这是史上最简单、清晰……
C++语言编写的 带正向传播、反向传播(Forward ……和Back Propagation）……任意Nodes数的人工神经元神经网络……。
大一学生、甚至中学生可以读懂。
适合于，没学过高数的程序员……照猫画虎编写人工智能、深度学习之神经网络……
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“我在网上看到过很多神经网络的实现方法，但这一篇是最简单、最清晰的。”
一位来自Umass的华人小哥Along Asong，写了篇神经网络入门教程，在线代码网站Repl.it联合创始人Amjad Masad看完以后，给予如是评价。
这篇教程发布仅一天时间，就在Hacker News论坛上收获了574赞。程序员们纷纷夸赞这篇文章的代码写得很好，变量名很规范，让人一目了然。
下面就让我们一起从零开始学习神经网络吧：
c++写一完整人工神经网络,要求输入层有9个Nodes,一个隐藏层有12个Nodes,输出层有5个Nodes,……含有反向传播、梯度下降法更新权重和偏置等。
- 神经网络的结构
- 前向传播（Forward Propagation）
- 反向传播（Back Propagation）
- 更新权重和偏置（梯度下降法）
下面是一个基本的实现：
// c++人工神经网络反向传播梯度下降更新权重偏置230810a18.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
#include <iostream>
#include <vector>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <string>
#include <sstream>
#include <iomanip> // 引入setprecision
int Ninpu9t = 9; //输入层Nodes数
int Nhidde12n = 12;//隐藏层Nodes数 4;// 11;
int nOutpu2t = 5;//输出层Nodes数 2;// 3;
double Lost001 = 9.0;
// 使用sigmoid作为激活函数
double sigmoid(double x) {
return 1.0 / (1.0 + std::exp(-x));
}
double sigmoid_derivative(double x) {
double s = sigmoid(x);
return s * (1 - s);
}
class NeuralNetwork {
private:
std::vector<std::vector<double>> weights1, weights2; // weights
std::vector<double> bias1, bias2; // biases
double learning_rate;
public:
NeuralNetwork() : learning_rate(0.1) { //01) {
srand(time(nullptr));
// 初始化权重和偏置
weights1.resize(Ninpu9t, std::vector<double>(Nhidde12n));
weights2.resize(Nhidde12n, std::vector<double>(nOutpu2t));
bias1.resize(Nhidde12n);
bias2.resize(nOutpu2t);
for (int i = 0; i < Ninpu9t; ++i)
for (int j = 0; j < Nhidde12n; ++j)
weights1[i][j] = (rand() % 2000 - 1000) / 1000.0; // [-1, 1]
for (int i = 0; i < Nhidde12n; ++i) {//for1100i
bias1[i] = (rand() % 2000 - 1000) / 1000.0; // [-1, 1]
for (int j = 0; j < nOutpu2t; ++j)
weights2[i][j] = (rand() % 2000 - 1000) / 1000.0; // [-1, 1]
}//for1100i
for (int i = 0; i < nOutpu2t; ++i)
bias2[i] = (rand() % 2000 - 1000) / 1000.0; // [-1, 1]
}
std::vector<double> forward(const std::vector<double>& input) {
std::vector<double> hidden(Nhidde12n);
std::vector<double> output(nOutpu2t);
for (int i = 0; i < Nhidde12n; ++i) {//for110i
hidden[i] = 0;
for (int j = 0; j < Ninpu9t; ++j)
{
hidden[i] += input[j] * weights1[j][i];
}
hidden[i] += bias1[i];
hidden[i] = sigmoid(hidden[i]);
}//for110i
for (int i = 0; i < nOutpu2t; ++i) {//for220i
output[i] = 0;
for (int j = 0; j < Nhidde12n; ++j)
{
output[i] += hidden[j] * weights2[j][i];
}
output[i] += bias2[i];
output[i] = sigmoid(output[i]);
}//for220i
return output;
}
void train(const std::vector<double>& input, const std::vector<double>& target) {
// Forward
std::vector<double> hidden(Nhidde12n);
std::vector<double> output(nOutpu2t);
std::vector<double> hidden_sum(Nhidde12n, 0);
std::vector<double> output_sum(nOutpu2t, 0);
for (int i = 0; i < Nhidde12n; ++i) {
for (int j = 0; j < Ninpu9t; ++j)
{
hidden_sum[i] += input[j] * weights1[j][i];
}
hidden_sum[i] += bias1[i];
hidden[i] = sigmoid(hidden_sum[i]);
}//for110i
for (int i = 0; i < nOutpu2t; ++i) {//for220i
for (int j = 0; j < Nhidde12n; ++j)
output_sum[i] += hidden[j] * weights2[j][i]; //注意 output_sum[]
output_sum[i] += bias2[i];
output[i] = sigmoid(output_sum[i]); //激活函数正向传播
}//for220i
//反向传播Backpropagation
std::vector<double> output_errors(nOutpu2t);
for (int i = 0; i < nOutpu2t; ++i) {//for2240i
output_errors[i] = target[i] - output[i];
//算损失综合总和:
Lost001 = 0.0;
Lost001 += fabs(output_errors[i]);
}//for2240i
std::vector<double> d_output(nOutpu2t);
for (int i = 0; i < nOutpu2t; ++i)
d_output[i] = output_errors[i] * sigmoid_derivative(output_sum[i]); //对output_sum[]做 激活函数的 导数 传播
std::vector<double> hidden_errors(Nhidde12n, 0);
for (int i = 0; i < Nhidde12n; ++i) {//for440i
for (int j = 0; j < nOutpu2t; ++j)
hidden_errors[i] += weights2[i][j] * d_output[j];
}//for440i
std::vector<double> d_hidden(Nhidde12n);
for (int i = 0; i < Nhidde12n; ++i)
d_hidden[i] = hidden_errors[i] * sigmoid_derivative(hidden_sum[i]); //对 hidden_errors层 做激活函数的 导数 传播
// Update weights and biases
for (int i = 0; i < Nhidde12n; ++i) {//for66i
for (int j = 0; j < nOutpu2t; ++j)
weights2[i][j] += learning_rate * d_output[j] * hidden[i]; //修改 隐藏层的 weights2
}//for66i
for (int i = 0; i < nOutpu2t; ++i)
bias2[i] += learning_rate * d_output[i];
for (int i = 0; i < Ninpu9t; ++i) {//for990i
for (int j = 0; j < Nhidde12n; ++j)
weights1[i][j] += learning_rate * d_hidden[j] * input[i]; //修改输入层的 weight1
}//for990i
for (int i = 0; i < Nhidde12n; ++i)
bias1[i] += learning_rate * d_hidden[i];
}//void train(const std::vector<double>& input, const std::vector<double>& target
}; //class NeuralNetwork {
int main() {
NeuralNetwork nn;
// Example
std::vector<double> input[5];
input[0] = { 0,1,0, 0,1,0, 0,1,0 }; //1“竖线”或 “1”字{ 1.0, 0.5, 0.25, 0.125 };
input[1] = { 0,0,0, 1,1,1,0,0,0 }; //-“横线”或 “-”减号{ 1.0, 0.5, 0.25, 0.125 };
input[2] = { 0,1,0, 1,1,1, 0,1,0 }; //+“+”加号{ 1.0, 0.5, 0.25, 0.125 };
input[3] = { 0,1,0, 0,2, 0, 0,3, 0.12 }; // '1'或 '|'字型{ 1.0, 0.5, 0.25, 0.125 };
input[4] = { 1,1,0, 9,0,9.8, 1,1,1 }; //“口”字型+{ 1.0, 0.5, 0.25, 0.125 };
std::vector<double> target[5];
target[0] = { 1.0, 0,0,0,0 };//1 , 0}; //0.0, 1.0, 0.5}; //{ 0.0, 1.0 };
target[1] = { 0, 1.0 ,0,0,0};//- 91.0, 0};// , 0, 0}; //
target[2] = { 0,0,1.0,0,0 };//+ 1.0, 0.5};
target[3] = { 1.0 ,0,0, 0.5 ,0}; //1
target[4] = { 0,0,0,0,1.0 }; //“口”
// Training
for (int i = 0; i < 50000/*00 */; ++i) {//for220i
for (int jj = 0; jj < 4; ++jj) {
nn.train(input[jj], target[jj]);
}//for2230jj
if (0 == i % 10000) {//if2250
printf(".");
std::cout << "[Lost:" << Lost001 << std::endl;
Lost001 = 0;
}//if2250
}//for220i
// Test
input[0] = { 0,1,0, 0,1,0, 0,1,0 }; //1{ 1.0, 0.5, 0.25, 0.125 };
std::vector<double> output = nn.forward(input[0]);
for (auto& val : output)
std::cout << val << " ";
std::cout << std::endl;
input[1] = { 0,0,0, 1,1,1, 0,0,0 };
//std::vector<double>
output = nn.forward(input[1]);
for (auto& val : output)
std::cout << val << " ";
std::cout << std::endl;
//-----------------------------------------------
std::string S;
// int D[9];
do {
std::cout << std::endl << "请输入一个包含9个由逗号分隔的数字的字符串: ";
std::getline(std::cin, S);
std::stringstream ss(S);
for (int i = 0; i < 9; ++i) {
std::string temp;
std::getline(ss, temp, ',');
input[1][i] = (double)std::stof(temp); // 将字符串转化为整数
}
std::cout << "数字数组为: ";
for (int i = 0; i < 9; ++i) {
std::cout << input[1][i] << " ";
}
output = nn.forward(input[1]);
std::cout << std::endl;
for (auto& val : output)
std::cout <<std::fixed<< std::setprecision(9)<< val << " ";
} while (1 == 1);
//====================================================
return 0;
}//main运行结果：
完整神经网络程序、和用法 可以私信或者 Email联系本人……
本人长期从事人工智能，神经网络，嵌入式 C/C++语言开发、培训……欢迎咨询！
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