Generalization ability of a perceptron with nonmonotonic transfer function

Jun ichi Inoue, Hidetoshi Nishimori, Yoshiyuki Kabashima

Research output: Contribution to journalArticlepeer-review


We investigate the generalization ability of a perceptron with nonmonotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning algorithms. By the perceptron algorithm the generalization error is shown to decrease by the [Formula Presented]-law similarly to the case of a simple perceptron in a restricted range of the parameter [Formula Presented] characterizing the nonmonotonic transfer function. For other values of [Formula Presented], the perceptron algorithm leads to the state where the weight vector of the student is just opposite to that of the teacher. The Hebbian learning algorithm has a similar property; it works only in a limited range of the parameter. The conventional AdaTron algorithm does not give a vanishing generalization error for any values of [Formula Presented]. We thus introduce a modified AdaTron algorithm that yields a good performance for all values of [Formula Presented]. We also investigate the effects of optimization of the learning rate as well as of the learning algorithm. Both methods give excellent learning curves proportional to [Formula Presented]. The latter optimization is related to the Bayes statistics and is shown to yield useful hints to extract maximum amount of information necessary to accelerate learning processes.

Original languageEnglish
Pages (from-to)849-860
Number of pages12
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
Publication statusPublished - 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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