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

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Platon 2013-6-6

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采纳的回答： Greg Heath

George Cybenko had prouven that NN are universal approximators for continuous functions (see http://en.wikipedia.org/wiki/Universal_approximation_theorem). Can Neural Network approximate piecewise continuous functions? In particular in MATLAB NN tool box?

I need a response with references.

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Walter Roberson 2013-6-8

A homework question?

Platon 2013-6-11

编辑：Platon 2013-6-11

No not really! But If you have a relevant response I thank you in advance

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Greg Heath 2013-6-8

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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 comp.ai.neural-nets newsgroup and FAQ before Googling.

Hope this helps.

Thank you for formally accepting my answer

Greg

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