Summation giving random wrong numbers
<p>I'm trying to implement an easy backpropagation algorithm for an exam (I'm a beginner programmer). 
I've got a set of arrays and I generate random weights to start the algorithm. 
I implemented the activation function following the math formula: <a href="https://i.stack.imgur.com/JaiqM.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/JaiqM.png" alt="enter image description here"></a></p>

<p><a href="https://chart.googleapis.com/chart?cht=tx&amp;chl=%5Csum_%7Bi=0%7D%5E%7Bn%7D%20w_%7Bx,y%7DI_%7Bx%7D" rel="nofollow noreferrer">formula</a></p>

<p>(where x index are for inputs and y index is for hidden neuron input)</p>

<p>My problem is that I get some summation results with very high exponential values that are incompatible with what I'd expect to be.</p>

<p>Here's my code: </p>

<pre><code>#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;math.h&gt;
#include &lt;time.h&gt;

#define INPUT_NEURONS   4
#define HIDDEN_NEURONS  7
#define OUTPUT_NEURONS  3
#define MAX_SAMPLES     150
#define LEARNING_RATE   0.1
#define RAND_WEIGHT ((double)rand()/(RAND_MAX+1))

double IHweight[INPUT_NEURONS][HIDDEN_NEURONS];  /* in-&gt;hid weight */
double HOweight[HIDDEN_NEURONS][OUTPUT_NEURONS]; /* hid-&gt;out weight */
//activation
double inputs[MAX_SAMPLES][INPUT_NEURONS];
double hidden[HIDDEN_NEURONS];
double target[MAX_SAMPLES][OUTPUT_NEURONS];
double actual[OUTPUT_NEURONS];
//errors
double errO[OUTPUT_NEURONS];
double errH[HIDDEN_NEURONS];
double Error = 0.0;
int sample = 0;

typedef struct {
    double sepal_lenght;
    double sepal_width;
    double petal_lenght;
    double petal_width;
    double output[OUTPUT_NEURONS];
} IRIS;
IRIS samples[MAX_SAMPLES] = {
    {   5.1,    3.5,    1.4,    0.2,    0.0,    0.0,    1.0 },
    {   4.9,    3.0,    1.4,    0.2,    0.0,    0.0,    1.0 },
    {   4.7,    3.2,    1.3,    0.2,    0.0,    0.0,    1.0 },
    {...},
};

double sigmoid(double val) {
    return (1.0 / (1.0 + exp(-val)));
}
double dsigmoid(double val) {
    return (val * (1.0 - val));
}
void assignRandomWeights() {
    int hid, inp, out;
    printf("Initializing weights...\n\n");
    for (inp = 0; inp &lt; INPUT_NEURONS; inp++) {
        for (hid = 0; hid &lt; HIDDEN_NEURONS; hid++) {
            IHweight[inp][hid] = RAND_WEIGHT;
            printf("Weights : input %d -&gt; hidden %d: %f\n",
                   inp, hid, IHweight[inp][hid]);
        }
    }
    for (hid = 0; hid &lt; HIDDEN_NEURONS; hid++) {
        for (out = 0; out &lt; OUTPUT_NEURONS; out++) {
            HOweight[hid][out] = RAND_WEIGHT;
            printf("hidden %d -&gt; output %d: %f\n", 
                   hid, out, HOweight[hid][out]);
        }
    }
    system("pause");
}

void activation() {
    int hid, inp, out;
    double sumH[HIDDEN_NEURONS] ;
    double sumO[OUTPUT_NEURONS];

    for (hid = 0; hid &lt; HIDDEN_NEURONS; hid++) {
        for (inp = 0; inp &lt; INPUT_NEURONS; inp++) {
            sumH[hid] += (inputs[sample][inp] * IHweight[inp][hid]);
            printf("\n%d Input %d = %.1f Weight = %f sumH = %g",
                   sample, inp, inputs[sample][inp], IHweight[inp][hid], sumH[hid]);
        }
        hidden[hid] = sigmoid(sumH[hid]);
        printf("\nHidden neuron %d activation = %f", hid, hidden[hid]);
    }
    for (out = 0; out &lt; OUTPUT_NEURONS; out++) {
        for (hid = 0; hid &lt; HIDDEN_NEURONS; hid++) {
            sumO[out] += (hidden[hid] * HOweight[hid][out]);
            printf("\n%d Hidden %d = %f Weight = %f sumO = %g",
                   sample, hid, hidden[hid], HOweight[hid][out], sumO[out]);
        }
        actual[out] = sigmoid(sumO[out]);
        printf("\nOutput neuron %d activation = %f", out, actual[out]);
    }
}

main () {
    srand(time(NULL));
    assignRandomWeights();
    for (int epoch = 0; epoch &lt; 1; epoch++) {
        for (int i = 0; i &lt; 1; i++) {
            sample = rand() % MAX_SAMPLES;
            inputs[sample][0] = samples[sample].sepal_lenght;
            inputs[sample][1] = samples[sample].sepal_width;
            inputs[sample][2] = samples[sample].petal_lenght;
            inputs[sample][3] = samples[sample].petal_width;
            target[sample][0] = samples[sample].output[0];
            target[sample][1] = samples[sample].output[1];
            target[sample][2] = samples[sample].output[2];
            activation();
        }
    }
}
</code></pre>

<p>I'm using a lot of <code>printf()</code> to check my results and i get </p>

<pre><code>...
41 Input 0 = 4.5 Weight = 0.321014 sumH = 1.31886e+267
41 Input 1 = 2.3 Weight = 0.772369 sumH = 1.31886e+267
41 Input 2 = 1.3 Weight = 0.526123 sumH = 1.31886e+267
41 Input 3 = 0.3 Weight = 0.271881 sumH = 1.31886e+267
Hidden neuron 6 activation = 1.000000
...
41 Hidden 0 = 0.974952 Weight = 0.343445 sumO = 1.24176e+267
41 Hidden 1 = 0.917789 Weight = 0.288361 sumO = 1.24176e+267
41 Hidden 2 = 0.999188 Weight = 0.972168 sumO = 1.24176e+267
41 Hidden 3 = 0.989726 Weight = 0.082642 sumO = 1.24176e+267
41 Hidden 4 = 0.979063 Weight = 0.531799 sumO = 1.24176e+267
41 Hidden 5 = 0.972474 Weight = 0.552521 sumO = 1.24176e+267
41 Hidden 6 = 1.000000 Weight = 0.707153 sumO = 1.24176e+267
Output neuron 1 activation = 1.000000
</code></pre>

<p>The <code>assignRandomweights()</code> and <code>sigmoid()</code> functions are ok as far as i can tell, the problem is in <code>activation()</code>.</p>

<p>Please help me understand why this happens and how to solve it.</p>