# ANN - learning AND / OR

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Hi all, my first time here so start with: I apologize for my bad english but i'm not a native english speaker... i'll try to do my best.. :D I wrote a little AAN with this characteristics: - It has to learn bit to bit AND and OR, so it takes two input (x1,x2) and calculate d = x1*w1 + x2*w2; (w1,w2) -> weights.. - the treshold i choosed is 0 and it is compared with d = x1 * w1 + x2 * w2, then if(d <= 0) d = 0; else d = 1; - weights are modified by this formulas wi(t+1) = wi(t) + n * (p - d) * xi with: n = learning rate, p = expected value, d = aim value. [i know you all guy know this stuff... but it's just for the sake of clarity]. - the program takes in inupt a file (exercise book) with this syntax (eg): 1 0 0 0 0 1 ecc and it means (first line): 1: first operand; 0: second operand; 0: expected result. And so on. All this works fine if this simple feed-forward perceptron try to learn how manage OR (learning rate 0.2... less than 20 example are enough), but it doesn't work if i try to give it an AND exercise book... The source is something like that (again apology: ugly coding style, don't try this at home! :D)
//main.cpp
#include "main.h"
#include "training.h"

struct exercise ex[ESEMPI];
struct weight w;
FILE *book = NULL; // exercise book

int main(int argc, char *argv[])
{
int n = 0;
double ris;
char filename[20];

w.wa = wrand();
w.wb = wrand();

cout << "Init weights: " << w.wa << " " << w.wb << endl;

cout << "Book filename: ";
cin	 >> filename;

book = fopen(filename, "r");
if(book == NULL)
{
cout << "fopen error" << endl;
exit(-1);
}

for(int i = 0; i < ESEMPI; i++)
n = getexercise(&ex, &w, n);
fclose(book);

cout << "Final weight: " << w.wa << " " << w.wb << endl;

for(;;)
{
cout << endl << "First operand: ";
cin >> ex[0].a;
cout << endl << "Second operand: ";
cin >> ex[0].b;

ris = (ex[0].a * w.wa) + (ex[0].b * w.wb);

if(ris < 0)
ris = 0;
if(ris > 0)
ris = 1;

cout <<  endl << ex[0].a << " OP " << ex[0].b << " = " << ris << endl;
}

return 0;
}


//main.h
#include <stdlib.h>
#include <stdio.h>
#include <iostream>

#define ESEMPI 20 // book size

using namespace std;


//training.cpp
#include "training.h"

double wrand()   // return a random number to initialize the weights
{
return (rand() / ((double)RAND_MAX + 1));
}

int getexercise(struct exercise *ex, struct weight *w, int n)
{	// open an exercise book and fills an array of
//	struct exercise

extern FILE *book;

ex->a = (fgetc(book) - 48);
fseek(book, n+=2, SEEK_SET);
ex->b = (fgetc(book) - 48);
fseek(book, n+=2, SEEK_SET);
ex->r = (fgetc(book) - 48);
fseek(book, n+=3, SEEK_SET);
learning(ex, w);
return n;

}

void learning(struct exercise *ex, struct weight *w)
{
double d;
double deltaa;
double deltab;
const double n = 0.2;

d = (ex->a * w->wa) + (ex->b * w->wb);

if(d <= 0)
d = 0;
else
d = 1;

if(d != ex->r)
{
deltaa = n * (ex->r - d) * ex->a;
deltab = n * (ex->r - d) * ex->b;
}
else
{
deltaa = 0;
deltab = 0;
}

w->wa = w->wa + deltaa;
w->wb = w->wb + deltab;
}


//training.h
#include "main.h"

struct exercise
{
double a;  // first operand
double b;  // second operand

double r;  // expected result
};

struct weight
{
double wa; // weight a
double wb; // weight b
};

double wrand();
int getexercise(struct exercise *ex, struct weight *w, int n);
void learning(struct exercise *ex, struct weight *w);


If anyone has some hints it would be very appreaciated... Thanx, fadeh [Edited by - fadeh on August 26, 2005 3:29:10 AM]

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It's been a while since I worked with ANNs, but if I'm not mistaken, it's possibly not a coding problem.

You'll never get it working with that threshold. You either add a bias to the node (you know, an input which is allways 1: d = x1*w1 + x2*w2 + 1*w3) or change the threshold to something positive (I would make the neuron biased).

If I'm wrong in my assumptions, I'm sure someone here will correct me.

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It just occurred to be maybe I should try to explain. I'm not very good at explaining but let's try:

You want d to be non-positive if the answer is false (A AND B = false)

So that means A * w1 + B * w2 must be equal or less than zero. Because it has to be less than zero for A = 0 and B = 1 or A = 1 and B = 0, both w1 and w2 will have to be non-positive (do the math. None of them can be positive because 1 and 0 must return the same answer as 0 and 1).

So we need w1 and w2 <=0. How will we ever get a positive d? It's not possible.

Now suppose you have a bias. Then you can get an answer with something like

w1 = 0.6; w2 = 0.6; w3 = -1;

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Many thanx man, now it works perfectly (adding a bias as u explained)... but another question went out: why doesn't work with xor? :D
If i had understood what you said the things don't work because:
0 XOR 1 = 1, 1 XOR 0 = 1, so wa > 0, wb > 0 but in that case the things don't work with 1 XOR 1 = 0... so if wc < 0 and |wc| > |wa + wb| the things are done for 1 XOR 1 but messed up for 0 XOR 1, 1 XOR 0... so let's choose wa < 0, wb < 0, wc > 1... this way 0 XOR 1, 1 XOR 0, XOR 1 are ok, but 0 XOR 0 no.... so it seems that the bias in this case doesn't work or i missing up something...?

Thanx

Bye,

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