Preprint available

[Ralph Linsker]

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                        How to Generate Ordered Maps by
                       Maximizing the Mutual Information
                       Between Input and Output Signals*

                                 Ralph Linsker

              IBM Research Division, T. J. Watson Research Center,
                   P. O. Box 218, Yorktown Heights, NY 10598

          *To appear in: Neural Computation 1(3):396-405 (1989).

          A learning rule that performs gradient ascent in the average
          mutual information  between input and output  signals is de-
          rived  for a  system having  feedforward and  lateral inter-
          actions.   Several processes  emerge as  components of  this
          learning rule:  Hebb-like modification, and  cooperation and
          competition among processing nodes.

          Topographic map formation is demonstrated using the learning
          rule.  An  analytic expression  relating the  average mutual
          information to  the response  properties of nodes  and their
          geometric  arrangement is  derived in  certain cases.   This
          yields a relation between the local map magnification factor
          and the  probability distribution  in the input  space.  The
          results provide new links  between unsupervised learning and
          information-theoretic optimization in a system whose proper-
          ties are biologically motivated.