RIDGE POLYNOMIAL NETWORKS

This paper presents a  polynomial  connectionist  network  called
RIDGE POLYNOMIAL NETWORK (RPN) that can uniformly approximate any
continuous function on a compact set in  multi-dimensional  input
space  $Re^{d}$, with arbitrary degree of accuracy.  This network
provides a more efficient and regular  architecture  compared  to
ord  inary  higher-order  feedforward  networks while maintaining
their fast learning propert y.

The ridge polynomial network is a generalization of the  pi-sigma
network  and   u  ses  a special form of ridge polynomials. It is
shown that any multivariate polynomial can  be  repre  sented  in
this  form,  and realized by an RPN.  Approximation capability of
the RPNs is shown by this representation theorem an d the  Weier-
strass  polynomial approximation theorem.  The RPN provides a na-
tural  mechanism  for  incremental  network  growth.   Simulation
results  on  a  surface  fitting  problem,  the classification of
high-dim ensional data and the realization of a multivariate  po-
lynomial  function  are given to highligh t the capability of the
network.   In  particular,  a  constructive   learning  algorithm
developed for the network is shown to yield smooth generalization
and steady learning.