紧急情况：矩阵的维度为零

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我运行代码来训练神经网络，并收到警告，矩阵长度为零，我不知道会发生什么，因为我在神经网络的输出变量中使用该零矩阵。

package main

import (
    "errors"
    "fmt"
    "log"
    "math"
    "math/rand"
    "time"

    "gonum.org/v1/gonum/floats"
    "gonum.org/v1/gonum/mat"
)

// sumAlongAxis sums a matrix along a
// particular dimension, preserving the
// other dimension.
func sumAlongAxis(axis int, m *mat.Dense) (*mat.Dense, error) {

    numRows, numCols := m.Dims()

    var output *mat.Dense

    switch axis {
    case 0:
        data := make([]float64, numCols)
        for i := 0; i < numCols; i++ {
            col := mat.Col(nil, i, m)
            data[i] = floats.Sum(col)
        }
        output = mat.NewDense(1, numCols, data)
    case 1:
        data := make([]float64, numRows)
        for i := 0; i < numRows; i++ {
            row := mat.Row(nil, i, m)
            data[i] = floats.Sum(row)
        }
        output = mat.NewDense(numRows, 1, data)
    default:
        return nil, errors.New("invalid axis, must be 0 or 1")
    }

    return output, nil
}

// sigmoid implements the sigmoid function
// for use in activation functions.
func sigmoid(x float64) float64 {
    return 1.0 / (1.0 + math.Exp(-x))
}

// sigmoidPrime implements the derivative
// of the sigmoid function for backpropagation.
func sigmoidPrime(x float64) float64 {
    return x * (1.0 - x)
}

// neuralNet contains all of the information
// that defines a trained neural network.
type neuralNet struct {
    config  neuralNetConfig
    wHidden *mat.Dense
    bHidden *mat.Dense
    wOut    *mat.Dense
    bOut    *mat.Dense
}

// neuralNetConfig defines our neural network
// architecture and learning parameters.
type neuralNetConfig struct {
    inputNeurons  int
    outputNeurons int
    hiddenNeurons int
    numEpochs     int
    learningRate  float64
}

// NewNetwork initializes a new neural network.
func newNetwork(config neuralNetConfig) *neuralNet {
    return &neuralNet{config: config}
}

// Train trains a neural network using backpropagation.
func (nn *neuralNet) train(x, y *mat.Dense) error {
    // Initialize biases/weights.
    randSource := rand.NewSource(time.Now().UnixNano())
    randGen := rand.New(randSource)

    wHiddenRaw := make([]float64, nn.config.hiddenNeurons*nn.config.inputNeurons)
    bHiddenRaw := make([]float64, nn.config.hiddenNeurons)
    wOutRaw := make([]float64, nn.config.outputNeurons*nn.config.hiddenNeurons)
    bOutRaw := make([]float64, nn.config.outputNeurons)

    for _, param := range [][]float64{wHiddenRaw, bHiddenRaw, wOutRaw, bOutRaw} {
        for i := range param {
            param[i] = randGen.Float64()
        }
    }

    wHidden := mat.NewDense(nn.config.inputNeurons, nn.config.hiddenNeurons, wHiddenRaw)
    bHidden := mat.NewDense(1, nn.config.hiddenNeurons, bHiddenRaw)
    wOut := mat.NewDense(nn.config.hiddenNeurons, nn.config.outputNeurons, wOutRaw)
    bOut := mat.NewDense(1, nn.config.outputNeurons, bOutRaw)

    // Define the output of the neural network.
    output := mat.NewDense(0, 0, nil)

    // Loop over the number of epochs utilizing
    // backpropagation to train our model.
    for i := 0; i < nn.config.numEpochs; i++ {

        // Complete the feed forward process.
        hiddenLayerInput := mat.NewDense(0, 0, nil)
        hiddenLayerInput.Mul(x, wHidden)
        addBHidden := func(_, col int, v float64) float64 { return v + bHidden.At(0, col) }
        hiddenLayerInput.Apply(addBHidden, hiddenLayerInput)

        hiddenLayerActivations := mat.NewDense(0, 0, nil)
        applySigmoid := func(_, _ int, v float64) float64 { return sigmoid(v) }
        hiddenLayerActivations.Apply(applySigmoid, hiddenLayerInput)

        outputLayerInput := mat.NewDense(0, 0, nil)
        outputLayerInput.Mul(hiddenLayerActivations, wOut)
        addBOut := func(_, col int, v float64) float64 { return v + bOut.At(0, col) }
        outputLayerInput.Apply(addBOut, outputLayerInput)
        output.Apply(applySigmoid, outputLayerInput)

        // Complete the backpropagation.
        networkError := mat.NewDense(0, 0, nil)
        networkError.Sub(y, output)

        slopeOutputLayer := mat.NewDense(0, 0, nil)
        applySigmoidPrime := func(_, _ int, v float64) float64 { return sigmoidPrime(v) }
        slopeOutputLayer.Apply(applySigmoidPrime, output)
        slopeHiddenLayer := mat.NewDense(0, 0, nil)
        slopeHiddenLayer.Apply(applySigmoidPrime, hiddenLayerActivations)

        dOutput := mat.NewDense(0, 0, nil)
        dOutput.MulElem(networkError, slopeOutputLayer)
        errorAtHiddenLayer := mat.NewDense(0, 0, nil)
        errorAtHiddenLayer.Mul(dOutput, wOut.T())

        dHiddenLayer := mat.NewDense(0, 0, nil)
        dHiddenLayer.MulElem(errorAtHiddenLayer, slopeHiddenLayer)

        // Adjust the parameters.
        wOutAdj := mat.NewDense(0, 0, nil)
        wOutAdj.Mul(hiddenLayerActivations.T(), dOutput)
        wOutAdj.Scale(nn.config.learningRate, wOutAdj)
        wOut.Add(wOut, wOutAdj)

        bOutAdj, err := sumAlongAxis(0, dOutput)
        if err != nil {
            return err
        }
        bOutAdj.Scale(nn.config.learningRate, bOutAdj)
        bOut.Add(bOut, bOutAdj)

        wHiddenAdj := mat.NewDense(0, 0, nil)
        wHiddenAdj.Mul(x.T(), dHiddenLayer)
        wHiddenAdj.Scale(nn.config.learningRate, wHiddenAdj)
        wHidden.Add(wHidden, wHiddenAdj)

        bHiddenAdj, err := sumAlongAxis(0, dHiddenLayer)
        if err != nil {
            return err
        }
        bHiddenAdj.Scale(nn.config.learningRate, bHiddenAdj)
        bHidden.Add(bHidden, bHiddenAdj)
    }

    nn.wHidden = wHidden
    nn.bHidden = bHidden
    nn.wOut = wOut
    nn.bOut = bOut

    return nil

}

func main() {
    // Define our input attributes.
    input := mat.NewDense(3, 4, []float64{
        1.0, 0.0, 1.0, 0.0,
        1.0, 0.0, 1.0, 1.0,
        0.0, 1.0, 0.0, 1.0,
    })

    // Define our labels.
    labels := mat.NewDense(3, 1, []float64{1.0, 1.0, 0.0})

    // Define our network architecture and
    // learning parameters.
    config := neuralNetConfig{
        inputNeurons:  4,
        outputNeurons: 1,
        hiddenNeurons: 3,
        numEpochs:     5000,
        learningRate:  0.3,
    }

    // Train the neural network.
    network := newNetwork(config)
    if err := network.train(input, labels); err != nil {
        log.Fatal(err)
    }

    // Output the weights that define our network!
    f := mat.Formatted(network.wHidden, mat.Prefix(" "))
    fmt.Printf("\nwHidden = % v\n\n", f)

    f = mat.Formatted(network.bHidden, mat.Prefix(" "))
    fmt.Printf("\nbHidden = % v\n\n", f)

    f = mat.Formatted(network.wOut, mat.Prefix(" "))
    fmt.Printf("\nwOut = % v\n\n", f)

    f = mat.Formatted(network.bOut, mat.Prefix(" "))
    fmt.Printf("\nbOut = % v\n\n", f)
}

正确答案

来自 mat 软件包的 documentation：

因此，当您使用 r 和 c 零调用 mat.NewDense(0, 0, nil) 时，正如您在上面的源代码中多次执行的那样，代码会出现恐慌，正如其文档所述。没有什么意外。

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