Error Back Propagation gets stuck in a wrong value - c

Question

I am currently doing an assignment which requires me to make a neural network of f(x) = x(1-x).
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define ITER 300000
#define L_RATE 0.5
#define N 11
#define I 1
#define J 4
#define K 1
#define SIGMOID(x) (1/(1+exp(-(x))))
So I am currently using 4 hiden nodes(J) and a learning rate of 0.5(L_RATE) and planning to have 11 datas(N) as inputs for training.
double error_v(double o, double t, double h)
{
return -(t-o)*o*(1-o)*h;
}
double error_w(double x, double h, double w, double t, double o)
{
return -x*h*(1-h)*w*(t-o)*o*(1-o);
}
These would be the error gradient for weight of each layers.
int main(void)
{
double x[N][I];
double t[N][K];
double w[J][I+1];
double v[K][J+1];
double net_w[N][J];
double net_v[N][K];
double h[N][J];
double o[N][K];
for(int n=0; n<N; n++)
{
for(int i=0; i<I; i++)
{
x[n][i] = 0.1 * n;
t[n][i] = x[n][i] * (1 - x[n][i]);
}
}
//INITIALIZE WEIGHT
srand(time(NULL));
for(int j=0; j<J; j++)
{
for(int i=0; i<I+1; i++)
{
w[j][i] = (double)rand()/RAND_MAX*2.0-1.0;
printf("%.2f ", w[j][i]);
}
}
for(int k=0; k<K; k++)
{
for(int j=0; j<J+1; j++)
{
v[k][j] = (double)rand()/RAND_MAX*2.0-1.0;
printf("%.2f ", v[k][j]);
}
}
for(int iter=0; iter<ITER; iter++)
{
for(int n=0; n<N; n++)
{
//Initialize net zero
for(int j=0; j<J; j++)
{
net_w[n][j] = 0;
}
for(int k=0; k<K; k++)
{
net_v[n][k] = 0;
}
//Sum up net_w and produce h
for(int j=0; j<J; j++)
{
for(int i=0; i<I; i++)
{
net_w[n][j] += x[n][i] * w[j][i];
}
net_w[n][j] += 1 * w[j][I];
h[n][j] = SIGMOID(net_w[n][j]);
}
//Sum up net_v and produce o
for(int k=0; k<K; k++)
{
for(int j=0; j<J; j++)
{
net_v[n][k] += h[n][k] * v[k][j];
}
net_v[n][k] += 1 * v[k][J];
o[n][k] = SIGMOID(net_v[n][k]);
}
}
So until here, I calculated the first net value by multiplying the input(including one bias) and weight(w) and the second net value by multiplying the 'sigmoided' value of the first net(including one bias) and weight(v).
for(int n=0; n<N; n++)
{
//error_v
for(int k=0; k<K; k++)
{
for(int j=0; j<J; j++)
{
v[k][j] -= L_RATE * error_v(o[n][k], t[n][k], h[n][j]);
}
v[k][J] -= L_RATE * error_v(o[n][k], t[n][k], 1);
}
}
for(int n=0; n<N; n++)
{
//error_w
for(int j=0; j<J; j++)
{
for(int i=0; i<I; i++)
{
for(int k=0; k<K; k++)
{
w[j][i] -= L_RATE * error_w(x[n][i], h[n][j], w[k][j], t[n][k], o[n][k]);
}
}
for(int k=0; k<K; k++)
{
w[j][I] -= L_RATE * error_w(1, h[n][j], w[k][j], t[n][k], o[n][k]);
}
}
}
}
But here's the problem. I corrected the error of the weight by multiplying the learning rate and the error gradient by the following formula.
I thought I had to use 3-for-loop for the second layer and 4-for-loop in respect of each number of input layer, hidden layer, output layer and training data.
printf("INPUT\n");
for(int n=0; n<N; n++)
{
printf("%.2f ", x[n][0]);
}
printf("\n");
printf("OUTPUT\n");
for(int n=0; n<N; n++)
{
printf("%.2f ", o[n][0]);
}
printf("\n");
printf("EXPECTED\n");
for(int n=0; n<N; n++)
{
printf("%.2f ", t[n][0]);
}
printf("\n");
return 0;
}
But when I print out the trained output, It doesn't get close to the expected data but rather gets stuck in a particular value.
I saw many others had been through this kind of problem, and their solution was giving random non zero values to the initial weight or changing the learning rate or number of iterations. I've done this numerous times but It doesn't seem to match my problem. I would be very thankful if someone could tell me what I am doing wrong right now.

Answer 1

In the loop //Sum up net_v and produce o where the v-weighted output from the hidden layer's neurons' activations h is accumulated in net_v, there's a wrong index k:
net_v[n][k] += h[n][k] * v[k][j];
should be
net_v[n][k] += h[n][j] * v[k][j];