Paper available in Neuroprose

[Hong Chen]

Ftp-Host: archive.cis.ohio-state.edu
Ftp-Filename: /pub/neuroprose/chen.dynamic_approx.ps.Z


The following paper chen.dynamic_approx.ps.Z (28 pages) is now
available via anonymous ftp from the neuroprose archive.  It appeared
in Nov. issue (1993) of IEEE Transactions on Neural Networks.

----------------------------------------------------------------------


        Approximations of Continuous Functionals by Neural Networks
               with Application to Dynamical Systems


                         Tianping Chen
                    Department of Mathematics
                        Fudan University
                      Shanghai, P.R. China


                           Hong Chen
                     VLSI Libraries, Inc.
                       3135 Kifer Road
                     Santa Clara, CA 95052
                             USA


ABSTRACT:	The main concern of this paper is to give several
strong results on neural network representation in an explicit form.
Under very mild conditions, a functional defined on a compact set in
C[a,b] or L^p[a,b], spaces of infinite dimensions, can be approximated
arbitrarily well by a neural network with one hidden layer.  In
particular, if U is a compact set in C[a,b], sigma is a bounded
sigmoidal function, and f is a continuous functional defined on U,
then for all u in U, f(u) can be approximated by the summation:

       c_i sigma( sum_{j=0}^m xi_{i,j} u(x_j) + theta_i)

where c_i, xi_{ij}, theta_i are real numbers. u(x_j) is the value of u
evaluated at point x_j.  These results are a significant development
beyond existing works, where theorems of approximating continuous
functions defined on R^n, a space of finite dimension by neural
networks with one hidden layer were given.  Finally, all the results
are shown applicable to the approximation of the output of dynamical
systems at any particular time.

----------------------------------------------------------------------


             Instruction for retrieving this paper:

unix% ftp archive.cis.ohio-state.edu

ftp-login: anonymous
ftp-password: <your email address>

ftp> cd pub/neuroprose
ftp> binary
ftp> get chen.dynamic_approx.ps.Z
ftp> bye

unix% uncompress chen.dynamic_approx.ps.Z

unix% lpr chen.dynamic_approx.ps    (or however you print postscript)