Preprints on Spiking and Product Unit Neural Networks

[Michael Schmitt]

Dear Colleagues,

the following two preprints are available on-line:

"Complexity of learning for networks of spiking neurons with nonlinear
synaptic interactions"
http://www.ruhr-uni-bochum.de/lmi/mschmitt/nonlinear.ps.gz
(8 pages gzipped PostScript),

"Product unit neural networks with constant depth and superlinear VC
dimension"
http://www.ruhr-uni-bochum.de/lmi/mschmitt/superlinear.ps.gz
(9 pages gzipped PostScript).

Both papers are going to be presented in talks at the International
Conference on Artificial Neural Networks ICANN 2001,
August 21-25, 2001, Vienna, Austria.

Regards,

Michael Schmitt

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TITLE: Complexity of Learning for Networks of Spiking Neurons with
  Nonlinear Synaptic Interactions

AUTHOR: Michael Schmitt

ABSTRACT
  We study model networks of spiking neurons where synaptic inputs
  interact in terms of nonlinear functions. These nonlinearities are
  used to represent the spatial grouping of synapses on the dendrites
  and to model the computations performed at local branches.  We
  analyze the complexity of learning in these networks in terms of the
  VC dimension and the pseudo dimension. Polynomial upper bounds on
  these dimensions are derived for various types of synaptic
  nonlinearities.

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TITLE: Product Unit Neural Networks with Constant Depth and
  Superlinear VC Dimension

AUTHOR: Michael Schmitt

ABSTRACT
  It has remained an open question whether there exist product unit
  networks with constant depth that have superlinear VC dimension. In
  this paper we give an answer by constructing two-hidden-layer
  networks with this property.  We further show that the pseudo
  dimension of a single product unit is linear. These results bear
  witness to the cooperative effects on the computational capabilities
  of product unit networks as they are used in practice.



--
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/