It took me quite a lot of time to understand the question, though. I do not post the test here as I am not sure if I am permitted to do that. This post serves for my personal use. Even though the original questions are written in Vietnamese, I will be writing my solutions in [...]
We starts with the formula (1) of the paper. We have: By chain rule, we have: We also have: – the th element of . – the th element of . So:
Show that is minimized at . Now we need to check what type of the found critical point is: So the found critical point is the global minimum.
The notation of this proof comes from the article Softmax Regression by UFLDL Tutorial. We have: When : When : Now we look carefully at the [...]