Answer to Q1) If sampling for next token do you need to apply mask during inference?
Yes you do! The models ability to transfer information across positions was trained in this manner, and changing it up will have unpredictable consequences. Let my try to give an example:
Tokens: 1:sally, 2:sold, 3:seashells, 4:on, 5:the, 6:____
In the above you are ...
It's not completely clear from your question, but it looks like you want to prove that exact inference in a Bayesian Network is both NP-Hard and P-Hard.
It appears that you have proven that it is NP-Hard, but are unsure how to show that it is also P-Hard.
This is more of a TCS question than an AI question, but shouldn't be too difficult. You just need to ...