Perceptron converging but returning odd results - c++

Question

I made a simple perceptron in c++ to study AI and even following a book(pt_br) i could not make my perceptron return an expected result, i tryed to debug and find the error but i didnt succeed.
My algorithm AND gate results (A and B = Y):
0 && 0 = 0
0 && 1 = 1
1 && 0 = 1
1 && 1 = 1
Basically its working as an OR gate or random.
I Tried to jump to Peter Norving and Russel book, but he goes fast over this and dont explain on depth one perceptron training.
I really want to learn every inch of this content, so i dont want to jump to Multilayer perceptron without making the simple one work, can you help?
The following code is the minimal code for operation with some explanations:
Sharp function:
int signal(float &sin){
if(sin < 0)
return 0;
if(sin > 1)
return 1;
return round(sin);
}
Perceptron Struct (W are Weights):
struct perceptron{
float w[3];
};
Perceptron training:
perceptron startTraining(){
//- Random factory generator
long int t = static_cast<long int>(time(NULL));
std::mt19937 gen;
gen.seed(std::random_device()() + t);
std::uniform_real_distribution<float> dist(0.0, 1.0);
//--
//-- Samples (-1 | x | y)
float t0[][3] = {{-1,0,0},
{-1,0,1},
{-1,1,0},
{-1,1,1}};
//-- Expected result
short d [] = {0,0,0,1};
perceptron per;
per.w[0] = dist(gen);
per.w[1] = dist(gen);
per.w[2] = dist(gen);
//-- print random numbers
cout <<"INIT "<< "W0: " << per.w[0] <<" W1: " << per.w[1] << " W2: " << per.w[2] << endl;
const float n = 0.1; // Lerning rate N
int saida =0; // Output Y
long int epo = 0; // Simple Couter
bool erro = true; // Loop control
while(erro){
erro = false;
for (int amost = 0; amost < 4; ++amost) { // Repeat for the number of samples x0=-1, x1,x2
float u=0; // Variable for the somatory
for (int entrad = 0; entrad < 3; ++entrad) { // repeat for every sinaptic weight W0=θ , W1, W2
u = u + (per.w[entrad] * t0[amost][entrad]);// U <- Weights * Inputs
}
// u=u-per.w[0]; // some references sau to take θ and subtract from U, i tried but without success
saida = signal(u); // returns 1 or 0
cout << d[amost] << " <- esperado | encontrado -> "<< saida<< endl;
if(saida != d[amost]){ // if the output is not equal to the expected value
for (int ajust = 0; ajust < 3; ++ajust) {
per.w[ajust] = per.w[ajust] + n * (d[amost] - saida) * t0[amost][ajust]; // W <- W + ɳ * ((d - y) x) where
erro = true; // W: Weights, ɳ: Learning rate
} // d: Desired outputs, y: outputs
} // x: samples
epo++;
}
}
cout << "Epocas(Loops): " << epo << endl;
return per;
}
Main with testing part:
int main()
{
perceptron per = startTraining();
cout << "fim" << endl;
cout << "W0: " << per.w[0] <<" W1: " << per.w[1] << " W2: " << per.w[2] << endl;
while(true){
int x,y;
cin >> x >> y;
float u=0;
u = (per.w[1] * x);
u = u + (per.w[2] * y);
//u=u-per.w[0];
cout << signal(u) << endl;
}
return 0;
}

Answer 1

In your main(), re-enable the line you commented out. Alternatively, you could write it like this to make it more illuminating:
float u = 0.0f;
u += (per.w[0] * float (-1));
u += (per.w[1] * float (x));
u += (per.w[2] * float (y));
The thing is that you trained the perceptron with three inputs, the first being hard-wired to a "-1" (making the first weight w[0] act like a constant "bias"). Accordingly, in your training function, your u is the sum of all THREE of those weight-input product.
However, in the main() you posted, you omit w[0] completely, thus producing a wrong result.