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NeuroCOLT
Technical Report NC-TR-01-103
2001-103
Product
Unit Neural Networks with Constant Depth and Superlinear VC Dimension
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.
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Postscript
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