Polynomial functions can be realized by finite size multilayer feedforward neural networks

Abstract

The authors present an analytic method to construct polynomial functions by multilayer feedforward neural networks. Because the polynomials consist of multiplication operations and linear weighted summations, if the multiplier can be constructed by a neural network, any polynomial function can be represented by a neural network (a single unit already has the function of weighted summation). The authors try to construct a neural network module with one hidden layer that works as a multiplier (it is referred to as a neural multiplier module). It is shown, in principle, that the multiplier can be approximated by a neural network with four hidden units, with arbitrary accuracy on a bounded closed set.<>