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For questions about the back-propagation (aka "backprop", and often abbreviated as "BP") algorithm, which is used to compute the gradient of the objective function (e.g. the mean squared error) with respect to the parameters (or weights) of the neural network, when trained with gradient descent.
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How to compute the gradient of the cross-entropy loss function with respect to the parameter...
ij} - \frac{e^{z_i}e^{z_j}}{(\sum_k e^{z_k})^2}
$$
Consider a cost $C$, and we wish to calculate the derivative with respect to the weights of the last layer, that is, we are running the first step of backpropagation …