So for every computable function, there is a neural network that computes it. That doesn't say anything about size or efficiency It also doesn't say anything a

So for every computable function, there is a neural network that computes it. That doesn't say anything about size or efficiency It also doesn't say anything about finding the desired function, rather than a different function which approximates it closely on some compact set but diverges from it outside that set. That's the trouble with extrapolation: you don't know how to compute the function you're looking for because you don't know anything about its behaviour outside of your sample.