Paper available in Neuroprose

[Kurt Hornik]

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A survey of learning in linear neural networks (24 pages)
Pierre Baldi (Caltech) && Kurt Hornik (TU Wien, Austria)

ABSTRACT:
  Networks of linear units are the simplest kind of networks, where
  the basic questions related to learning, generalization, and
  self-organisation can sometimes be answered analytically.  We survey
  most of the known results on linear networks, including: (1)
  back-propagation learning and the structure of the error function
  landscape; (2) the temporal evolution of generalization; (3)
  unsupervised learning algorithms and their properties.  The
  connections to classical statistical ideas, such as principal
  component analysis (PCA), are emphasized as well as several simple
  but challenging open questions.  A few new results are also
  spread across the paper, including an analysis of the effect of
  noise on back-propagation networks and a unified view of all
  unsupervised algorithms. 

-Kurt Hornik (Kurt.Hornik at ci.tuwien.ac.at)