A wide enough NN can represent any arbitrary binary function, but it's not obvious that one can learn it.
Infinite wide networks are a newly active field and has recently shown some promising results, theoretically [1, 2] and empirically [3].
[1] https://arxiv.org/abs/2001.06931 [3] https://arxiv.org/abs/1806.07572 [2] https://ai.googleblog.com/2020/03/fast-and-easy-infinitely-w...