How to make a Neural Network to solve XOR problem

2023年2月26日2023年2月27日

This program is based on the following page
https://qiita.com/ufoo68/items/9e4ca04578ba0f5fa5ff

This program solves the XOR problem using MLP with one hidden layer.

#include <stdio.h>
#include <math.h>
#include <time.h>
#include <stdlib.h>
//num of units
#define NUM_INPUT 2
//#define NUM_HIDDEN 20
#define NUM_HIDDEN 2

double sigmoid(double x) {
    return 1/(1+exp(-x));
}

//derivative of sigmoid function
double d_sigmoid(double x) {
    double a = 0.1;
    return a*x*(1-x);
}

int main(void) {
    srand((unsigned)time(NULL));
//train data
    double train_x[4][NUM_INPUT+1] = {{0, 0, -1},{0, 1, -1},{1, 0, -1},{1, 1, -1}};
    double d[4] = {0, 1, 1, 0};
//net
    double w[NUM_HIDDEN+1][NUM_INPUT+1];
    double v[NUM_HIDDEN+1];
    double y[4][NUM_HIDDEN+1];
    double z[4];
    double eta = 0.1;
    int epoch = 1000000;
//other
    int i, j, k, l;
    double tmp = 0;

//update weights using rand()
    for(l=0; l<NUM_HIDDEN+1; l++) {
        for(i=0; i<NUM_INPUT+1; i++) {
            w[l][i] = ((double)rand() / ((double)RAND_MAX + 1));
        }
    }
    for(i=0; i<NUM_HIDDEN+1; i++) {
        v[i] = ((double)rand() / ((double)RAND_MAX + 1));
    }

//tain
    for(k=0; k<epoch; k++) {
        //feedforward
        for(j=0; j<4; j++) {
            //hidden
            for(l=0; l<NUM_HIDDEN; l++) {
                for(i=0; i<NUM_INPUT+1; i++) {
                    tmp += train_x[j][i] * w[l][i];
                }
                y[j][l] = sigmoid(tmp);
                tmp = 0;
            }
            y[j][NUM_HIDDEN] = -1;
            //output
            for(i=0; i<NUM_HIDDEN+1; i++) {
                tmp += y[j][i] * v[i];
            }
            z[j] = sigmoid(tmp);
            tmp = 0;

        //backward
            //output
            for(i=0; i<NUM_HIDDEN+1; i++) {
                v[i] = v[i] - eta * y[j][i] * d_sigmoid(z[j]) * (z[j] - d[j]);
            }

            //hidden
            for(l=0; l<NUM_INPUT+1; l++) {
                for(i=0; i<NUM_HIDDEN+1; i++) {
                    w[i][l] = w[i][l] - eta * train_x[j][l] * d_sigmoid(y[j][i]) * d_sigmoid(z[j]) * (z[j] - d[j]) * v[i];
                }
            }
        }

		/*
        //print detail
        printf("z=");
        for(i=0; i<4; i++) {
            printf("%f ", z[i]);
        }
        printf("epoch:%d\n",k);
		*/
    }

//predict
    for(j=0; j<4; j++) {
        //hidden
        for(l=0; l<NUM_HIDDEN; l++) {
            for(i=0; i<NUM_INPUT+1; i++) {
                tmp += train_x[j][i] * w[l][i];
            }
            y[j][l] = sigmoid(tmp);
            tmp = 0;
        }
        y[j][NUM_HIDDEN] = -1;
        //output
        for(i=0; i<NUM_HIDDEN+1; i++) {
            tmp += y[j][i] * v[i];
        }
        z[j] = sigmoid(tmp);
        tmp = 0;
    }

//print result
    printf("z=");
    for(i=0; i<4; i++) {
        printf("%f ", z[i]);
    }
    printf("epoch:%d\n",k);


    for(i=0; i<NUM_INPUT+1; i++) {
        for(l=0; l<NUM_HIDDEN+1; l++) {
		  printf("w[%d][%d]:%f\n", i, l, w[i][l]);
        }
    }

    for(i=0; i<NUM_HIDDEN+1; i++) {
	  printf("v[%d]:%f\n",i, v[i]);
    }


    return 0;
}

Save this program as a name "mlp.c", compile ">gcc mlp.c" and execute ">./a.exe"