Why does the sigma in the output of your model represent the uncertainty/variance?

[hihunjin]

Hi. Im Heonjin.

I have a question on your paper2017/phd_thesis.

Above image is from your phd_thesis page number 38.(or 2017 paper page #5)

I'm not sure that this $\sigma^2$ represents the aleatoric uncertainty, a.k.a. variance. This is juat an output of a model. You used this in your loss for training. This is not calculated by the $y$ itself. Could you explain this?
In my opinion, you should calculate this variance $\sigma^2$ from the $y_i$s.