我在尝试用C#实现一个反向传播神经网络时遇到了一个问题。在训练网络时，所有的输出要么是0.49…，要么是0.51…

这是我的网络类

namespace BackPropNetwork{public class Network {    public double[][] Values { get; set; }    public double[][] Deltas { get; set; }    public double[][][] Weights { get; set; }    public Network(params int[] size)    {        Values = new double[size.Length][];        Weights = new double[size.Length][][];        Deltas = new double[size.Length][];        Random r = new Random();        for(int i = 0; i < size.Length; i++)        {            Values[i] = new double[size[i]];            Weights[i] = new double[size[i]][];            Deltas[i] = new double[size[i]];            if (i != size.Length - 1) {                for (int j = 0; j < size[i]; j++)                {                    Weights[i][j] = new double[size[i + 1]];                    for(int k= 0; k < size[i + 1]; k++)                    {                        Weights[i][j][k] = r.NextDouble() ;                    }                }            }        }    }    public double[] FeedThrough (double[] input)    {        if(input.Length!= Values[0].Length)        {            throw new InvalidOperationException();        }        Values[0] = input;        for(int i = 0; i < Values.Length-1; i++)        {            for(int j = 0; j < Values[i + 1].Length; j++)            {                Values[i + 1][j] = Sigmoid(GetPassValue(i, j),false);            }        }        return Values[Values.Length - 1];    }    double GetPassValue(int layer,int neuron)    {        double sum = 0;        for(int i = 0; i < Values[layer].Length; i++)        {            sum += Values[layer][i] * Weights[layer][i][neuron];        }        return sum;    }    public double Sigmoid(double d, bool dir)    {        if (dir)        {            return d * (1 - d);        }else        {            return 1 / (1 + Math.Exp(d));        }    }    public void CorrectError(double[] error)    {        for(int i = Values.Length - 1; i >= 0; i--)        {            if (i !=Values.Length - 1)            {                error = new double[Values[i].Length];                for(int j = 0; j < Values[i].Length; j++)                {                    error[j] = 0;                    for(int k = 0; k < Values[i + 1].Length; k++)                    {                        error[j] += Weights[i][j][k] * Deltas[i + 1][k];                    }                }                }            for(int j = 0; j < Values[i].Length; j++)            {                Deltas[i][j] = error[j] * Sigmoid(Values[i][j],true);            }        }    }    public void ApplyCorrection(double rate)    {        for(int i = 0; i < Values.Length-1; i++)        {            for(int j = 0; j < Values[i].Length; j++)            {                for(int k = 0; k < Values[i + 1].Length; k++)                {                    Weights[i][j][k] = rate * Deltas[i + 1][k] * Values[i][j];                }            }        }    }}

}

这是我的测试类：

namespace BackPropagationTest{class Program{    static void Main(string[] args)    {        Network n = new Network(3, 5, 5, 1);        double[][] input = new double[][] { new double[] { 1, 0, 1 }, new double[] { 1, 1, 1 }, new double[] { 0, 0, 0 }, new double[] {0, 1, 0 } };        double[][] output = new double[][] { new double[] { 0 },new double[] { 1 }, new double[] { 0 }, new double[] { 0 } };        for (int i = 0; i < 10; i++)        {            for(int j = 0; j < input.Length; j++)            {                var x = n.FeedThrough(input[j]);                double[] error = new double[output[0].Length];                for(int k= 0; k < x.Length; k++)                {                    error[k] = output[j][k] - x[k];                }                n.CorrectError(error);                n.ApplyCorrection(0.01);                for(int k = 0; k < x.Length; k++)                {                     Console.Write($"Expected: {output[j][k]} Got: {x[k]} ");                }                Console.WriteLine();            }            Console.WriteLine();        }    }}

}

这是我的输出：

Expected: 0 Got: 0.270673949003643Expected: 1 Got: 0.500116517554687Expected: 0 Got: 0.499609458404919Expected: 0 Got: 0.50039031963377Expected: 0 Got: 0.500390929619276Expected: 1 Got: 0.500390929999612Expected: 0 Got: 0.499609680732027Expected: 0 Got: 0.500390319841144Expected: 0 Got: 0.50039092961941Expected: 1 Got: 0.500390929999612Expected: 0 Got: 0.499609680732027Expected: 0 Got: 0.500390319841144Expected: 0 Got: 0.50039092961941Expected: 1 Got: 0.500390929999612Expected: 0 Got: 0.499609680732027Expected: 0 Got: 0.500390319841144

这种情况一直持续下去。

编辑1：

我在ApplyCorrection()函数中做了一个更改，将

 Weights[i][j][k] = rate * Deltas[i + 1][k] * Values[i][j];

替换为

 Weights[i][j][k] += rate * Deltas[i + 1][k] * Values[i][j];

现在权重似乎已经更新了，但对于这个实现的正确性我仍然存疑。也就是说，我仍然需要帮助 🙂

编辑2：

我之前没有对输出层的总误差进行求和，而是单独反向传播每个样本的误差。现在我已经这样做了，但输出结果仍然令人困惑：

我还将输出对从(0,1)改为(-1, 1)，试图使计算出的误差值更大。这是经过1000000个周期，学习率为0.1后的结果：

Expected: -1 Got: 0.999998429209274Expected: 1 Got: 0.999997843901661Expected: -1 Got: 0.687098308461306Expected: -1 Got: 0.788960893508226Expected: -1 Got: 0.999998429209274Expected: -1 Got: 0.863022549216158Expected: -1 Got: 0.788960893508226Expected: -1 Got: 0.999998474717769

回答：

尝试使用下面的代码，看看误差是否在减少还是保持不变。

public double Sigmoid(double d, bool dir){    if (dir)    {        return d * (1 - d);    }else    {        if (d < -45.0) return 0.0;        else if (d > 45.0) return 1.0;        else return 1.0 / (1.0 + Math.Exp(-d));    }}