Neural network does not learn XOR (converges to 0.5 output) - c++

Question

I wrote a multilayer perceptron which should be able to learn XOR. However, whatever I do it converges to an output of 0.5 for inputs (1,1), (0,1) and (1,0). While for the input (0,0) it converges to zero. Does anyone have an idea where my mistake is?
Forward pass:
void MLP::feedforward() {
for(int hidden = 0; hidden < nHidden; hidden++) {
hiddenNeurons.at(hidden) = 0;
for(int input = 0 ; input < nInput; input ++) {
hiddenNeurons.at(hidden) += inputNeurons.at(input)*weightItoH(input,hidden);
}
}
//Propagate towards the output layer
for(int i =0; i< nOutput; i ++) {
outputNeurons.at(i) = 0;
for(int j = 0; j <nHidden; j++) {
outputNeurons.at(i) += hiddenNeurons.at(j) * weightHtoO(j,i);
}
outputNeurons.at(i) = sigmoid(outputNeurons.at(i));
}
}
Backpropagation:
void MLP::backPropagation(int i) {
float learningRate = 0.75;
float error = desiredOutput[i] - outputNeurons[0];
// Calculate delta for output layer
for(int i=0; i<nOutput; i++) {
outputDelta.at(i) = error * dersigmoid(outputNeurons[i]);
}
//Calculate delta for hidden layer
for(int i = 0; i < nHidden; i++) {
hiddenDelta.at(i) = 0;//zero the values from the previous iteration
//add to the delta for each connection with an output neuron
for(int j = 0; j < nOutput; j ++) {
hiddenDelta.at(i) += outputDelta.at(j) * weightHtoO(i,j) ;
}
}
//Adjust weights Input to Hidden
for(int i = 0; i < nInput; i ++) {
for(int j = 0; j < nHidden; j ++) {
weightItoH(i,j) += learningRate * hiddenDelta.at(j);
}
}
//Adjust weights hidden to Output
for(int i = 0; i < nOutput; i++) {
for(int j = 0; j < nHidden; j ++) {
weightHtoO(j,i) += learningRate * outputDelta.at(i) * hiddenNeurons.at(j);
}
}
}
Input
nInputPatterns = 4;
inputPatterns.assign(nInputPatterns, vector<int>(2));
inputPatterns[0][0] = 1;
inputPatterns[0][1] = 1;
inputPatterns[1][0] = 0;
inputPatterns[1][1] = 1;
inputPatterns[2][0] = 1;
inputPatterns[2][1] = 0;
inputPatterns[3][0] = 0;
inputPatterns[3][1] = 0;
desiredOutput = {0,1,1,0};
Sigmoid function and macro's
#define sigmoid(value) (1/(1+exp(-value)));
#define dersigmoid(value) (value*(1-value));
//Macro's
#define weightItoH(input,hidden) weightsIH.at(nInput*hidden+input)
#define weightHtoO(hidden,output) weightsHO.at(nHidden*output+hidden)
C++ file: http://pastebin.com/8URZAHSy
Header file: http://pastebin.com/YiMXpmZX

Answer 1

There's no random initialization. This is needed to break the symmetry; else all your neurons learn the exact same values. That's effectively the same as having one neuron, and one neuron is insufficient for XOR.