Preprint on Radial Basis Function Neural Networks

[Michael Schmitt]

Dear Colleagues,

a preprint of the paper

"Radial basis function neural networks have superlinear VC dimension"
by Michael Schmitt,
accepted for the 14th Annual Conference on Computational Learning Theory

COLT'2001,

is available on-line from

http://www.ruhr-uni-bochum.de/lmi/mschmitt/rbfsuper.ps.gz
(19 pages gzipped PostScript).

Regards,

Michael Schmitt

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TITLE: Radial basis function neural networks have superlinear VC
dimension

AUTHOR: Michael Schmitt

ABSTRACT
  We establish superlinear lower bounds on the Vapnik-Chervonenkis
  (VC) dimension of neural networks with one hidden layer and local
  receptive field neurons. As the main result we show that every
  reasonably sized standard network of radial basis function (RBF)
  neurons has VC dimension $\Omega(W\log k)$, where $W$ is the number
  of parameters and $k$ the number of nodes. This significantly
  improves the previously known linear bound. We also derive
  superlinear lower bounds for networks of discrete and continuous
  variants of center-surround neurons. The constants in all bounds are
  larger than those obtained thus far for sigmoidal neural networks
  with constant depth.

  The results have several implications with regard to the
  computational power and learning capabilities of neural networks
  with local receptive fields.  In particular, they imply that the
  pseudo dimension and the fat-shattering dimension of these networks
  is superlinear as well, and they yield lower bounds even when the
  input dimension is fixed.  The methods presented in this paper might
  be suitable for obtaining similar results for other kernel-based
  function classes.


--
Michael Schmitt
LS Mathematik & Informatik, Fakultaet fuer Mathematik
Ruhr-Universitaet Bochum, D-44780 Bochum, Germany
Phone: +49 234 32-23209 , Fax: +49 234 32-14465
http://www.ruhr-uni-bochum.de/lmi/mschmitt/