Neural Networks are universal approximators, It is true for picewise continuous functions?

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George Cybenko had prouven that NN are universal approximators for continuous functions (see Can Neural Network approximate piecewise continuous functions? In particular in MATLAB NN tool box?
I need a response with references.

Accepted Answer

Greg Heath
Greg Heath on 8 Jun 2013
Yes. However, like fourier series, values at finite discontinuities will be the average of the left and right values.
If you don't have a text, my guess is that if you search on something like
neural uniform approximation
you should find something.
Try the newsgroup and FAQ before Googling.
Hope this helps.
Thank you for formally accepting my answer

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