神经网络/BP（反向传播）代码示例

#include <iostream>
#include <cstdlib>
#include <cmath>
#include <vector>
using namespace std;


const int NX = 784, NB = 500, NY = 10;//输入层X，隐藏层B，输出层Y节点数
const double eta = 0.06;//学习率

struct Node {
	double val{};
	double bias{};
	vector<double> weight;
} x[NX], b[NB], y[NY];//输入层X，隐藏层B，输出层Y
double g[NY], e[NB];//用于反向传播
double trainx[NX], trainy[NY];//训练数据



double sigmoid(double x) { return 1.0 / (1.0 + exp(-x)); }

double get_rand_weight() { return rand() % 10 / 5.0 - 1; } //生成(-1,1)随机数
double get_rand_bias() { return rand() % 10 / 500.0 - 0.01; } //生成(-0.01,0.01)随机数


//网络初始化
void init() {
	for (int i = 0; i < NX; i++) {
		//x[i].bias = get_rand_bias();
		for (int j = 0; j < NB; j++) {
			x[i].weight.push_back(get_rand_weight());
		}
	}
	for (int i = 0; i < NB; i++) {
		b[i].bias = get_rand_bias();
		for (int j = 0; j < NY; j++) {
			b[i].weight.push_back(get_rand_weight());
		}
	}
	for (int i = 0; i < NY; i++) {
		y[i].bias = get_rand_bias();
	}
};

//前向传播
void forward() {
	//首先需要清空隐藏层和输出层原有的非参数数据！！！
	for (int i = 0; i < NB; i++) b[i].val = 0;
	for (int i = 0; i < NY; i++) y[i].val = 0;
	//输入层读取数据
	for (int i = 0; i < NX; i++) x[i].val = trainx[i];
	//输入层->隐藏层
	for (int i = 0; i < NX; i++) {
		for (int j = 0; j < NB; j++) {
			b[j].val += x[i].val * x[i].weight[j];
		}
	}
	//隐藏层求值
	for (int i = 0; i < NB; i++) {
		b[i].val = sigmoid(b[i].val - b[i].bias);
	}
	//隐藏层->输出层
	for (int i = 0; i < NB; i++) {
		for (int j = 0; j < NY; j++) {
			y[j].val += b[i].val * b[i].weight[j];
		}
	}
	//输出层求值
	for (int i = 0; i < NY; i++) {
		y[i].val = sigmoid(y[i].val - y[i].bias);
	}
}

//反向传播
void back() {
	
	//计算g和e
	for (int i = 0; i < NY; i++) {
		g[i] = y[i].val * (1 - y[i].val) * (trainy[i] - y[i].val);
	}
	
	for (int i = 0; i < NB; i++) {
		double res = 0;
		for (int j = 0; j < NY; j++) {
			res += b[i].weight[j] * g[j];
		}
		e[i] = b[i].val * (1 - b[i].val) * res;
	}
	
	//更新w, theta, v, gamma
	for (int i = 0; i < NB; i++)
		for (int j = 0; j < NY; j++)
			b[i].weight[j] += eta * b[i].val * g[j];
	for (int i = 0; i < NY; i++)
		y[i].bias -= eta * g[i];
	for (int i = 0; i < NX; i++)
		for (int j = 0; j < NB; j++)
			x[i].weight[j] += eta * x[i].val * e[j];
	for (int i = 0; i < NB; i++)
		b[i].bias -= eta * e[i];
}


FILE *fImg, *fAns;
int result[1000000] = {0}; //每次训练的结果，正确为1，错误为0
void train(int Case) {
	//读入一张新的图片
	//除了前16字节，接下来的信息都是一张一张的图片
	//每张图片大小为28*28 = 784 = NX，每个char表示该像素对应的灰度，范围为0至255
	unsigned char img[NX], ans;
	fread(img, 1, NX, fImg);
	for (int i = 0; i < NX; i++) trainx[i] = (double)img[i] / 255.0;
	//读入该图片对应的答案
	//除了前8字节，第k个字节对应第k张图片的正确答案
	fread(&ans,1,1,fAns);
	for(int i = 0; i < NY; i++) trainy[i] = (i == ans) ? 1 : 0;
	
	//前向传播，计算答案是否正确
	forward();
	int res = 0;
	for (int i = 0; i <= 9; i++)
		if (y[i].val > y[res].val)
			res = i;
	result[Case] = (res == ans) ? 1 : 0;
	
	for (int i = 0; i < 28; i++) {
		for (int j = 0; j < 28; j++) {
			if (trainx[i * 28 + j] != 0) cout << 'X';
			else cout << ' ';
		}
		cout << endl;
	}
	cout << "Test Case #" << Case <<", result is " << res << ", answer is " << (int)ans << endl;
	
	
	//反向传播
	back();
	
	//输出最近100局的正确率
	int P = 100, cnt = 0;
	if(Case % P == 0) {
		for(int i = 0; i < P; i++)
			cnt += result[Case - i];
		cout << Case << " " << cnt << endl;
	}
}

int main() {
	fImg=fopen("train-images.idx3-ubyte","rb");
	fseek(fImg, 16, SEEK_SET);
	fAns=fopen("train-labels.idx1-ubyte","rb");
	fseek(fAns, 8, SEEK_SET);
	freopen("result.txt", "w", stdout);
	init();
	for (int Case = 1; Case <= 60000; Case++) {
		train(Case);
	}
	return 0;
}