Training a multilayer Neural Network with XOR training set

Question

Selim Özel on 3 Feb 2012

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https://www.mathworks.com/matlabcentral/answers/27946-training-a-multilayer-neural-network-with-xor-training-set

Commented: Ghiordy Ferney Contreras Contreras on 17 Jun 2022

I'm trying to understand neural networks by training one with XOR training data. If I use training data of "and" or "or" functions neural network works fine. On the other hand it does not achieve satisfactory results with XOR, although there is a hidden layer with non-linear sigmoid activation function.

Can someone take a look at the code and guide me?

Thank you

clear all;
close all;
clc;
training_set = [ 0 0 0; 
               0 1 1; 
               1 0 1; 
               1 1 0]; 
[row_set column_set] = size(training_set);
y_test = ones(row_set,1);
w = 0.01*randn(3,2); [row column]=size(w);
delta_w = ones(3,2);
v = 0.01*randn(3,1); 
delta_v = ones(3,1); 
z = ones(3,1);
n = 1;
iteration = 0;
while(iteration < 1000)   
    i = randint(1,1,[1 row_set]);
    x1 = training_set(i,1);
    x2 = training_set(i,2);
    x = [1 ;x1 ;x2];
    for h=1:1:column
        z(h+1) = sigmoid(w(:,h)'*x); % Computes hidden layer   
        %z(h+1) = myStep(w(:,h)'*x);
    end
    %y = myStep(v'*z); % Computes output from hidden layer
    y = sigmoid(v'*z);
    delta_v = n*(training_set(i,column_set)-y)*z;
    for h=1:1:column
        delta_w(:,h) =  n*((training_set(i,column_set)-y)*v(h+1))*z(h+1)*(1-z(h+1))*x;
    end
    w = delta_w + w;
    v = delta_v + v;
    iteration = iteration + 1;
end
 for i=1:1:length(training_set)
    x1 = training_set(i,1);   
    x2 = training_set(i,2);   
    x = [1 ;x1 ;x2];    
    for h=1:1:column
        z(h+1) = sigmoid(w(:,h)'*x); % Computes hidden layer        
    end     
    if (sigmoid(v'*z) > 0.5) y_test(i) =1; else y_test(i)=0; end;
    %y_test(i) = sigmoid(v'*z);
 end
 if (y_test == training_set(:,column_set))
     'Correct match!'
 else
     'Non-Correct match!'
 end