Bounds on the number of hidden neurons in multilayer perceptrons

Fundamental issues concerning the capability of multilayer perceptrons with one hidden layer are investigated. The studies are focused on realizations of functions which map from a finite subset of Eⁿ into E^d. 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 Eⁿ into E^d. A nontrivial lower bound is also obtained for realizations of injective functions. This result can be applied in studies of pattern recognition and database retrieval. An upper bound is given for realizing binary-valued functions that are related to pattern-classification problems