### Abstract

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 language | English |
---|---|

Pages (from-to) | 849-860 |

Number of pages | 12 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Generalization ability of a perceptron with nonmonotonic transfer function'. Together they form a unique fingerprint.

## Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*58*(1), 849-860. https://doi.org/10.1103/PhysRevE.58.849