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What do you mean by "good approximation"? Arbitrarily close?

Can you give an example of such a function? They very well may exist. But I think we can agree that non-differentiability of the target function is not sufficient.

The function that describes the neural network itself has to be differentiable. Whether we can create a differentiable function/NN for any kind of input remains to be shown.



Can you give an example of such a function?

Brownian motion. Try using a NN to model stock prices (not Brownian exactly, but same concept).


> Try using a NN to model stock prices

IIRC, the first neural network book I read in the 1990s had that as the big illustrative application in the latter part of the book.


Yes, but it doesn't work well.

There are plenty of other time series problems where NNs don't outperform classical methods such as ARIMA.


Once again I ask: What do you mean with "works well". Just because some other ML method is better in practice doesn't mean that a NN can not achieve the same degree of approximation in theory.


What do you mean with "works well"

There is no empirical data to support that it is more effective than other methods.

Theory is not that valuable when evaluating papers in AI. It is all about the empirical results.


I'm wondering if the ARIMA models aren't a very simple case of NN (time convolution+regression) ?




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