Why use softmax as opposed to standard normalization?

Question

In the output layer of a neural network, it is typical to use the softmax function to approximate a probability distribution:

Answer 1

The choice of the softmax function seems somehow arbitrary as there are many other possible normalizing functions. It is thus unclear why the log-softmax loss would perform better than other loss alternatives.

From "An Exploration of Softmax Alternatives Belonging to the Spherical Loss Family" https://arxiv.org/abs/1511.05042

The authors explored some other functions among which are Taylor expansion of exp and so called spherical softmax and found out that sometimes they might perform better than usual softmax.