M. Leshno et al., MULTILAYER FEEDFORWARD NETWORKS WITH A NONPOLYNOMIAL ACTIVATION FUNCTION CAN APPROXIMATE ANY FUNCTION, Neural networks, 6(6), 1993, pp. 861-867
Several researchers characterized the activation function under which
multilayer feedforward networks can act as universal approximators. We
show that most of all the characterizations that were reported thus f
ar in the literature are special cases of the following general result
: A standard multilayer feedforward network with a locally bounded pie
cewise continuous activation function can approximate any continuous f
unction to any degree of accuracy if and only if the network's activat
ion function is not a polynomial. We also emphasize the important role
of the threshold, asserting that without it the last theorem does not
hold.