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Capacity of Structured Multilayer Networks with Shared Weights

Summary: Capacity of Structured Multilayer Networks
with Shared Weights
Sabine Kr¨oner 1 and Reinhard Moratz 2
1 Technische Informatik I, TU Hamburg­Harburg, D­21071 Hamburg
2 AG Angewandte Informatik, Universit¨at Bielefeld, Postfach 100131,
D­33501 Bielefeld, Germany
Abstract. The capacity or Vapnik­Chervonenkis dimension of a feedfor­
ward neural architecture is the maximum number of input patterns that
can be mapped correctly to fixed arbitrary outputs. So far it is known
that the upper bound for the capacity of two­layer feedforward architec­
tures with independent weights depends on the number of connections
in the neural architecture [1].
In this paper we focus on the capacity of multilayer feedforward networks
structured by shared weights. We show that these structured architec­
tures can be transformed into equivalent conventional multilayer feed­
forward architectures. Known estimations for the capacity are extended
to achieve upper bounds for the capacity of these general multi­layer
feedforward architectures. As a result an upper bound for the capacity
of structured architectures is derived that increases with the number of
independent network parameters. This means that weight sharing in a


Source: Albert-Ludwigs-Universität Freiburg, Institut für Informatik,, Lehrstuhls für Mustererkennung und Bildverarbeitung


Collections: Computer Technologies and Information Sciences