Neural networks process in constant time per input/output (token or whatever). But some prompts could produce more tokens.
As you increase the size of the window, doesn't the size of the NN have to increase? So if you want to just use an NN for this, the bigger the problem it can handle, the bigger the window, so the longer per token produced; but also the more tokens produced, so it's longer on that front as well. I don't know if that adds up to polynomial time or not.
Note well: I'm not disagreeing with your overall assertion. I don't know if NNs can do this; I'm inclined to think they can't. All I'm saying is that even NNs are not constant time in problem size.
As you increase the size of the window, doesn't the size of the NN have to increase? So if you want to just use an NN for this, the bigger the problem it can handle, the bigger the window, so the longer per token produced; but also the more tokens produced, so it's longer on that front as well. I don't know if that adds up to polynomial time or not.
Note well: I'm not disagreeing with your overall assertion. I don't know if NNs can do this; I'm inclined to think they can't. All I'm saying is that even NNs are not constant time in problem size.