我一直在研究CNTK，并决定创建一个模型来实现异或函数，以确保我掌握了基础知识。我创建了下面的文件，但由于模型表现非常差，我猜我遗漏了一些基本的东西。

command = Train:Output:DumpNodeInfomodelPath = "Models\xor.dnn"deviceId = -1makeMode = falsefeatureDimension = 2labelDimension = 1Train = [    action = "train"    BrainScriptNetworkBuilder = {        FDim = $featureDimension$        LDim = $labelDimension$        features = Input {FDim}        labels = Input {LDim}        W0 = ParameterTensor {(FDim:FDim)} ; b0 = ParameterTensor {FDim}        W1 = ParameterTensor {(LDim:FDim)} ; b1 = ParameterTensor {LDim}        o1 = W0*features + b0        z = Sigmoid (W1*o1 + b1)        ce = SquareError (labels, z)        errs = ClassificationError (labels, z)        # root nodes        featureNodes    = (features)        labelNodes      = (labels)        criterionNodes  = (ce)        evaluationNodes = (errs)        outputNodes     = (z)    }    SGD = [        epochSize = 0        minibatchSize = 1        learningRatesPerSample = 0.4        maxEpochs = 50    ]    reader=[        readerType="CNTKTextFormatReader"        file="Train_xor.txt"                input = [            features = [                dim = $featureDimension$                alias = X                format = "dense"            ]            labels = [                dim = $labelDimension$                alias = y                format = "dense"            ]        ]    ]]Output = [    action="write"    reader=[        readerType="CNTKTextFormatReader"        file="Train_xor.txt"                input = [            features = [                dim = $featureDimension$                alias = X                format = "dense"            ]            labels = [                dim = $labelDimension$                alias = y                format = "dense"            ]        ]    ]    outputNodeNames = z    outputPath = "Output\xor.txt"]DumpNodeInfo = [    action = "dumpNode"    printValues = true]

输入文件看起来像这样

|y 0 |X 0 0|y 1 |X 1 0|y 1 |X 0 1|y 0 |X 1 1

我得到的输出是

0.4901560.4900920.4899840.489920

如果有帮助的话，节点转储看起来如下

b0=LearnableParameter [2,1]   learningRateMultiplier=1.000000  NeedsGradient=true  -0.00745151564  0.0358283482  #################################################################### b1=LearnableParameter [1,1]   learningRateMultiplier=1.000000  NeedsGradient=true  -0.0403601788  #################################################################### ce=SquareError ( labels , z ) errs=ClassificationError ( labels , z ) features=InputValue [ 2 ] labels=InputValue [ 1 ] o1=Plus ( o1.PlusArgs[0] , b0 ) o1.PlusArgs[0]=Times ( W0 , features ) W0=LearnableParameter [2,2]   learningRateMultiplier=1.000000  NeedsGradient=true  -0.0214280766 0.0442263819  -0.0401388146 0.0261882655  #################################################################### W1=LearnableParameter [1,2]   learningRateMultiplier=1.000000  NeedsGradient=true  -0.0281925034 0.0214234442  #################################################################### z=Sigmoid ( z._ ) z._=Plus ( z._.PlusArgs[0] , b1 ) z._.PlusArgs[0]=Times ( W1 , o1 )

回答：

你的隐藏单元中肯定需要一些非线性，比如 o1 = Tanh(W0*features + b0)。一般来说，通过SGD学习异或函数时使用两个隐藏单元是比较棘手的：有很多随机初始化可能会导致发散。如果你有三个或更多的隐藏单元，学习会变得容易得多。