Let say we want to do regression for simple
f = x * y using standart deep neural network.
I remember that there are reseraches that tells that NN with one hiden layer can apoximate any function, but I have tried and without normalization NN was unable approximate even this simple multiplication. Only log-normalization of data helped
m = x*y => ln(m) = ln(x) + ln(y).
But that looks like a cheat. Can NN do this without log-normalization? The unswer is obviously(as for me) - yes, so the question is more what should be type/configuration/layout of such NN?