Cross entropy applied to backpropagation in neural network - c++

Question

I watched this awesome video by Dave Miller on making a neural network from scratch in C++ here: https://vimeo.com/19569529
Here is the full source code referenced in the video: http://inkdrop.net/dave/docs/neural-net-tutorial.cpp
It uses mean squared error as the cost function. I'm interested in using a neural network for binary classification though and so would like to use cross-entropy as the cost function. I was hoping to add this to this code if possible, since I've already been playing around with it.
How would that be applied specifically here?
Would the only difference be in how the error is calculated for the output layer...or do the equations change all the way through backpropogation?
Does anything change at all? Is MSE versus cross-entropy solely used to get an idea of the overall error and not independently relevant to backpropogation?
Edit for clarity:
Here are the relevant functions.
//output layer - seems like error is just target value minus calculated value
void Neuron::calcOutputGradients(double targetVal)
{
double delta = targetVal - m_outputVal;
m_gradient = delta * Neuron::transferFunctionDerivative(m_outputVal);
}
double Neuron::sumDOW(const Layer &nextLayer) const
{
double sum = 0.0;
// Sum our contributions of the errors at the nodes we feed.
for (unsigned n = 0; n < nextLayer.size() - 1; ++n) {
sum += m_outputWeights[n].weight * nextLayer[n].m_gradient;
}
return sum;
}
void Neuron::calcHiddenGradients(const Layer &nextLayer)
{
double dow = sumDOW(nextLayer);
m_gradient = dow * Neuron::transferFunctionDerivative(m_outputVal);
}
void Neuron::updateInputWeights(Layer &prevLayer)
{
// The weights to be updated are in the Connection container in the neurons in the preceding layer
for (unsigned n = 0; n < prevLayer.size(); ++n) {
Neuron &neuron = prevLayer[n];
double oldDeltaWeight = neuron.m_outputWeights[m_myIndex].deltaWeight;
//calculate new weight for neuron with momentum
double newDeltaWeight = eta * neuron.getOutputVal() * m_gradient + alpha * oldDeltaWeight;
neuron.m_outputWeights[m_myIndex].deltaWeight = newDeltaWeight;
neuron.m_outputWeights[m_myIndex].weight += newDeltaWeight;
}
}

Answer 1

Finally found the answer here: https://visualstudiomagazine.com/articles/2014/04/01/neural-network-cross-entropy-error.aspx
You only have to change how the error at the output layer is calculated.
The relevant function to be changed is:
void Neuron::calcOutputGradients(double targetVal)
For mean square errors use:
double delta = targetVal - m_outputVal;
m_gradient = delta * Neuron::transferFunctionDerivative(m_outputVal);
For cross entropy just use:
m_gradient = targetVal - m_outputVal;