Threshold-induced phase transitions in perceptrons

Ansgar H. L. West, David Saad

Research output: Contribution to journalArticlepeer-review


Error rates of a Boolean perceptron with threshold and either spherical or Ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one-step replica symmetry breaking (RSB) treatment. For unbiased output distribution and non-zero stability of the patterns, we find a critical load, α p, above which two solutions to the saddlepoint equations appear; one with higher free energy and zero threshold and a dominant solution with non-zero threshold. We examine this second-order phase transition and the dependence of α p on the required pattern stability, κ, for both one-step RSB and replica symmetry (RS) in the spherical case and for one-step RSB in the Ising case.

Original languageEnglish
Pages (from-to)3471-3496
Number of pages26
JournalJournal of Physics A: Mathematical and General
Issue number10
Publication statusPublished - 21 May 1997

Bibliographical note

Copyright of Institute of Physics


  • boolean perceptron
  • spherical or Ising constraint
  • replica symmetry breaking (RSB) treatment
  • second-order phase transition


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