I think it's mostly accurate in L2 norm and not point by point. So every functio... | Hacker News

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		leni536 on Aug 21, 2015 \| parent \| context \| favorite \| on: A visual proof that neural nets can compute any fu... I think it's mostly accurate in L2 norm and not point by point. So every function in L2 can be approximated arbitrarily in L2 norm.

chestervonwinch on Aug 21, 2015 [–]

This is not true. The theorem proves point-wise convergence for a continuous functions on a compact subset of R^n. See theorem 2, page 6: http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf

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