I have a question. They show that any given depth-ell network, computing F, is w.h.p. approximated by some subnetwork of a random depth-2ell network. But there

I have a question. They show that any given depth-ell network, computing F, is w.h.p. approximated by some subnetwork of a random depth-2ell network. But there is a theorem that even depth-2 networks can approximate any continuous function F. If the assumptions were the same, then their theorem would imply any continuous function F is w.h.p. approximated by some subnetwork of a depth-4 network. So what is the difference in assumptions, i.e. what’s the significance of F being computed by a depth-ell network? What functions can a depth-ell+1 network approximate that a depth-ell network can’t? I’d guess it has to do with Lipschitz assumptions and bounded parameters but would be awesome if someone can clarify!