[benibraz]

A wide enough NN can represent any arbitrary binary function, but it's not obvious that one can learn it.

[labelbias]

Yet the best NNs are deep, not wide.

[benibraz]

What do you mean by 'the best'? Deeper architectures are popular because they quiet easy to train. They do work well in practice on many tasks (especially vision) but they have their limits.

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...