1. 神经网络基础知识
1.1 神经元
神经网络（Neural Net）是由大量的处理单元相互连接形成的网络。神经元是神经网络的最小单元，神经网络由若干个神经元组成。一个神经元的结构如下：
上面的神经元x1，x2，x3和1是输入，hw,b(x)是输出。
其中f(x)是激活函数，常用的激活函数有sigmoid函数和tanh（双曲正切）函数。
sigmoid函数：
tanh（双曲正切）函数：
1.2 神经网络
神经网络由若干个层次，相邻层次之间的神经元存在输入的关系。第一层称为输入层，最后一层称为输出层，中间的层次称为隐含层。
1.3 信号前向传播和误差反向传播
设神经网络有n层，第1层为L1，第2层为L2，第n层为Ln，第p(p=1,2,...n)层的神经元节点数量是mp。aj(k)表示第k层第j个节点的输出值。则对于L1（也就是输入层），有
第(k+1)层第j个神经元的输出
设一个训练样本的误差为
整体误差函数
为了防止过拟合，增加了第二项L2正则化。
目标是求(w,b)，使得J(w,b)最小。为此使用梯度下降法，每次迭代按照下面的公式对w和b进行更新
第n层（也就是输出层）的输出神经元j，其残差为
第k层第i个节点的残差为
求解(w,b)的过程如下：
1) 对于所有的k，令w(k):=0，b(k):=0；
2) 信号前向传播，根据每个样本的输入值和w(k)、w(k)，逐层计算出hw,b(x)；
3) 误差反向传播，逐层计算出每一层每个神经元的残差；
4) 对w和b的值进行更新。
反复进行步骤(2)~(4)，直到完成指定的迭代次数为止。
2. MLlib神经网络的实现
MLlib的神经网络类是NerualNet。主要参数包括：
Size：Array[Int]，神经网络每一层的节点数量；
Layer：神经网络的层数；
Activation_function：激活函数，可以是sigm或tanh
Ouput_function：输出函数，可以是sigm、softmax或linear。
代码：
import org.apache.log4j.{ Level, Logger }import org.apache.spark.{ SparkConf, SparkContext }import breeze.linalg.{DenseMatrix => BDM,max => Bmax,min => Bmin}import scala.collection.mutable.ArrayBuffer/** * Created by Administrator on 2017/7/27. */object NNTest { def main(args: Array[String]) = { // 设置运行环境 val conf = new SparkConf().setAppName("Neural Net") .setMaster("spark://master:7077").setJars(Seq("E:\\Intellij\\Projects\\MachineLearning\\MachineLearning.jar")) val sc = new SparkContext(conf) Logger.getRootLogger.setLevel(Level.WARN) // 随机生成样本数据 Logger.getRootLogger.setLevel(Level.WARN) val sampleRow = 1000 val sampleColumn = 5 val randSamp_01 = RandSampleData.RandM(sampleRow, sampleColumn, -10, 10, "sphere") // 归一化 val norMax = Bmax(randSamp_01(::, breeze.linalg.*)) val norMin = Bmin(randSamp_01(::, breeze.linalg.*)) val nor1 = randSamp_01 - (BDM.ones[Double](randSamp_01.rows, 1)) * norMin val nor2 = nor1 :/ ((BDM.ones[Double](nor1.rows, 1)) * (norMax - norMin)) // 转换样本 val randSamp_02 = ArrayBuffer[BDM[Double]]() for (i <- 0 to sampleRow - 1) { val mi = nor2(i, ::) val mi1 = mi.inner val mi2 = mi1.toArray val mi3 = new BDM(1, mi2.length, mi2) randSamp_02 += mi3 } val randSamp_03 = sc.parallelize(randSamp_02, 10) sc.setCheckpointDir("hdfs://master:9000/ml/data/checkpoint") randSamp_03.checkpoint() val trainRDD = randSamp_03.map(f => (new BDM(1, 1, f(::, 0).data), f(::, 1 to -1))) // 训练，建立模型 val opts = Array(100.0, 50.0, 0.0) trainRDD.cache val numExamples = trainRDD.count() println(s"Number of Examples: $numExamples") val NNModel = new NeuralNet(). setSize(Array(5, 10, 10, 10, 10, 10, 1)). setLayer(7). setActivation_function("tanh_opt"). setLearningRate(2.0). setScaling_learningRate(1.0). setWeightPenaltyL2(0.0). setNonSparsityPenalty(0.0). setSparsityTarget(0.05). setInputZeroMaskedFraction(0.0). setDropoutFraction(0.0). setOutput_function("sigm"). NNtrain(trainRDD, opts) // 测试模型 val NNPrediction = NNModel.predict(trainRDD) val NNPredictionError = NNModel.Loss(NNPrediction) println(s"NNerror = $NNPredictionError") val showPrediction = NNPrediction.map(f => (f.label.data(0), f.predict_label.data(0))).take(100) println("Prediction Result") println("Value" + "\t" + "Prediction" + "\t" + "Error") for (i <- 0 until showPrediction.length) println(showPrediction(i)._1 + "\t" + showPrediction(i)._2 + "\t" + (showPrediction(i)._2 - showPrediction(i)._1)) var tmpWeight = NNModel.weights(0) for (i <-0 to 5) { tmpWeight = NNModel.weights(i) println(s"Weight of Layer ${i+1}") for (j <- 0 to tmpWeight.rows - 1) { for (k <- 0 to tmpWeight.cols - 1) { print(tmpWeight(j, k) + "\t") } println() } } }} 以上代码建立了一个7层的神经网络，各层的节点数量为Array(5, 10, 10, 10, 10, 10, 1)，对Sphere函数进行了测试。
运行结果：
Number of Examples: 1000epoch: numepochs = 1 , Took = 17 seconds; Full-batch train mse = 0.066738, val mse = 0.000000.epoch: numepochs = 2 , Took = 12 seconds; Full-batch train mse = 0.069649, val mse = 0.000000.epoch: numepochs = 3 , Took = 10 seconds; Full-batch train mse = 0.055260, val mse = 0.000000.epoch: numepochs = 4 , Took = 10 seconds; Full-batch train mse = 0.016346, val mse = 0.000000.epoch: numepochs = 5 , Took = 9 seconds; Full-batch train mse = 0.013802, val mse = 0.000000.epoch: numepochs = 6 , Took = 13 seconds; Full-batch train mse = 0.045142, val mse = 0.000000.epoch: numepochs = 7 , Took = 7 seconds; Full-batch train mse = 0.031211, val mse = 0.000000.epoch: numepochs = 8 , Took = 7 seconds; Full-batch train mse = 0.016334, val mse = 0.000000.epoch: numepochs = 9 , Took = 9 seconds; Full-batch train mse = 0.013348, val mse = 0.000000.epoch: numepochs = 10 , Took = 7 seconds; Full-batch train mse = 0.017879, val mse = 0.000000.epoch: numepochs = 11 , Took = 7 seconds; Full-batch train mse = 0.012627, val mse = 0.000000.epoch: numepochs = 12 , Took = 7 seconds; Full-batch train mse = 0.018080, val mse = 0.000000.epoch: numepochs = 13 , Took = 7 seconds; Full-batch train mse = 0.016755, val mse = 0.000000.epoch: numepochs = 14 , Took = 7 seconds; Full-batch train mse = 0.012250, val mse = 0.000000.epoch: numepochs = 15 , Took = 7 seconds; Full-batch train mse = 0.044833, val mse = 0.000000.epoch: numepochs = 16 , Took = 7 seconds; Full-batch train mse = 0.024345, val mse = 0.000000.epoch: numepochs = 17 , Took = 7 seconds; Full-batch train mse = 0.039005, val mse = 0.000000.epoch: numepochs = 18 , Took = 7 seconds; Full-batch train mse = 0.012298, val mse = 0.000000.epoch: numepochs = 19 , Took = 7 seconds; Full-batch train mse = 0.012371, val mse = 0.000000.epoch: numepochs = 20 , Took = 6 seconds; Full-batch train mse = 0.014077, val mse = 0.000000.epoch: numepochs = 21 , Took = 7 seconds; Full-batch train mse = 0.040328, val mse = 0.000000.epoch: numepochs = 22 , Took = 6 seconds; Full-batch train mse = 0.036575, val mse = 0.000000.epoch: numepochs = 23 , Took = 6 seconds; Full-batch train mse = 0.033986, val mse = 0.000000.epoch: numepochs = 24 , Took = 6 seconds; Full-batch train mse = 0.026421, val mse = 0.000000.epoch: numepochs = 25 , Took = 6 seconds; Full-batch train mse = 0.036776, val mse = 0.000000.epoch: numepochs = 26 , Took = 6 seconds; Full-batch train mse = 0.011838, val mse = 0.000000.epoch: numepochs = 27 , Took = 6 seconds; Full-batch train mse = 0.010749, val mse = 0.000000.epoch: numepochs = 28 , Took = 6 seconds; Full-batch train mse = 0.012717, val mse = 0.000000.epoch: numepochs = 29 , Took = 6 seconds; Full-batch train mse = 0.011883, val mse = 0.000000.epoch: numepochs = 30 , Took = 7 seconds; Full-batch train mse = 0.010562, val mse = 0.000000.epoch: numepochs = 31 , Took = 6 seconds; Full-batch train mse = 0.010591, val mse = 0.000000.epoch: numepochs = 32 , Took = 6 seconds; Full-batch train mse = 0.010389, val mse = 0.000000.epoch: numepochs = 33 , Took = 6 seconds; Full-batch train mse = 0.015908, val mse = 0.000000.epoch: numepochs = 34 , Took = 6 seconds; Full-batch train mse = 0.012413, val mse = 0.000000.epoch: numepochs = 35 , Took = 6 seconds; Full-batch train mse = 0.010442, val mse = 0.000000.epoch: numepochs = 36 , Took = 6 seconds; Full-batch train mse = 0.056686, val mse = 0.000000.epoch: numepochs = 37 , Took = 6 seconds; Full-batch train mse = 0.054850, val mse = 0.000000.epoch: numepochs = 38 , Took = 6 seconds; Full-batch train mse = 0.019422, val mse = 0.000000.epoch: numepochs = 39 , Took = 6 seconds; Full-batch train mse = 0.016443, val mse = 0.000000.epoch: numepochs = 40 , Took = 6 seconds; Full-batch train mse = 0.010289, val mse = 0.000000.epoch: numepochs = 41 , Took = 7 seconds; Full-batch train mse = 0.022615, val mse = 0.000000.epoch: numepochs = 42 , Took = 6 seconds; Full-batch train mse = 0.010723, val mse = 0.000000.epoch: numepochs = 43 , Took = 6 seconds; Full-batch train mse = 0.010289, val mse = 0.000000.epoch: numepochs = 44 , Took = 6 seconds; Full-batch train mse = 0.033933, val mse = 0.000000.epoch: numepochs = 45 , Took = 7 seconds; Full-batch train mse = 0.030156, val mse = 0.000000.epoch: numepochs = 46 , Took = 7 seconds; Full-batch train mse = 0.022068, val mse = 0.000000.epoch: numepochs = 47 , Took = 7 seconds; Full-batch train mse = 0.029382, val mse = 0.000000.epoch: numepochs = 48 , Took = 6 seconds; Full-batch train mse = 0.021275, val mse = 0.000000.epoch: numepochs = 49 , Took = 6 seconds; Full-batch train mse = 0.039427, val mse = 0.000000.epoch: numepochs = 50 , Took = 7 seconds; Full-batch train mse = 0.016674, val mse = 0.000000.NNerror = 0.016674267332022572Prediction ResultValue Prediction Error0.6048934040010798 0.19097551722554007 -0.413917886775539760.5917463309959767 0.35726681238891195 -0.234479518607064790.5798180746808277 0.19232727566724744 -0.387490799013580240.39808885303777447 0.1926440400752866 -0.205444812962487870.4140924247674261 0.19529777426853168 -0.21879465049889440.08847408598189055 0.19110126347316514 0.102627177491274590.3583460134199821 0.21170344602417424 -0.14664256739580790.29635258460747904 0.3549086780038481 0.058556093396369080.21947238532147648 0.19156569159762857 -0.027906693723847910.5357166982629155 0.36018248221537214 -0.175534216047543320.5547810234563126 0.1912501730851674 -0.363530850371145240.40529948654006304 0.21826323152039923 -0.18703625501966380.4765320387665492 0.34409113646061484 -0.132440902305934360.05759629179315594 0.1914373047341408 0.133841012940984880.25415182638221206 0.29169483353745973 0.0375430071552476650.2731217394258585 0.19452719525740314 -0.078594544168455350.021103715077802527 0.19131792203441428 0.170214206956611740.24098254783013137 0.334302879677641 0.093320331847509620.6300811731076671 0.3595001582783692 -0.27058101482929790.41827613603130404 0.195477735057971 -0.222798400973333030.2526404805902617 0.1945578268820965 -0.058082653708165180.16619916368077442 0.191265206532793 0.0250660428520185770.007724491831775392 0.1909446242319318 0.18322013240015640.08926696720959378 0.19197139383958237 0.102704426629988590.4822857005955674 0.19244393418394434 -0.289841766411623070.12166559083216193 0.19242076231047756 0.070755171478315630.2883494676971952 0.30939742289582284 0.021047955198627620.38817298742061984 0.1909921814285587 -0.197180805992061140.34588396966368695 0.1957690915303307 -0.150114878133356250.19958641570784796 0.19348928314854685 -0.00609713255930111050.31340425691874024 0.19828489007869293 -0.115119366840047310.31775749422734 0.19211592601952254 -0.125641568207817470.48789392695999645 0.19120722177454247 -0.2966867051854540.4359840834351843 0.3604340050247724 -0.075550078410411890.17359981155470314 0.1914334455263964 0.017833633971693270.3629355770221922 0.2004476969345776 -0.16248788008761460.4627621372503198 0.2111988404691097 -0.25156329678121010.49652077030838826 0.19101585452942166 -0.30550491577896660.12618599928245963 0.19939585850613975 0.073209859223680120.45276204270081455 0.1924159942977412 -0.260346048403073350.2837721853443281 0.2016124468403725 -0.082159738503955580.34590164213713354 0.3601210376231753 0.0142193954860417860.1961497656762427 0.19408639222665872 -0.00206337344958398840.22135763175909048 0.27616370537642354 0.0548060736173330560.43356473411523927 0.19150317510575426 -0.2420615590094850.09566706862199378 0.19087327269062435 0.095206204068630560.29830626566849494 0.19959705355592236 -0.098709212112572580.3070532379895792 0.34322116560057725 0.0361679276109980740.07052673330364767 0.19118739087384276 0.120660657570195090.5501181200918814 0.2024015375945202 -0.347716582497361260.31894277127298554 0.1917670097886867 -0.127175761484298850.08585450906008718 0.20848620726607436 0.122631698205987180.20245657700014166 0.19218060734066275 -0.0102759696594789120.1712767340967007 0.1913375355437103 0.0200608014470096130.3779192242827297 0.2035011707996587 -0.174418053483071020.241909871430447 0.19089783315658176 -0.0510120382738652460.40578032667620945 0.3561807946562045 -0.0495995320200049440.20834390560196567 0.19103138812628986 -0.0173125174756758040.49675932490421343 0.1915234454414188 -0.30523587946279460.2342257039800733 0.1920213029433058 -0.042204401036767510.18045883957051312 0.20420037376704497 0.0237415341965318550.2309607430153665 0.1912620988835584 -0.03969864413180810.40644947116571745 0.19173032204451546 -0.2147191491212020.11691561072493983 0.19280159115148832 0.075885980426548480.05696889589626215 0.19083593927270395 0.133867043376441790.47164532559761124 0.2506614607550888 -0.220983864842522420.6208470748110626 0.35822718159638256 -0.262619893214680040.46559040490785325 0.2083058633813562 -0.257284541526497050.5052214973114583 0.19867901868911944 -0.306542478622338850.4127229537166962 0.35982142534462497 -0.052901528372071240.16960925650784137 0.19135483819811452 0.0217455816902731580.19722393334464125 0.19080547758699506 -0.0064184557576461850.4335762052660574 0.20920751654239156 -0.224368688723665830.1496556423910719 0.19090570957335065 0.041250067182278750.3015215343928844 0.1922591754560472 -0.109262358936837220.0 0.19143943303505245 0.191439433035052450.36555981464056164 0.19189800228180368 -0.173661812358757970.3963164889187304 0.19451555510717428 -0.201800933811556120.313325868748335 0.19168776655589245 -0.121638102192442560.5034713123520999 0.3339326133308013 -0.169538699021298530.4224576693623929 0.3539965263782299 -0.068461142984162950.08523050351506854 0.19132247714662606 0.106091973631557520.26080914691197654 0.19095418139777426 -0.069854965514202280.1324640982588358 0.19304336020222349 0.06057926194338770.13055674031551295 0.19224589387242375 0.061689153556910790.23625412018106318 0.1917614371123628 -0.0444926830687003840.5019570376831385 0.3081554524341633 -0.193801585248975170.030390738837917763 0.19083521852879112 0.160444479690873360.34274552561551896 0.19120112478612986 -0.15154440082938910.4514974655646171 0.1916124319598441 -0.2598850336047730.531777023034474 0.3515396924867077 -0.180237330547766360.367772718094668 0.3317275143536775 -0.036045203740990520.41600472261866916 0.22278029398575255 -0.19322442863291660.36506543552315474 0.325628070833062 -0.0394373646900927350.314008782918081 0.32408907795815034 0.0100802950400693540.2925887989109779 0.1921158349811155 -0.100472963929862380.4658619691058588 0.2146831464338164 -0.25117882267204240.2280242270958607 0.19158705334902099 -0.036437173746839720.5003581077100195 0.19149431703681175 -0.30886379067320780.4448442553362914 0.19086228548828346 -0.2539819698480079Weight of Layer 11.3741710823232989 1.0997962988037757 -2.3077515870713716 2.0946962013291297 2.24588083756021 0.7186952475525394 -1.1885813301306254 0.25046447165487246 -1.253986920617667 1.535570764339994 0.1440090623878452 1.2110656874633237 -0.23784821158321864 -0.5133767761738681 0.5355594752965599 -0.9862762256909807 2.234245108441277 -0.5216923380767392 2.0496153507146033 -0.9000455162282417 1.3406201642695788 2.1185256789014897 1.038387978643167 -0.011886136436036997 2.4017180810229086 0.5342060426581219 2.188686239727936 -0.604587031465719 0.061697537675081446 -0.48429030459304306 -1.234468451038262 0.7790398934631602 -0.22067594788975725 -2.0414139797176176 -0.9324514648411226 0.798505045375407 0.843464180836847 1.8612698144445792 2.290144904438349 1.2291878648431667 2.3639566790099784 -2.1175568466779437 2.1488480623696975 2.253851655104785 -1.879142801282798 -0.23011616258273254 2.4342506675413413 -2.184430097374211 1.3446335417651347 0.39411399422872706 -1.4588967794444714 2.6567285233270366 -0.8576819932211762 -1.9914472547514181 1.4277752508742856 0.6379599194760166 -0.3783031968398195 1.4158689111045317 1.5318358789872808 -1.201612551759085 Weight of Layer 2-1.264966034912716 2.045363428231917 0.39087016834115496 1.0930481252787911 -1.571245354275874 -0.9655062462170442 2.1709800176902982 -1.025175316866544 -1.5230797088149843 1.769571487127593 0.2347823358786302 -0.7297761283100554 -0.7576138927387723 -0.16523415352888424 -1.8516805610014189 1.3715533800487367 1.95737270209438 0.08246852496952446 1.0190398538209786 0.38679398113645574 0.529334650423367 0.43356573369591683 -1.494114816211369 0.47441528091212 -0.4329092188524354 1.8318597886945986 1.7458297556728688 -2.0957897682487707 -0.12195567981037991 0.0378548041005975 -0.6616871154791367 -1.2988919749370011 -2.0146727073983346 -2.0369675326219587 -0.6502946004953208 -0.5031500283188425 1.2033687522496184 -0.35900710238718897 -1.213965816985491 -0.6247306519040674 -1.172636102729738 0.1492977187034359 0.7805087252939967 0.42756349073372346 1.9444610499195103 -1.684949676049153 -2.214370792742285 1.4529568002779754 -0.817314868362314 -2.0437576009396534 1.414190131329268 0.8002930022447152 0.5103985267247684 1.072725074367445 0.7728306875824079 1.3280098832755556 -0.5723175992914568 1.8965322712004982 1.9131475857947766 0.7116308703102919 -1.1337078046228692 1.4624037563264591 -1.2661436485440505 0.2074359557718086 1.7605365810734208 0.5503309132836761 -0.12889849968368497 -1.5813673816630978 0.3179522409763945 -1.4093501587164268 0.37747278027064335 2.0973248562810287 1.3796729017078182 -1.32247724141541 0.05176617793309023 0.2797968400006565 0.2649190482622152 0.3553074482253876 -1.236624823614366 -1.7608721088406603 1.0024974314351445 -2.174840973945128 -0.6578975450189226 2.301788638015837 1.1479110741419556 -0.3844810208733819 -1.757161551068665 0.005888873948249745 1.0889152043326655 -0.4907523692459491 -1.5314215158890179 -2.068119203282905 -0.6966652421295678 1.7172836960101752 -1.030902225947676 1.7894526684520087 1.5213695041770878 -2.0310793395869613 -0.23638299504893515 -0.9900330517352804 -1.0052522373970076 -0.25640336055482327 0.5747216493939299 -0.6727702236294272 -0.0968976241335074 1.828632192751469 -1.2027447051840479 1.462449341909922 1.866886724932346 0.337038328583328 Weight of Layer 31.836452591890687 -1.1016514469136454 1.9551193591759655 -1.5732459452330396 -1.1800834414335224 -1.1923893040285825 0.06312897816177482 1.457981772832194 1.7288840730921886 1.0295473067747805 -0.6835578234742354 -1.281488825782123 1.9855453373804615 -0.21337154884305315 -0.8204219180246067 -0.8260103421573441 -1.3974890573670238 -0.18789338539658415 1.5852967650612315 -0.9475186470859063 -1.0100358806860719 1.0069697324461917 0.7336707009234793 -0.8190101361063539 -1.9821987263863545 -2.0789438096783956 -1.1812929830305807 -0.12007384037833814 -1.8876632918570322 -0.8968914717818263 1.3471019678011835 -0.152196929664138 -0.9273968120578239 -0.5427506117781439 -1.6379161635634556 1.6603536697042776 -0.2826332939784261 -1.7089295991871511 -0.3086776080327076 -0.838637438570992 0.45911079203796323 0.26754055606009786 -1.8482009521236713 -0.23130366979329475 -0.37585662596248814 0.4900765346436331 0.6860109049091877 -0.9572551404136589 0.30380993421860114 -1.73380834254428 -0.9187544507012596 -2.143513804630084 1.9614638862521159 0.513675117374747 1.7364284348955028 1.4300160181482728 -0.028644837063659466 0.9434705098905873 -1.256117787020064 -2.286119449246773 0.8392807137479158 1.0463524997789728 0.22524746294136241 -2.065346398428731 -1.3984782782329925 0.8064849904915904 -0.020036943079112954 1.3571828713761132 1.8168106691174883 1.1732287314521193 -1.1216050426635968 -0.7992471983374778 1.4737000544885857 -1.2629467521609772 -2.166720398969067 -0.13444189253030867 -0.06990910534870051 -1.1475378284991893 0.7939976065553747 -0.6034315465733754 1.2609824176884306 -1.0556544940783124 -1.2600392532679041 0.20515032057156965 -0.9368115470081553 1.8486189613353239 -1.748953620555969 0.5962310435917523 -1.6677307685118707 1.6475809798433472 0.8635630357973535 -1.794106867032129 0.23576724690928239 1.9345586718254242 1.8665220736111652 1.715231095424259 1.4448153663136947 1.4585220061056003 -2.097657471713302 0.8605510379359859 0.48221398085417627 1.5176826373865975 1.4652552486449435 1.9094578768378816 1.1144707218150902 0.4891850304975143 -1.6217012198757983 -0.26648664353939455 -0.702859436768092 1.0351022938433367 Weight of Layer 4-0.911096181634767 1.393613461284606 -0.9330396913369214 1.2364172665419595 0.6539246160388238 -0.3497594712315348 -0.5272926339150141 1.0073562856426537 -0.7754136627565675 0.3978221698601255 0.6516969484538829 -2.1313935565863322 0.6870222803829747 -0.14063545929924332 -1.4601798330750633 -0.5046337368523596 0.45490880803140493 -0.3469665791558201 -1.1242340473155688 -1.2723993607026778 0.7754297084802044 -0.1971882092105515 1.268461391063688 1.433232422744769 -1.9734642121928314 -2.1500226866603094 1.69187327087415 -0.5342565995220732 -1.8236939987229444 -0.9248308295424809 -1.0585137171567485 -0.758573013381397 -1.4786474341672335 -1.3004208980147893 -1.4206386974340788 -1.83226719079787 1.853287649173723 -1.5346566916523345 0.18937676571029147 -2.14876104739136 0.19300765463829608 2.2600431704632133 -0.7439149441396848 -0.7944037931661944 -1.5998484896496197 -1.6524100951400051 1.5947517659570918 -1.8662327423253926 1.2338013894973758 -0.4884517327249603 -1.933617967710128 -0.16207327398832927 -0.257515806279318 0.8147979296307275 1.3995976816521387 2.094656544970861 -0.9941271469702547 1.6445550567163796 -1.8006734384410419 -1.639945317843356 -0.04008156577686328 -1.5983003403214098 -0.5203002571128433 1.7875581773282712 -1.094555900585581 1.2068765635018603 2.1254252250165493 -0.32295734337741594 -1.3909813447797978 -1.7675398403329456 1.6196489153696365 -0.11330208718956442 1.2249494342821745 -0.9623282852038381 0.5949871990921731 -0.4589253834864904 -1.4480879152384845 0.41124565810833846 1.8266387733496516 -1.3444906678350586 -1.8466017258629779 -1.2710822759712612 -2.3672244544192775 0.07985138355524748 1.1928505759997003 0.1224150977985233 1.581079240096574 -1.800780284328034 -1.7595274297258634 1.2703227203108252 -0.01664878904783711 -1.9795940886734285 -0.020392614773247077 -1.4314141516158432 -1.365137154825855 1.7302923882870662 1.9823859978980145 0.35232814451148275 0.7343215278791788 1.394419951767305 1.2499547753082167 -1.549641575886935 1.848772251833023 0.7361855983730334 0.6310928126046181 -0.8813463668969193 0.004308048034432659 0.43321638933450207 0.8087966273251945 0.07110982269880414 Weight of Layer 50.03585680860332078 0.6094562888567525 1.7968463081634347 -2.362627715032082 2.2247821225164652 -1.0784288939947677 -1.0554498524378448 0.5861411371363056 -1.3689382763820177 -1.6272403702710627 -1.6503549168843508 1.6301987233118784 -0.8906914047579433 0.24243168770601023 0.4009515829010596 -1.0758568810272509 -0.9051235220484805 -2.2014662058001826 -0.6016562255004753 -1.54618907737507 0.3068858681819345 -0.1910939351954038 0.3949377293208745 -0.7652271919004981 0.68090033725971 1.2348269143656605 2.197797374061151 0.7456474083783481 2.177221715481275 0.577448303135589 0.6713302440403498 -1.422241156275792 0.3923309252775803 2.016732930847877 0.9072966194060744 -1.173786606850799 0.762874680679405 0.5785929523331224 -0.2517270024395546 2.0525009570621475 1.3299906196120428 -0.3016789963343337 1.6433222480576049 1.4658027315448252 -0.7093708542273217 -0.363654080609567 0.14670807608588535 1.2229445344521144 2.0365363421196743 -0.025435674952313806 1.1537986276254326 -1.2324297702242806 0.7761473466711113 0.8799485068219668 -0.5873930067918902 0.3139747558740749 -1.6573144697633098 0.7038102951541025 -1.408818539999227 2.097157257533922 -0.7036366036514073 0.4160486916023455 0.8262172799352652 -1.4795358417499833 0.2852056896956041 -1.542169273346858 -1.3692080951184145 -0.18564381183893783 1.4773933766691916 1.566187371091047 2.2303361972935196 1.6867117590655034 -2.2562477027382437 -0.7074433661402227 0.31697668962943404 -0.7387985710568243 -1.1533917617505614 -1.2255743400186403 -1.0127411060516087 -1.3756205847124954 1.930937272879095 0.5512007768312437 -1.8860525843110458 1.83432047092595 1.7499230942835498 -0.05470238124314854 0.1415405841710963 0.5347734456158572 0.8685622790833061 1.0117880568953437 -1.0680283034993974 -0.6423950104042628 2.0957313900176207 -0.3292735667051877 0.4115339082100468 0.2448817017887727 -0.36690487429065827 1.0946609803320706 -1.2972731428065445 0.929738769296319 -0.8483315095032794 0.9886368647914796 -1.1490945738647198 0.48817906098502184 1.201937687948849 -1.8405795878382836 1.6127096671527423 -2.0480015245423417 -0.9757299992342688 0.5211781810863436 Weight of Layer 6-1.1548299180301753 -1.6001306147116388 -2.387282014077577 -1.082677370520492 -0.013943138965433734 0.10533899958501511 0.5742412321742517 -1.5014155245560539 0.8057997937824102 1.8479652037781695 -0.23508934192649694