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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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#include <time.h>
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#define INNODE 2 // 输入层神经元个数
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#define HIDENODE 10 // 隐藏层神经元个数
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#define OUTNODE 1 // 输出层神经元个数
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/**
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* 步长（学习率）
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*/
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double StudyRate = 1.6;
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/**
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* 允许最大误差
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*/
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double threshold = 1e-4;
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/**
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* 最大迭代次数
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*/
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int mostTimes = 1e6;
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/**
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* 训练集大小
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*/
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int trainSize = 0;
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/**
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* 测试集大小
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*/
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int testSize = 0;
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/**
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* 样本
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*/
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typedef struct Sample{
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double out[30][OUTNODE]; // 输出
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double in[30][INNODE]; // 输入
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}Sample;
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/**
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* 神经元结点
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*/
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typedef struct Node{
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double value; // 当前神经元结点输出的值
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double bias; // 当前神经元结点偏偏置值
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double bias_delta; // 当前神经元结点偏置值的修正值
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double *weight; // 当前神经元结点向下一层结点传播的权值
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double *weight_delta; // 当前神经元结点向下一层结点传播的权值的修正值
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}Node;
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/**
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* 输入层
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*/
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Node inputLayer[INNODE];
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/**
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* 隐藏层
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*/
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Node hideLayer[HIDENODE];
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/**
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* 输出层
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*/
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Node outLayer[OUTNODE];
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double Max(double a, double b){
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return a > b ? a : b;
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}
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/**
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* 激活函数sigmoid
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* @param x 输入值
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* @return 输出值
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*/
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double sigmoid(double x){
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double y;//请补全sigmod函数的计算结果
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y=1/(exp(-x)+1);
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return y;
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}
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/**
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* 读取训练集
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* @param filename 文件名
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* @return 训练集
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*/
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Sample * getTrainData(const char * filename){
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Sample * result = (Sample*)malloc(sizeof (Sample));
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FILE * file = fopen(filename, "r");
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if(file != NULL){
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int count = 0;
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while (fscanf(file, "%lf %lf %lf", &result->in[count][0], &result->in[count][1], &result->out[count][0]) != EOF){
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++count;
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}
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trainSize = count;
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printf("%s The file has been successfully read!\n", filename);
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fclose(file);
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return result;
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} else{
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return result;
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fclose(file);
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printf("%s Encountered an error while opening the file!\n\a", filename);
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return NULL;
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}
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}
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/**
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* 读取测试集
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* @param filename 文件名
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* @return 测试集
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*/
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Sample * getTestData(const char * filename){
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Sample* result=(Sample*)malloc(sizeof(Sample));/*在内存中分配足够的空间来存储一个Sample结构，并将指向该内存块的指针存储在result变量中*/
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FILE * file = fopen(filename, "r");//打开文件
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if(file != NULL){
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int count=0;
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while(fscanf(file,"%lf %lf",&result->in[count][0],&result->in[count][1])!=EOF)
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{
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++count;
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}
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testSize=count;
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printf("%s The file has been successfully read!\n", filename);
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fclose(file);
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return result;
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}
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//将最终的count的值存储在名为testSize的全局变量中，以便后续使用
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//返回result
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else{
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fclose(file);
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printf("%s Encountered an error while opening the file!\n\a", "TextData.txt");
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return NULL;
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}
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}
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/**
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* 打印样本
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* @param data 要打印的样本
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* @param size 样本大小
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*/
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void printData(Sample * data, int size){
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if(data==NULL)
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printf("Sample is empty!");
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else{
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int i;
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for(i=0;i<testSize;i++)
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{
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printf("%4.3lf %4.3lf %4.3f",data->in[i][0],data->in[i][1],data->out[i][0]);
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printf("\n");
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}
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}
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}
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/**
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* 初始化函数
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*/
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void init(){
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// 设置时间戳为生成随机序列的种子
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srand(time(NULL));
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// 输入层的初始化
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for (int i = 0; i < INNODE; ++i) {
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inputLayer[i].weight = (double *)malloc(sizeof (double ) * HIDENODE);//开辟了一个数组
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inputLayer[i].weight_delta = (double *) malloc(sizeof (double ) * HIDENODE);
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inputLayer[i].bias = 0.0;
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inputLayer[i].bias_delta = 0.0;
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}
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// 输出层权值初始化
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for (int i = 0; i < INNODE; ++i) {
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for (int j = 0; j < HIDENODE; ++j) {
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inputLayer[i].weight[j] = rand() % 10000 / (double )10000 * 2 - 1.0;
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inputLayer[i].weight_delta[j] = 0.0;
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}
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}
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// 初始化隐藏层结点
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for (int i = 0; i < HIDENODE; ++i) {
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/*为隐藏层节点 i 分配了一个 double 类型的数组，用于存储该节点向下一层节点传播的权重。
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使用malloc 函数在堆内存中分配足够的空间，以存储 OUTNODE 个 double 类型的权重值。
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*/
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hideLayer[i].weight =(double*)malloc(sizeof(double)*OUTNODE);
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/*为隐藏层节点 i 分配了一个用于存储权重修正值的数组。这个数组将在神经网络的训练过程中用于存储权重的更新值。
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使用malloc 函数在堆内存中分配足够的空间，以存储 OUTNODE 个 double 类型的权重值。
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*/
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hideLayer[i].weight_delta =(double*)malloc(sizeof(double)*OUTNODE);
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/*为隐藏层节点 i 初始化了一个随机的偏置值。
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这个值通常是一个在 -1.0 到 1.0 之间的随机数，用于调整该节点的激活函数的阈值。
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*/
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hideLayer[i].bias = rand()%10000/(double)10000*2-1.0;
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/*初始化了隐藏层节点 i 的偏置值修正值，初始值为0.0。*/
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hideLayer[i].bias_delta = 0.0;
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}
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// 初始化隐藏层权值
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for (int i = 0; i < HIDENODE; ++i) {
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for (int j = 0; j < OUTNODE; ++j) {
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hideLayer[i].weight[j] = rand() % 10000 / (double )10000 * 2 - 1.0;
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hideLayer[i].weight_delta[j] = 0.0;
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}
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}
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for (int i = 0; i < OUTNODE; ++i) {
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outLayer[i].bias = rand() % 10000 / (double )10000 * 2 - 1.0;
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outLayer[i].bias_delta = 0.0;
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}
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}
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/**
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* 重置修正值
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*/
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void resetDelta(){
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for (int i = 0; i < INNODE; ++i) {
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for (int j = 0; j < HIDENODE; ++j) {
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inputLayer[i].weight_delta[j] = 0.0;
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}
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}
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for (int i = 0; i < HIDENODE; ++i) {
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hideLayer[i].bias_delta = 0.0;
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for (int j = 0; j < OUTNODE; ++j) {
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hideLayer[i].weight_delta[j] = 0.0;
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}
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}
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for (int i = 0; i < OUTNODE; ++i) {
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outLayer[i].bias_delta = 0.0;
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}
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}
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int main() {
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// 初始化
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init();
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// 获取训练集
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Sample * trainSample = getTrainData("TrainData.txt");
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printf("\n");
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printData(trainSample, trainSize);
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for (int trainTime = 0; trainTime < mostTimes; ++trainTime) {
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// 重置梯度信息
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resetDelta();
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// 当前训练最大误差
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double error_max = 0.0;
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// 开始训练（累计bp）
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for (int currentTrainSample_Pos = 0; currentTrainSample_Pos < trainSize; ++currentTrainSample_Pos) {
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// 输入自变量
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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inputLayer[inputLayer_Pos].value = trainSample->in[currentTrainSample_Pos][inputLayer_Pos];
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}
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/** ----- 开始正向传播 ----- */
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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double sum = 0.0;
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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sum += inputLayer[inputLayer_Pos].value * inputLayer[inputLayer_Pos].weight[hideLayer_Pos];
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}
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sum -= hideLayer[hideLayer_Pos].bias;
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hideLayer[hideLayer_Pos].value = sigmoid(sum);
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}
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE ; ++outLayer_Pos) {
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double sum = 0.0;
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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sum+=hideLayer[hideLayer_Pos].value*hideLayer[hideLayer_Pos].weight[outLayer_Pos];/*计算每一个隐藏层节点的value和权值的乘积，相加得到sum
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*/
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}
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/*更新sum，使sum减去偏置值;
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*/
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sum-=outLayer[outLayer_Pos].bias; /*利用sigmod函数对得到的sum进行激活，把激活后的结果赋值给对应的输出层节点value(outLayer[outLayer_Pos].value)。 */
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outLayer[outLayer_Pos].value=sigmoid(sum);
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}
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/** ----- 计算误差 ----- */
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double error = 0.0;
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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double temp = fabs(outLayer[outLayer_Pos].value - trainSample->out[currentTrainSample_Pos][outLayer_Pos]);
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// 损失函数
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error += temp * temp / 2.0;
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}
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error_max = Max(error_max, error);
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/** ----- 反向传播 ----- */
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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double bias_delta = -(trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value)
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* outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value);
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outLayer[outLayer_Pos].bias_delta += bias_delta;
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}
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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double weight_delta = (trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value)
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* outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value)
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* hideLayer[hideLayer_Pos].value;
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hideLayer[hideLayer_Pos].weight_delta[outLayer_Pos] += weight_delta;
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}
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}
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//
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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double sum = 0.0;
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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sum += -(trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value)
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* outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value)
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* hideLayer[hideLayer_Pos].weight[outLayer_Pos];
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}
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hideLayer[hideLayer_Pos].bias_delta += sum * hideLayer[hideLayer_Pos].value * (1.0 - hideLayer[hideLayer_Pos].value);
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}
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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double sum = 0.0;
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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sum += (trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value)
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* outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value)
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* hideLayer[hideLayer_Pos].weight[outLayer_Pos];
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}
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inputLayer[inputLayer_Pos].weight_delta[hideLayer_Pos] += sum * hideLayer[hideLayer_Pos].value * (1.0 - hideLayer[hideLayer_Pos].value)
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* inputLayer[inputLayer_Pos].value;
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}
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}
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}
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// 判断误差是否达到允许误差范围
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if(error_max < threshold){
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printf("\a Training completed!Total training count:%d, maximum error is:%f\n", trainTime + 1, error_max);
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break;
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}
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// 误差无法接受，开始修正
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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inputLayer[inputLayer_Pos].weight[hideLayer_Pos] += StudyRate
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* inputLayer[inputLayer_Pos].weight_delta[hideLayer_Pos] /
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(double) trainSize;
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}
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}
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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hideLayer[hideLayer_Pos].bias += StudyRate
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* hideLayer[hideLayer_Pos].bias_delta / (double )trainSize;
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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hideLayer[hideLayer_Pos].weight[outLayer_Pos] += StudyRate
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* hideLayer[hideLayer_Pos].weight_delta[outLayer_Pos] / (double )trainSize;
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}
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}
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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outLayer[outLayer_Pos].bias += StudyRate
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* outLayer[outLayer_Pos].bias_delta / (double )trainSize;
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}
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}
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// 训练完成，读取测试集
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Sample * testSample = getTestData("TestData.txt");
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printf("The predicted results are as follows:\n");
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for (int currentTestSample_Pos = 0; currentTestSample_Pos < testSize; ++currentTestSample_Pos) {
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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inputLayer[inputLayer_Pos].value = testSample->in[currentTestSample_Pos][inputLayer_Pos];
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}
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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double sum = 0.0;
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for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) {
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sum += inputLayer[inputLayer_Pos].value * inputLayer[inputLayer_Pos].weight[hideLayer_Pos];
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}
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sum -= hideLayer[hideLayer_Pos].bias;
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hideLayer[hideLayer_Pos].value = sigmoid(sum);
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}
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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double sum = 0.0;
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for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) {
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sum += hideLayer[hideLayer_Pos].value * hideLayer[hideLayer_Pos].weight[outLayer_Pos];
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}
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sum -= outLayer[outLayer_Pos].bias;
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outLayer[outLayer_Pos].value = sigmoid(sum);
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}
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for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) {
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testSample->out[currentTestSample_Pos][outLayer_Pos] = outLayer[outLayer_Pos].value;
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}
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}
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printData(testSample, testSize);
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return 0;
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}
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步骤6：
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文字大致描述bp神经网络：
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通过一些训练数据（包含输入的信息和应该输出的信息），让bp神经网络能够在输入测试数据后，在没有输出范例的情况下按要求输出数据。该训练过程为：先将输入层、隐藏层、输出层的各个数值——值，权重、偏置值等初始化，将输入数据原封不动传递给输入层神经元，每个输入层神经元对于将值按照一定权重传递给隐藏层神经元。每个隐藏层神经元将所接受到的值收集起来，减去事先初始化好的偏置值后，将剩下的值通过sigmod函数映射到【0,1】之间，将映射结果作为自身的值。每一个隐藏层神经元将自身的值按照一定权重传递给输出层神经元，输出层神经元将所接收到的值收集起来，减去自身偏置值后，将剩下的值通过sigmod函数映射到【0,1】之间作为自身的值，即预期输出的值。通过分析该输出与应该输出的数据之间的误差，反向传播，将误差分摊给各个神经元——调整其权重，已达到下一次输入数据后缩小误差的目的。一组训练数据训练完后，倘若最大误差不符合要求，则将进行下一次训练。通过反复训练，将最大误差缩小到要求范围之内，即达成训练学习要求。
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实验习题1：
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适当提高学习率可以加快更新权重值的速度，从而加快训练速度，缩短得到输出数据的时间。
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实验习题2：
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适当增加隐藏层神经元个数可以有效减小误差。
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实验习题3：
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不同的激活函数直接影响了神经网络的拟合能力和收敛速度。
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