Technical Report

[ANDERSON%BROWNCOG.BITNET@MITVMA.MIT.EDU]

     A technical report is available from the Brown University
Department of Cognitive and Linguistic Sciences:

                       Technical Report 88-01
            Department of Cognitive and Linguistic Sciences
                         Brown University

          Representing Simple Arithmetic in Neural Networks

        Susan R. Viscuso, James A. Anderson and Kathryn T. Spoehr

     This report discuses neural network models of qualitative
     multiplication.  We review past research in magnitude representation
     and cognitive arithmetic.  We then develop a framework for
     building neural network models that exhibit behaviors that
     mimic the empirical results.  The simulations show that neural
     net models can carry out qualitative multiplication given
     an adequate representation of magnitude information.  It is
     possible to model a number of interesting psychological
     effects such as associative interference, practice effects,
     and the symbolic distance effect.  However, this set of
     simulations clearly shows that neural networks are not
     satisfactory as devices for doing accurate arithmetic.  It is
     possible to spend many hours of supercomputer CPU time teaching
     multiplication to a network, and still have a system that makes
     many errors.  If, however, instead of accuracy we view this
     simulation as developing a very simple kind of `number sense,'
     with the formation and use of internal representations
     of sizes of numbers, then the simulation is more interesting.
     When real mathematicians and real physicists think about
     mathematics and physics, they rarely use logic or formal
     reasoning, but use past experience and their intuitive understanding
     of the complex systems they work on.  We suspect a useful
     goal for network models may be to develop similar qualitative
     intuition in complex problem solving domains.

This technical report can be obtained by sending an email
message to Anderson at BROWNCOG  (BITNET) or a request to:

                   James A. Anderson
                   Department of Cognitive and Linguistic Sciences
                   Box 1978
                   Brown University
                   Providence, RI 02912

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