Phase Transitions in a Neural Model of Problem Solving

  • Maria Pietronilla Penna
  • Eliano Pessa
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)


In order to model the process of acquisition of competence by children in solving problems of addition between integer numbers, we introduced a generalization of a celebrated neural network model, the Harmony Theory proposed by Smolensky. The generalization consists in allowing a variable number of atoms of knowledge, as well as variable strengths associated to them. The variation of these quantities depends on the rightness of the answer given by the network to a particular addition problem. We monitored the average values of correctly solved problems and the maximum values of ∆C/T, C being the specific heat and T the temperature, as defined by Smolensky, in order to find evidence for phase transitions in a simulated learning process. We found only partial evidence of such phase transitions. Besides, the network performance was strongly dependent on the structuration of initial dotation of knowledge atoms.


Phase Transition Simulated Annealing Network Performance Structure Case Initial Knowledge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    D.R. Hofstadter, Fluid concepts and creative analogies, Basic Books, New York 1995.Google Scholar
  2. [2]
    S.Kirpatrick, C.D.Gelatt, M.P.Vecchi. Optimization by simulated annealing. Science, 220:671–680, 1983.MathSciNetCrossRefGoogle Scholar
  3. [3]
    R.S.Siegler, Children’s Thinking, Third Edition, Prentice-Hall, Englewood Cliffs, NJ, 1998.Google Scholar
  4. [4]
    P.Smolensky. Information Processing in Dynamical Systems: Foundations of Harmony Theory. In J.L.McClelland, D.E.Rumelhart, editors, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. I, pages 154–281, MIT Press, Cambridge MA, 1986.Google Scholar

Copyright information

© Springer-Verlag London Limited 2002

Authors and Affiliations

  • Maria Pietronilla Penna
    • 1
  • Eliano Pessa
    • 1
  1. 1.Dipartimento di Filosofia — Sezione PsicologiaUniversità degli Studi di PaviaPaviaItaly

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