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    $\begingroup$ why isn't this the best answer ? pretty darned intuitive and completely scientific $\endgroup$ Commented Jun 2, 2019 at 12:41
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    $\begingroup$ " it does not imply that your activation function would perform worse", it can actually and cause a "learning slowdown". It's not just about easy computation, unlike mse, cross entropy helps to cancel out the sigmaprime term, which can be very small if the output of neuron is close to 1/0 (this causes the gradients of the cost function to be very small as well). $\endgroup$ Commented Mar 10, 2021 at 5:39