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Studies in Computational Intelligence 1070 Yanan Sun Gary G. Yen Mengjie Zhang Evolutionary Deep Neural Architecture Search: Fundamentals, Methods, and Recent Advances Studies in Computational Intelligence Volume 1070 SeriesEditor JanuszKacprzyk,PolishAcademyofSciences,Warsaw,Poland The series “Studies in Computational Intelligence” (SCI) publishes new develop- mentsandadvancesinthevariousareasofcomputationalintelligence—quicklyand withahighquality.Theintentistocoverthetheory,applications,anddesignmethods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms,evolutionarycomputation,artificialintelligence,cellularautomata,self- organizingsystems,softcomputing,fuzzysystems,andhybridintelligentsystems. Ofparticularvaluetoboththecontributorsandthereadershiparetheshortpublica- tiontimeframeandtheworld-widedistribution,whichenablebothwideandrapid disseminationofresearchoutput. This series also publishes Open Access books. A recent example is the book Swan,Nivel,Kant,Hedges,Atkinson,Steunebrink:TheRoadtoGeneralIntelligence https://link.springer.com/book/10.1007/978-3-031-08020-3. IndexedbySCOPUS,DBLP,WTIFrankfurteG,zbMATH,SCImago. AllbookspublishedintheseriesaresubmittedforconsiderationinWebofScience. · · Yanan Sun Gary G. Yen Mengjie Zhang Evolutionary Deep Neural Architecture Search: Fundamentals, Methods, and Recent Advances YananSun GaryG.Yen DepartmentofArtificialIntelligence, SchoolofElectricalandComputer CollegeofComputerScience Engineering,IntelligentSystems SichuanUniversity andControlLaboratory Chengdu,Sichuan,China OklahomaStateUniversity Stillwater,OK,USA MengjieZhang SchoolofEngineeringandComputer Science VictoriaUniversityofWellington Wellington,NewZealand ISSN 1860-949X ISSN 1860-9503 (electronic) StudiesinComputationalIntelligence ISBN 978-3-031-16867-3 ISBN 978-3-031-16868-0 (eBook) https://doi.org/10.1007/978-3-031-16868-0 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsofreprinting,reuseofillustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The use of Evolutionary Computation (EC) methods to create optimal or nearly optimalDeepNeuralNetwork(DNN)architecturesisreferredtoasevolutionarydeep neural architecture design. The design process of architectures is often formalized asanoptimizationproblem,whereECalgorithmsarecorrectlycreatedtotacklethe optimizationproblem. DNNshavehadremarkablesuccessinmanycomplicatedpracticalapplications inrecentyears.ItiswellknownthattheperformanceofaDNNisonlypromising whenthearchitectureisappropriate.Thearchitecture,ontheotherhand,istypically createdbyhand,needingahighlevelofskillthatisinscarcesupplyinpractice.A promisingdeeparchitectureisdifficulttocreateinpracticewithoutthiskindofskill, whichisfrequentlyDNNexpertiseanddomainunderstandingoftheproblemtobe solved.Reinforcementlearningtechniques,gradient-basedoptimizationalgorithms, andECmethodsarethethreecommonmethodsutilizedtoconstructthearchitectures of DNNs in the literature. This book mainly focuses on the EC methods for deep neuralarchitecturedesign. In this book, we will first introduce the fundamentals of commonly used EC methods,includingGeneticAlgorithm(GA)[1],ParticleSwarmOptimization(PSO) [2],DifferentialEvolution(DE)[3],andGeneticProgramming(GP)[4].Following that,wewillgothroughtwodifferentformsofevolutionarydeepneuralarchitecture designalgorithms.TheyarethedesignalgorithmsforunsupervisedDNNs,andthe design algorithms for supervised DNNs. In addition, we will also discuss some recent efforts to speed up the execution of such algorithms. These algorithms are primarily based on the authors recent work, which has been published in journals and international conferences devoted to EC and neural networks. We think that bypresentingthemalltogetherinthisbook,readerswillbeabletoabsorbrelated informationmorequicklyandconveniently. Thisbookiscomposedoffiveparts,andeachpartisfulfilledwiththenecessary contentindifferentchapters.IntheremainderofPart1,wewillprovideanoverview v vi Preface of the fundamentals and backgrounds on EC and deep learning with a focus on differenttypesofcommonlyusedDNNs. Chengdu,China YananSun Stillwater,USA GaryG.Yen Wellington,NewZealand MengjieZhang References 1. JohnHenryHollandetal.Adaptationinnaturalandartificialsystems:anintroductoryanalysis withapplicationstobiology,control,andartificialintelligence.MITpress,1992. 2. James Kennedy and R Eberhart Particle Swarm Optimization. Ieee int. In Conf. on Neural Networks,volume4,1995. 3. RainerStornandKennethPrice.DifferentialevolutionâASasimpleandefficientheuristicfor globaloptimizationovercontinuousspaces,1997.URLhttps://doi.org/10.1023/A:100820282 1328. 4. WolfgangBanzhaf,PeterNordin,RobertEKeller,andFrankDFrancone.Geneticprogram- ming:anintroduction,volume1.MorganKaufmannSanFrancisco,1998. Contents PartI FundamentalsandBackgrounds 1 EvolutionaryComputation ..................................... 3 1.1 GeneticAlgorithms(GAs) ................................. 3 1.2 ParticleSwarmOptimization(PSO) ......................... 4 1.3 DifferentialEvolution(DE) ................................ 5 1.4 GeneticProgramming(GP) ................................ 6 1.5 ChapterSummary ........................................ 7 References .................................................... 7 2 DeepNeuralNetworks ......................................... 9 2.1 DeepBeliefNetworks .................................... 12 2.2 StackedAuto-Encoders ................................... 13 2.2.1 SparseAuto-Encoders ............................. 14 2.2.2 WeightDecayAuto-Encoders ...................... 15 2.2.3 DenoisingAuto-Encoders(DAEs) ................... 15 2.2.4 ContractiveAuto-Encoders ......................... 16 2.2.5 ConvolutionalAuto-Encoders(CAEs) ............... 17 2.2.6 VariationalAuto-Encoders(VAEs) .................. 18 2.3 ConvolutionalNeuralNetworks(CNNs) ..................... 19 2.3.1 CNNSkeleton .................................... 20 2.3.2 Convolution ...................................... 20 2.3.3 Pooling .......................................... 21 2.3.4 ReflectPadding ................................... 22 2.3.5 BatchNormalization(BN) ......................... 23 2.3.6 ResNetBlocks(RBs)andDenseNetBlocks(DBs) ..... 23 2.4 BenchmarksforDeepNeuralNetworks ..................... 24 2.5 ChapterSummary ........................................ 27 References .................................................... 28 vii viii Contents PartII EvolutionaryDeepNeuralArchitectureSearch forUnsupervisedDNNs 3 ArchitectureDesignforStackedAEsandDBNs .................. 39 3.1 Introduction ............................................. 39 3.2 RelatedWorkandMotivations ............................. 40 3.2.1 UnsupervisedDeepLearning ....................... 40 3.2.2 EvolutionaryAlgorithmsforEvolvingNeural Networks ........................................ 41 3.3 AlgorithmDetails ........................................ 43 3.3.1 FrameworkofEUDNN ............................ 43 3.3.2 EvolvingConnectionWeightsandActivation Functions ........................................ 45 3.3.3 Fine-TuningConnectionWeights ................... 47 3.3.4 Discussion ....................................... 48 3.4 ExperimentalDesign ..................................... 49 3.4.1 PerformanceMetric ............................... 50 3.4.2 PeerCompetitors ................................. 50 3.4.3 ParameterSettings ................................ 51 3.5 ExperimentalResultsandAnalysis ......................... 52 3.5.1 PerformanceofEUDNN ........................... 52 3.5.2 AnalysisonPre-trainingofEUDNN ................. 54 3.5.3 AnalysisonFine-TuningofEUDNN ................ 55 3.5.4 RepresentationVisualizations ....................... 56 3.6 ChapterSummary ........................................ 57 References .................................................... 58 4 ArchitectureDesignforConvolutionalAuto-Encoders ............ 61 4.1 Introduction ............................................. 61 4.2 MotivationofFCAE ...................................... 62 4.3 AlgorithmDetails ........................................ 64 4.3.1 AlgorithmOverview .............................. 64 4.3.2 EncodingStrategy ................................ 64 4.3.3 ParticleInitialization .............................. 65 4.3.4 FitnessEvaluation ................................ 66 4.3.5 VelocityCalculationandPositionUpdate ............ 67 4.3.6 DeepTrainingonGlobalBestParticle ............... 70 4.4 ExperimentalDesign ..................................... 70 4.4.1 PeerCompetitors ................................. 70 4.4.2 ParameterSettings ................................ 70 4.5 ExperimentalResultsandAnalysis ......................... 71 4.5.1 OverviewPerformance ............................ 71 4.5.2 EvolutionTrajectoryofPSOAO ..................... 72 4.5.3 PerformanceonDifferentNumbersofTraining Examples ........................................ 73 4.5.4 Investigationonx-ReferenceVelocityCalculation ..... 74 Contents ix 4.6 ChapterSummary ........................................ 75 References .................................................... 75 5 ArchitectureDesignforVariationalAuto-Encoders ............... 79 5.1 Introduction ............................................. 79 5.2 AlgorithmDetails ........................................ 80 5.2.1 AlgorithmOverview .............................. 80 5.2.2 StrategyofGeneEncoding ......................... 81 5.2.3 InitializationofPopulation ......................... 85 5.2.4 Evaluation ....................................... 86 5.2.5 CrossoverOperatorandMutationOperator ........... 88 5.2.6 EnvironmentalSelection ........................... 90 5.3 ExperimentalDesign ..................................... 90 5.3.1 ParameterSetting ................................. 91 5.3.2 PeerCompetitors ................................. 91 5.3.3 PerformanceEvaluation ........................... 92 5.4 ExperimentalResultsandAnalysis ......................... 93 5.4.1 OverallPerformance .............................. 93 5.4.2 EvolutionTrajectoryofEvoVAE .................... 97 5.4.3 RunningTime .................................... 99 5.4.4 TheObtainedArchitecture ......................... 99 5.4.5 AblationExperiments ............................. 102 5.5 ChapterSummary ........................................ 103 References .................................................... 104 PartIII Evolutionary Deep Neural Architecture Search for SupervisedDNNs 6 ArchitectureDesignforPlainCNNs ............................. 109 6.1 Introduction ............................................. 109 6.2 AlgorithmDetails ........................................ 110 6.2.1 AlgorithmOverview .............................. 110 6.2.2 StrategyofGeneEncoding ......................... 111 6.2.3 InitializationofPopulation ......................... 112 6.2.4 EvaluationofFitness .............................. 113 6.2.5 SlackBinaryTournamentSelection ................. 115 6.2.6 OffspringGeneration .............................. 116 6.2.7 EnvironmentalSelection ........................... 117 6.2.8 SelectandDecodeBestIndividual .................. 118 6.3 ExperimentalDesign ..................................... 118 6.3.1 PeerCompetitors ................................. 119 6.3.2 ParameterSettings ................................ 119 6.4 ExperimentalResultsandDiscussion ........................ 119 6.4.1 OverallResults ................................... 120 6.4.2 PerformanceofWeightInitialization ................. 122 6.4.3 Discussion ....................................... 123

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