MULTILAYER FEEDFORWARD NETWORKS WITH NON-POLYNOMIAL ACTIVATION FUNCTIONS CAN APPROXIMATE ANY FUNCTION
Moshe Leshno, Shimon Schocken · Faculty Digital Archive (New York University Florence) · 1991
Several researchers characterized the activation functions under which multilayer feedforward networks can act as universal approximators. We show that all the characterizations that were reported thus far in the literature ark special cases of the following general result: a standard multilayer feedforward network can approximate any continuous function to any degree of accuracy if and only if the network's activation functions are not polynomial. We also emphasize the important role of the threshold, asserting that without it the last theorem doesn't hold.