Threshold-induced phase transitions in perceptrons

Ansgar H. L. West, David Saad

Research output: Contribution to journalArticle

Abstract

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
Volume30
Issue number10
DOIs
Publication statusPublished - 21 May 1997

Fingerprint

self organizing systems
Replica
Perceptron
replicas
Phase Transition
Symmetry Breaking
broken symmetry
thresholds
Ising
Critical Load
output
Output
Saddlepoint
Biased
Error Rate
High Energy
Free Energy
free energy
Symmetry
Zero

Bibliographical note

Copyright of Institute of Physics

Keywords

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

Cite this

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Threshold-induced phase transitions in perceptrons. / West, Ansgar H. L.; Saad, David.

In: Journal of Physics A: Mathematical and General, Vol. 30, No. 10, 21.05.1997, p. 3471-3496.

Research output: Contribution to journalArticle

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