Universal approximation just says there exists a solution, not that there's a reasonable way to find it with a bounded amount of training data. The networks used in proofs typically have contrived and impractical architectures.
The problem that remains is how effective is the learning.
The distinction I'm trying to draw is a tiny bit nuanced - since we know NN's are broadly applicable if we can figure out how to train them, the posters "can NN be used here" is really "can we figure out how to train it". My question is, since Sudoko solution obviously has better, non NN approaches, does spending time on that lead to anything generally useful, or would you be better off spending the same time working out how to train a NN on a more appropriate problem domain?
