//
// DigitImage.cs
//public static byte[] ByteArrayFromImage(Bitmap bmp){Rectangle rect = new Rectangle(0, 0, bmp.Width, bmp.Height);BitmapData data = bmp.LockBits(rect, ImageLockMode.ReadOnly, bmp.PixelFormat);IntPtr ptr = data.Scan0;int numBytes = data.Stride * bmp.Height;byte[] image_bytes = new byte[numBytes];System.Runtime.InteropServices.Marshal.Copy(ptr, image_bytes, 0, numBytes);bmp.UnlockBits(data);return image_bytes;}

从那里开始，信息被安排成结构，使其有可能随机访问训练和测试数据集的每个图像中的每个像素。每个原始图像都显示成网格排列的数千个数字。由于各个数字具有一致的尺寸，因此可以隔离每个数字并将其存储在DigitImage类的实例中。数字像素存储为字节数组列表，这些字节数组代表每个单独数字的扫描线。这是在DigitImages类库中完成的。

namespace digitImages
{public class DigitImage{public static int digitWidth = 28;public static int nTypes = 10;static Random random = new Random(DateTime.Now.Millisecond + DateTime.Now.Second);public static DigitImage[] trainingImages = new DigitImage[10];public static DigitImage[] testImages = new DigitImage[10];public Bitmap image = null;public byte[] imageBytes;List<byte[]> pixelRows = null;...public static void loadPixelRows(int Expected, bool testing){if (testing){byte[] imageBytes = DigitImage.testImages[Expected].imageBytes;Bitmap image = DigitImage.testImages[Expected].image;if (DigitImage.testImages[Expected].pixelRows == null){DigitImage.testImages[Expected].pixelRows = new List<byte[]>();for (int i = 0; i < image.Height; i++){int index = i * image.Width;byte[] rowBytes = new byte[image.Width];for (int w = 0; w < image.Width; w++){rowBytes[w] = imageBytes[index + w];}DigitImage.testImages[Expected].pixelRows.Add(rowBytes);}}}else{byte[] imageBytes = DigitImage.trainingImages[Expected].imageBytes;Bitmap image = DigitImage.trainingImages[Expected].image;if (DigitImage.trainingImages[Expected].pixelRows == null){DigitImage.trainingImages[Expected].pixelRows = new List<byte[]>();for (int i = 0; i < image.Height; i++){int index = i * image.Width;byte[] rowBytes = new byte[image.Width];for (int w = 0; w < image.Width; w++){rowBytes[w] = imageBytes[index + w];}DigitImage.trainingImages[Expected].pixelRows.Add(rowBytes);}}}}

主窗体

public class MyPanel : System.Windows.Forms.Panel{// non-flicker drawing panelpublic MyPanel(){this.SetStyle(System.Windows.Forms.ControlStyles.UserPaint |System.Windows.Forms.ControlStyles.AllPaintingInWmPaint |System.Windows.Forms.ControlStyles.OptimizedDoubleBuffer,true);}}

这是程序如何将784输入的灰度表示绘制为隐藏层权重，以及将10个隐藏层绘制为输出层权重的方式：

private void rangeOfHiddenWeights(out double MIN, out double MAX)
{List<double> all = new List<double>();for (int N = 0; N < NeuralNetFeedForward.hiddenLayer.nNeurons; N++){foreach (double d in NeuralNetFeedForward.hiddenLayer.neurons[N].weights){all.Add(d);}}all.Sort();MIN = all[0];MAX = all[all.Count - 1];
}private void drawWeights(Graphics ee, HiddenLayer hidLayer)
{int weightPixelWidth = 4;int W = (digitImages.DigitImage.digitWidth * (weightPixelWidth + 1));int H = (digitImages.DigitImage.digitWidth * (weightPixelWidth));int wid = H / 10;int yOffset = 0;int xOffset = 0;bool drawRanges = false;double mind = 0;double maxd = 0;rangeOfHiddenWeights(out mind, out maxd);double range = maxd - mind;Bitmap bmp = new Bitmap(W, H + wid);Graphics e = Graphics.FromImage(bmp);for (int N = 0; N < hidLayer.nNeurons; N++){double[] weights = hidLayer.neurons[N].weights;// draw hidden to output neuron weights for this hidden neurondouble maxout = double.MinValue; // max weight of last hidden layer to output layerdouble minout = double.MaxValue; // min weight of last hidden layer to output layerfor (int output = 0; output < NeuralNetFeedForward.outputLayer.nNeurons; output++){if (N < NeuralNetFeedForward.outputLayer.neurons[output].weights.Length){double Weight = NeuralNetFeedForward.outputLayer.neurons[output].weights[N];if (Weight > maxout){maxout = Weight;}if (Weight < minout){minout = Weight;}double Mind = NeuralNetFeedForward.outputLayer.neurons[output].weights.Min();double Maxd = NeuralNetFeedForward.outputLayer.neurons[output].weights.Max();double Range = Maxd - Mind;double R = ((Weight - Mind) * 255.0) / Range;int r = Math.Min(255, Math.Max(0, (int)R));Color color = Color.FromArgb(r, r, r);int X = (wid * output);int Y = H;e.FillRectangle(new SolidBrush(color), X, Y, wid, wid);}else{maxout = 0;minout = 0;}}// draw the input to hidden layer weights for this neuronfor (int column = 0; column < digitImages.DigitImage.digitWidth; column++){for (int row = 0; row < digitImages.DigitImage.digitWidth; row++){double weight = weights[(digitImages.DigitImage.digitWidth * row) + column];double R = ((weight - mind) * 255.0) / range;int r = Math.Min(255, Math.Max(0, (int)R));int x = column * weightPixelWidth;int y = row * weightPixelWidth;int r2 = r;if (hidLayer.neurons[N].isDropped){r2 = Math.Min(255, r + 50);}Color color = Color.FromArgb(r, r2, r);e.FillRectangle(new SolidBrush(color), x, y, weightPixelWidth, weightPixelWidth);}}xOffset += W;if (xOffset + W >= this.ClientRectangle.Width){xOffset = 0;yOffset += W;}ee.DrawImage(bmp, new Point(xOffset, yOffset));}
}

输入层

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;namespace NeuralNetFeedForward
{class InputLayer{public double[] inputs;public void setInputs(byte[] newInputs){inputs = new double[newInputs.Length];for (int i = 0; i < newInputs.Length; i++){// squash inputinputs[i] = (double)newInputs[i] / 255.0;}}}
}

隐藏层

class HiddenLayer{// public static int nNeurons = 15; // originalpublic int nNeurons = 30;public HiddenNeuron[] neurons;public NeuralNetFeedForward network;public HiddenLayer(int N, NeuralNetFeedForward NETWORK){network = NETWORK;nNeurons = N;neurons = new HiddenNeuron[nNeurons];for (int i = 0; i < neurons.Length; i++){neurons[i] = new HiddenNeuron(i, this);}}public void backPropagate(){foreach (HiddenNeuron n in neurons){n.backPropagate();}}public void activate(){foreach (HiddenNeuron n in neurons){n.activate();}}}
}

隐藏层神经元的类。为了清楚起见，省略了一些有关dropouts的实验代码。只有3个函数：activate，backPropagate和initWeights，它们将权重初始化为随机值。请注意，在向后传递时，必须根据该神经元对该错误的贡献来计算每个输出的误差。由于输出层权重在向后传递时发生变化，因此必须保存先前的正向传递权重并用于计算误差。这里的另一个难题是程序允许使用四个不同的激活功能。稍后再详细介绍。

class HiddenNeuron
{public int index = 0;public double ERROR = 0;public double[] weights = new double[digitImages.DigitImage.digitWidth * digitImages.DigitImage.digitWidth];public double[] oldWeights = new double[digitImages.DigitImage.digitWidth * digitImages.DigitImage.digitWidth];public double sum = 0.0;public double sigmoidOfSum = 0.0;public HiddenLayer layer;public HiddenNeuron(int INDEX, HiddenLayer LAYER){layer = LAYER;index = INDEX;initWeights();}public void initWeights(){weights = new double[digitImages.DigitImage.digitWidth * digitImages.DigitImage.digitWidth];for (int y = 0; y < weights.Length; y++){weights[y] = NeuralNetFeedForward.randomWeight();}}public void activate(){sum = 0.0;for (int y = 0; y < weights.Length; y++){sum += NeuralNetFeedForward.inputLayer.inputs[y] * weights[y];}sigmoidOfSum = squashFunctions.Utils.squash(sum);}public void backPropagate(){// see example:// https://web.archive.org/web/20150317210621/https://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdfdouble sumError = 0.0;foreach (OutputNeuron o in NeuralNetFeedForward.outputLayer.neurons){sumError += (o.ERROR* o.oldWeights[index]);}ERROR = squashFunctions.Utils.derivative(sigmoidOfSum) * sumError;for (int w = 0; w < weights.Length; w++){weights[w] += (ERROR * NeuralNetFeedForward.inputLayer.inputs[w]) * layer.network.learningRate;}}
}

输出层

class OutputLayer
{public NeuralNetFeedForward network;public HiddenLayer hiddenLayer;public int nNeurons = 10;public OutputNeuron[] neurons;public OutputLayer(HiddenLayer h, NeuralNetFeedForward NETWORK){network = NETWORK;hiddenLayer = h;neurons = new OutputNeuron[nNeurons];for (int i = 0; i < nNeurons; i++){neurons[i] = new OutputNeuron(this);}}public void activate(){foreach (OutputNeuron n in neurons){n.activate();}}public void backPropagate(){foreach (OutputNeuron n in neurons){n.backPropagate();}}
}class OutputNeuron
{public OutputLayer outputLayer;public double sum = 0.0;public double sigmoidOfSum = 0.0;public double ERROR = 0.0;public double [] weights;public double[] oldWeights;public double expectedValue = 0.0;public OutputNeuron(OutputLayer oL){outputLayer = oL;weights = new double[outputLayer.hiddenLayer.nNeurons];oldWeights = new double[outputLayer.hiddenLayer.nNeurons];initWeights();}public void activate(){sum = 0.0;for (int y = 0; y < weights.Length; y++){sum += outputLayer.hiddenLayer.neurons[y].sigmoidOfSum * weights[y];}sigmoidOfSum = squashFunctions.Utils.squash(sum);}public void calculateError(){ERROR = squashFunctions.Utils.derivative(sigmoidOfSum) * (expectedValue - sigmoidOfSum);}public void backPropagate(){// see example:// https://web.archive.org/web/20150317210621/https://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdfcalculateError();int i = 0;foreach (HiddenNeuron n in outputLayer.hiddenLayer.neurons){oldWeights[i] = weights[i]; // to be used for hidden layer back propagationweights[i] += (ERROR * n.sigmoidOfSum) * outputLayer.network.learningRate;i++;}}public void initWeights(){for (int y = 0; y < weights.Length; y++){weights[y] = NeuralNetFeedForward.randomWeight();}}}

class NeuralNetFeedForward
{// settingspublic enum ActivationType { SIGMOID, TANH, RELU, LEAKYRELU };public ActivationType activationType = ActivationType.LEAKYRELU;public double learningRate = 0.01;public List<inferenceError> errors = new List<inferenceError>();public static int expected;public static Random rand = new Random(DateTime.Now.Millisecond);public static InputLayer inputLayer;public static HiddenLayer hiddenLayer;public static OutputLayer outputLayer;public int nFirstHiddenLayerNeurons = 30;public void setExpected(int EXPECTED){expected = EXPECTED;for (int i = 0; i < NeuralNetFeedForward.outputLayer.neurons.Length; i++){if (i == EXPECTED){NeuralNetFeedForward.outputLayer.neurons[i].expectedValue = 1.0;}else{NeuralNetFeedForward.outputLayer.neurons[i].expectedValue = 0.0;}}}public void create(){inputLayer = new InputLayer();hiddenLayer = new HiddenLayer(nFirstHiddenLayerNeurons, this);outputLayer = new OutputLayer(hiddenLayer, this);}public NeuralNetFeedForward(int NNeurons){nFirstHiddenLayerNeurons = NNeurons;create();}public NeuralNetFeedForward(){create();}public static double dotProduct(double[] a, double[] b){double result = 0.0;for (int i = 0; i < a.Length; i++){result += a[i] * b[i];}return result;}public static double randomWeight(){double span = 50000;int spanInt = (int)span;double magnitude = 10.0;return ((double)(NeuralNetFeedForward.rand.Next(0, spanInt * 2) - spanInt)) / (span * magnitude);}public bool testInference(int EXPECTED, out int guessed, out double confidence){setExpected(EXPECTED);activate();guessed = answer(out confidence);return (guessed == EXPECTED);}public void train(int nIterations, int EXPECTED){setExpected(EXPECTED);for (int n = 0; n < nIterations; n++){activate();backPropagate();}}public void activate(){hiddenLayer.activate();outputLayer.activate();}public void backPropagate(){outputLayer.backPropagate();hiddenLayer.backPropagate();}public int answer(out double confidence){confidence = 0.0;double max = 0;int result = -1;for (int n = 0; n < NeuralNetFeedForward.outputLayer.nNeurons; n++){double s = NeuralNetFeedForward.outputLayer.neurons[n].sigmoidOfSum;if (s > max){confidence = s;result = n;max = s;}}return result;}
}

实用工具

public class Utils
{public enum ActivationType { SIGMOID, TANH, RELU, LEAKYRELU };public static ActivationType activationType = ActivationType.LEAKYRELU;public static double squash(double x){if (activationType == ActivationType.TANH){return hyTan(x);}else if (activationType == ActivationType.RELU){return Math.Max(x, 0);}else if (activationType == ActivationType.LEAKYRELU){if (x >= 0){return x;}else{return x * 0.15;}}else{return sigmoid(x);}}public static double derivative(double x){if (activationType == ActivationType.TANH){return derivativeOfTanHofX(x);}else if (activationType == ActivationType.RELU){return x > 0 ? 1 : 0;}else if (activationType == ActivationType.LEAKYRELU){return x >= 0 ? 1 : 0.15;}else{return derivativeOfSigmoidOfX(x);}}public static double sigmoid(double x){double s = 1.0 / (1.0 + Math.Exp(-x));return s;}public static double derivativeOfSigmoid(double x){double s = sigmoid(x);double sPrime = s * (1.0 - s);return sPrime;}public static double derivativeOfSigmoidOfX(double sigMoidOfX){double sPrime = sigMoidOfX * (1.0 - sigMoidOfX);return sPrime;}public static double hyTan(double x){double result = Math.Tanh(x);return result;}public static double derivativeOfTanH(double x){double h = hyTan(x);return derivativeOfTanHofX(h);}public static double derivativeOfTanHofX(double tanHofX){return 1.0 - (tanHofX * tanHofX);}public static double dotProduct(double[] a, double[] b){double result = 0.0;for (int i = 0; i < a.Length; i++){result += a[i] * b[i];}return result;}}

有待改进