Simple CNTK network output similar for all samples

Question

I've been looking in to CNTK and decided to create a create a model for an xor function to make sure I understood the basics. I created the files below but since the model does horribly bad I'm guessing I am missing something fundamental.

command = Train:Output:DumpNodeInfo

modelPath = "Models\xor.dnn"
deviceId = -1
makeMode = false
featureDimension = 2
labelDimension = 1

Train = [
    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
]

The input file looks like this

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

And I get this output

0.490156
0.490092
0.489984
0.489920

If it helps, the node dump looks like the following

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 )

Answer 1

You definitely need some nonlinearity in your hidden units such as o1 = Tanh(W0*features + b0) In general, learning xor with two hidden units via sgd is tricky: there are many random initializations that can lead to divergence. It becomes much more easy to learn if you have 3 or more hidden units.