The question comes from the following scenario, assume we have the traveler problem which is NP (the one where a traveler wants to visit all countries with the lowest cost(by summing up all flights))
So basically Neural Network can not just predict, but generate results from things they've learned, for instance, training a network on various test cases of the aforementioned problem, after a proper training may result with the optimal result, something which is computationally finite, which happens on a computer, which can be imitated by a Turing Machine, and finally inferring that a problem which is considered NP falls into the category of P.
I would like to hear your thoughts of what point am I missing here
Some might say that because you're depending on a Gradient-Descent or so, you're already missing the optimum finding, but for me, it looks like the NN can actually learn the better paths and find an optimum. Although it sounds like maintaining several local-best spots in our search dimension but something tells me there's a difference here