HN isn't an academic publishing track, it's a reflection of what the world actually posts on the internet. You're free to not like the titles some people use to get eyeballs on their content, but this was clearly not clickbait warranting removal, and it's certainly not HN's job to police page titles on the wider web: we just upvote the cool content, and if enough people like it, it hits the front page.
So really, you're complaining that not enough people on HN mind catchy titles enough to downvote a post based on its cover, rather than the book it links to =)
What about discontinuous functions?
Do we have tight error bounds proofs for neural networks as approximators ?
It doesn't tell you whether for a particular function f:
- a particular network structure is suitable,
- a trained network with particular weight value is suitable,
and it obviously doesn't answer the most useful question:
- given this network with this weights, what's the largest approximation error for this function f?
There are many approximation methods in approximation theory that can answer this last question.
Do we have these answers for neural networks?
Not in general that I'm aware of.
I agree the result is not practical, but you asked what is known. There have been some refinements (the citations on that page give a reasonable flavor, fwiw).