Threshold-induced phase transitions in perceptrons

West, Ansgar H. L. and Saad, David (1997). Threshold-induced phase transitions in perceptrons. Journal of Physics A: Mathematical and General, 30 (10), pp. 3471-3496.

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.

Publication DOI: https://doi.org/10.1088/0305-4470/30/10/023
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: Copyright of Institute of Physics
Uncontrolled Keywords: boolean perceptron,spherical or Ising constraint,replica symmetry breaking (RSB) treatment,second-order phase transition,Physics and Astronomy(all),Statistical and Nonlinear Physics,Mathematical Physics
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://iopscien ... -4470/30/10/023 (Publisher URL)
Published Date: 1997-05-21
Authors: West, Ansgar H. L.
Saad, David ( 0000-0001-9821-2623)

Download

[img]

Version: Accepted Version

| Preview

Export / Share Citation


Statistics

Additional statistics for this record