MSE Vs Entropy (2)


This is the mean square error representation for a binary classification neural network, in which, our model outputs only one value; as a result, the mean square error graph has only one value which is globally optimal.
Convex





While the mean square error representation for a categorical neural network, in which, our model outputs more than one value; the mean square error graph has more than one value which is locally sufficient solutions. As a result, if we use the mean square error, the problem will have no solution, and for that reason, we use the cross-entropy loss instead. 
Nonconvex


Finally, here is the cross-entropy graph:

Loss Functions in Deep Learning | Deep Learning Academy

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