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Analog neural nets with gaussian or other common noise distribution cannot recognize arbitrary regular languages.

Authors
  • Maass, W
  • Sontag, E D
Type
Published Article
Journal
Neural computation
Publication Date
Apr 01, 1999
Volume
11
Issue
3
Pages
771–782
Identifiers
PMID: 10085429
Source
Medline
License
Unknown

Abstract

We consider recurrent analog neural nets where the output of each gate is subject to gaussian noise or any other common noise distribution that is nonzero on a sufficiently large part of the state-space. We show that many regular languages cannot be recognized by networks of this type, and we give a precise characterization of languages that can be recognized. This result implies severe constraints on possibilities for constructing recurrent analog neural nets that are robust against realistic types of analog noise. On the other hand, we present a method for constructing feedforward analog neural nets that are robust with regard to analog noise of this type.

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