BOUNDS ON THE NUMBER OF HIDDEN NEURONS IN MULTILAYER PERCEPTRONS

This paper investigates some fundamental issues concerning the capability of multilayer perceptrons with one hidden layer. The studies are focused on realizations of functions which map from a finite subset of E(n) into E(d). Both real-valued and binary-valued functions are considered. In particular, a least upper bound is derived for the number of hidden neurons needed to realize an arbitrary function which maps from a finite subset of E(n) into E(d). A nontrivial lower bound is also obtained for realizations of injective functions. This result will be useful in studying pattern recognition and database retrieval. In addition, an upper bound is given for realizing binary-valued functions that are related to pattern classification problems.