假設神經元的輸入是一個4維的向量 X=[x1,x2,x3,x4]，其中xi的值為0或者1，並且只取4中樣本：

• x1=[1,0,0,0]
• x2=[0,1,0,0]
• x3=[0,0,1,0]
• x4=[0,0,0,1]

對這一組樣本，採用一個很小的隨機數來模擬生成20000個樣本，同時，將神經元的4個輸出值對映到[0,1]，即4個分類分別是[0.25,0.5,0.75,1]。

程式碼實現如下：

#include <iostream>
#include <vector>

using namespace std;

vector<vector<double>> inputData;
vector<double> weight;
double actual_output;  //網路的實際輸出
vector<double> input;

//生成numofSample個樣本，一共分為numofLable類，每個樣本的標籤是當前樣本的下標i%numofLable
void getSamplesData(int numofSamples, int numofLable)
{
	const int iterations = numofSamples; // 樣本數量
	for (int i = 0; i < iterations; i++)
	{
		int index = i % numofLable;
		vector<double> dvect(numofLable, 0);
		dvect[index] = 1;
		for (size_t i = 0; i != dvect.size(); i++)
		{
			dvect[i] += (5e-3*rand() / RAND_MAX - 2.5e-3);
		}
		inputData.push_back(dvect);
	}
}

//初始化初始權重，包括4個節點和1個偏置，隨機設定為0~0.05之間的一個值
void intialWeight()
{
	cout << "初始化權重為：" << endl;
	// 4個連結和一個偏置w0
	for (int i = 0; i != 5; i++)
	{
		weight.push_back(0.05*rand() / RAND_MAX);
		cout << weight[i] << endl;
	}
}

//前向計算，輸入時資料層的4維的訓練資料，actual_output是網路當前的輸出
void cmtForward(const vector<double>& inVect)
{
	double dsum = weight[4];//先把偏置加上
	for (size_t i = 0; i != inVect.size(); i++)
	{
		dsum += (inVect[i] * weight[i]);
	}
	actual_output = 1 / (1 + exp(-1 * dsum));   // S函式的非線性變換
	//actual_output = 2 * (1 / (1 + exp(-2 * dsum))) - 1;  //T函式的非線性變換
	//dsum > 0 ? actual_output = dsum : actual_output = 0;  //R函式的非線性變換
}

//權重調整，相當於後向計算，輸入時訓練資料和期望的輸出
void updataWeight(const vector<double>& inVect, const double true_output)
{
	double learnRate = 0.05; // 權重更新引數
	for (size_t i = 0; i != weight.size() - 1; i++)
	{
		weight[i] += (learnRate*(true_output - actual_output)*actual_output*(1 - actual_output)*inVect[i]);
	}
	// w0單獨計算
	weight[4] += (learnRate*(true_output - actual_output)*actual_output*(1 - actual_output) * 1);
}


void main()
{
	getSamplesData(20000, 4);  //生成20000個數據，分為4類
	intialWeight();    //初始化權重，隨機生成5個0~0.05之間的數值

	//執行20000次迭代
	for (int i = 0; i < 20000; i++)
	{
		input = inputData[i];
		double lable = (double)(i % 4) / 4 + 0.25;  //資料標籤轉換到0~1

		cmtForward(input);    //前向傳播計算
		updataWeight(input, lable);   //權重調整

		if (i % 111 == 0)
		{
			cout << "當前執行第 " << i << " 次迭代" << endl;
			cout << "輸入資料： [ " << input[0] << "," << input[1] << "," << input[2] << "," << input[3]
				<< " ]" << "   " << "網路輸出：" << actual_output << endl << endl;
		}
	}
	cout << "優化後的權重係數：[ " << weight[0] << "," << weight[1] << "," << weight[2] << "," <<
		weight[3] << " ]" << "   偏置： " << weight[4] << endl;
	system("pause");
}
 

S函式的迭代實現結果：

T函式的迭代實現結果：

R函式的迭代實現結果：