Comments on "Approximation capability in C(Rn) by multilayer feedforward networks and related problems"

In the above paper Chen et al. investigated the capability of uniformly approximating functions in C(Rn) by standard feedforward neural networks. They found that the boundedness condition on the sigmoidal function plays an essential role in the approximation, and conjectured that the boundedness of the sigmoidal function is a necessary and sufficient condition for the validity of the approximation theorem. However, we find that the conjecture is not correct, that is, the boundedness condition is not sufficient or necessary in C(Rn). Instead, boundedness and unequal limits at infinities conditions on the activation functions are sufficient, but not necessary in C(Rn).