensitieshavethesamedistancestoeachother.UseWassersteindistance,theygrowlinearlyfromlefttorightOptimalTransporta

distancebetweentwoprobabilitiesSJTUDeepLearningLecture.44OptimalTransport—Origins:Monge’sProblemOptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.45SJTUDeepLearningLecture.46OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.47OptimalTransport—Origins:Monge’sProblemOptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.48SJTUDeepLearningLecture.49OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.50OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.51OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.52OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.53OptimalTransport—Origins:Monge’sProblemSJTUDeepLearningLecture.54OptimalTransport—Origins:Monge’sProblemMonge’sProblem:

FindanoptimalT(transportmap)MongeProblem:ExistenceandUniquenessSJTUDeepLearningLecture.55MongeProblemifthesolutionexists,itmaynotbeuniqueThesolutiontoaMongeProblemmaynotexistKantorovichRelaxationSJTUDeepLearningLecture.56KantorovichProblem(continuous)ThreeclassesofOTproblemsallowforonevs.manyWassersteinDistancesSJTUDeepLearningLecture.57

WassersteindistanceandGANSJTUDeepLearningLecture.58

WassersteindistanceDualdistance

WGANSJTUDeepLearningLecture.59

WGANSJTUDeepLearningLecture.60WGANSJTUDeepLearningLecture.61WGAN_GPSJTUDeepLearningLecture.62WhysomeexperimentsfailforWGAN?WhathappensinWGAN?WGAN_GPSJTUDeepLearningLecture.63

WGAN_GPSJTUDeepLearningLecture.64WGAN_GPfortextgenerationSJTUDeepLearningLecture.65ComparisonamongOriginalGAN,WGANandWGAN_GPSJTUDeepLearningLecture.66AlmostnoneedtoadjustparametersinneuralnetworkforWGAN_GPoriginalGANWGANWGAN_GPEpoch=100RandomfullyconnectednetworkComparisonamongOriginalGAN,WGANandWGAN_GPSJTUDeepLearningLecture.67originalGANWGANWGAN_GPThenetworkarchitectureiscriticaltothequalityofthepictureandtheoriginalGANmaybebetterthanWGANandWGAN_GP

Epoch=100.ThenetworkarchitectureisadjustedbyoriginalGANDeeplearningGANAPPLICATIONSApplicationanditsmodelPix2pixCycleGANSJTUArtificialIntelligenceLecture.69Application1—pix2pix

SJTUArtificialIntelligenceLecture.70

Image-to-imagetranslationwithconditionaladversarialnetworks,/pdf/1611.07004.pdfTheprocessofpix2pixSJTUArtificialIntelligenceLecture.71

DiscriminatorDreal/fake

DiscriminatorDreal/fake

realrealfakeApplication1—pix2pix

SJTUArtificialIntelligenceLecture.72conditionedApplication1—pix2pixSJTUArtificialIntelligenceLecture.73

ObjectiveoftheconditionalGANComparedtotheunconditioneddiscriminator

MixtheGANobjectivewithareconstructionloss—L1loss

Thefinalobjective

Application1—pix2pixGeneratorSJTUArtificialIntelligenceLecture.74TwochoicesforthearchitectureofthegeneratorThe“U-Net”isanencoder-decoderwithskipconnectionsbetweenmirroredlayers(eachlayeriandlayern−i)intheencoderanddecoderstacks.U-Net:ConvolutionalNetworksforBiomedicalImageSegmentationSJTUArtificialIntelligenceLecture.75Application1—pix2pixDiscriminator—calledPatchGANSJTUArtificialIntelligenceLecture.76

Application1—resultsdifferentlossestestSJTUArtificialIntelligenceLecture.77Application1—resultsDifferentpatchestestSJTUArtificialIntelligenceLecture.78Application1—resultsSJTUArtificialIntelligenceLecture.79U-Net:thegeneratorarchitectureApplication1—otherresultsSJTUArtificialIntelligenceLecture.80Application1—otherresultsSJTUArtificialIntelligenceLecture.81ApplicationanditsmodelPix2pixCycleGANSJTUArtificialIntelligenceLecture.82Application2—CycleGANSJTUArtificialIntelligenceLecture.83Imagetranslation:improvedmodelofpix2pixUnpairedImage-to-ImageTranslationusingCycle-ConsistentAdversarialNetworks/abs/1703.10593Application2—CycleGANDatadifferencewithpix2pixSJTUArtificialIntelligenceLecture.84pix2pixCycleGANApplication2—CycleGANBenefitofunpaireddata:wideapplicationSJTUArtificialIntelligenceLecture.85Application2—CycleGANSJTUArtificialIntelligenceLecture.86TheprocessofCycleGAN

Application2—CycleGAN

SJTUArtificialIntelligenceLecture.87Application2—CycleGANObjective:adversariallosses+cycleconsistencylossAdversarialloss1:Thesametoadversarialloss2:SJTUArtificialIntelligenceLecture.88

SJTUArtificialIntelligenceLecture.89Application2—CycleGAN

Application2—CycleGANSJTUArtificialIntelligenceLecture.90Application2—CycleGANFinalObjectiveSJTUArtificialIntelligenceLecture.91

Application2—CycleGANGenerator(encoder-decoder)SJTUArtificialIntelligenceLecture.92Discriminator(PatchGAN)Application2—resultsSJTUArtificialIntelligenceLecture.93Application2—resultsSJTUArtificialIntelligenceLecture.94Application2—resultsSJTUArtificialIntelligenceLecture.95NeuralArchitectureSearchDeepLearninganditsApplicationNeuralArchitectureSearchGoalAutomaticallysearchforaneuralarchitecturenetworkarchitecturescanfulfillthelearningpurpose,wherefeatureengineeringandmodelselectionarebothdonebyNASNASisitselfalsoatypicalpipelineofAutoMLSearchSpaceThetypeofoperationineachlayerTheconnectionoftwolayersThehyper-parametersforeachoperation97SJTUDeepLearningLecture.PipelineofNAS

iterativeNeuralArchitectureSearchSearchSpaceOperationsforeachlayerConnectionbetweenlayersSearchStrategyReinforcementLearningEvolutionaryAlgorithmDARTSEvaluationMetricDirectEvaluationSurrogateModelProxyDatasetLargeSearchSpaceIntractabletoenumerateallcandidatesInefficientSearchStrategyHardtoinvolveexpertsknowledgeCostlyEvaluationMetricTimeconsumingtoevaluateeachcandidateneuralarchitectureThreeAspectsofNASDifficulties99SJTUDeepLearningLecture.SearchSpaceGlobalSearchSpaceCell-BasedSearchSpace100SJTUDeepLearningLecture.GlobalSearchSpaceChained-structuredSearchSpaceThenetworkisasimplesequencearchitectureThesearchspaceconsistsofoperationineachlayer,andthecorrespondinghyper-parametersChained-structuredSearchSpacewithSkipConnectionsEachlayerreceivesmultipleinputsMartinW,AmbrishR,TejaswiniP.ASurveyonNeuralArchitectureSearch.arXivpreprintarXiv:1905.01392,2019.101SJTUDeepLearningLecture.GlobalSearchSpaceArchitectureTemplateSearchSpaceArchitecturesareseparatedintosequentiallyconnectedsegmentsEachsegmentsisparameterizedbyasetofnodeswithconvolutionsastheiroperation.Segmentsbeginw/aconvolutionandconcludewithmaxpoolingtoreducefeaturedimensions.Themaximumnumberofconvops,andthenumberoffiltersarefixedaspartofthetemplate102Architecturetemplaterelaxestheconnectionpattern,butrestrictsthenumberoffiltersMartinW,AmbrishR,TejaswiniP.ASurveyonNeuralArchitectureSearch.arXivpreprintarXiv:1905.01392,2019.SJTUDeepLearningLecture.Cell-BasedSearchSpaceMotivationEffectivehandcraftedarchitecturesaredesignedw/repetitionsoffixedstructuresCellTwotypes:normalcellandreducedcellReducedcellservestodown-sample,

normalcellmaintainsthespatialsizeTopologyandoperationsinallnormalcellsorreducedcellsarethesameThenumberoffilterscanbedifferentindifferentcells103ElskenT,MetzenJH,HutterF.Neuralarchitecturesearch:Asurvey[J].arXivpreprintarXiv:1808.05377,2018.BasicCellsStackthecellsSJTUDeepLearningLecture.ComparisonGlobalSearchSpaceLargerTime-consumingCell-BasedSearchSpaceSmallerMoreefficientEasytotransferacrossdatasetsArchitecturetemplate(akindofglobalsearchspace)issimilartocell-basedsearchspace.Butitdoesn’trestrictthesametopologyinsegments(cells)104SJTUDeepLearningLecture.SearchStrategyReinforcementLearningEvolutionaryAlgorithmSurrogateModel-BasedOptimizationOne-shotArchitectureSearch105SJTUDeepLearningLecture.NASwithRLRNNasthecontroller(optimizer)toselecttheoperationsineachlayerandthecorrespondinghyper-parametersOnceamodelarchitectureisselectedbythecontroller,itisevaluatedonthevalidationdatasetandreceivesanaccuracyRAccuracyRisthenusedtotrainthecontrollerastherewardZophB,LeQV.Neuralarchitecturesearchwithreinforcementlearning[J].arXivpreprintarXiv:1611.01578,2016.106SJTUDeepLearningLecture.EvolutionaryAlgorithmEvolutionaryalgorithms(EA)arepopulation-basedglobaloptimizerforblack-boxfunctionsEssentialComponentsInitializationParentSelectionRecombinationandMutationSurvivorSelectionProcedureInitializethefirstgenerationofthepopulationSelectparentsfromthepopulationforreproductionApplyrecombinationandmutationoperationstocreatenewindividualsEvaluatethefitnessofthenewindividualsSelectthesurvivorsofthepopulationLoopMartinW,AmbrishR,TejaswiniP.ASurveyonNeuralArchitectureSearch.arXivpreprintarXiv:1905.01392,2019.107SJTUDeepLearningLecture.SurrogateModel-BasedOptimizationSurrogatemodel-basedoptimizersuseasurrogatemodeltoapproximatetheresponsefunctionThesurrogateitselfismodeledasamachinelearningmodelThesurrogatemodelistrainedonameta-datasetwhichcontainsarchitecturedescriptionsalongwiththeirresponsevalues,whicharegatheredduringthearchitecturesearchMartinW,AmbrishR,TejaswiniP.ASurveyonNeuralArchitectureSearch.arXivpreprintarXiv:1905.01392,2019.108SJTUDeepLearningLecture.NeuralArchitectureSearchDeepLearninganditsApplicationNeuralArchitectureSearchGoalAutomaticallysearchforaneuralarchitecturenetworkarchitecturescanfulfillthelearningpurpose,wherefeatureengineeringandmodelselectionarebothdonebyNASNASisitselfalsoatypicalpipelineofAutoMLSearchSpa