IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7908-2656-2_3.html
   My bibliography  Save this book chapter

Geometry of Learning in Multilayer Perceptrons

In: COMPSTAT 2004 — Proceedings in Computational Statistics

Author

Listed:
  • Shun-ichi Amari

    (RIKEN, Brain Science Institute)

  • Hyeyoung Park

    (Kyungpook National University, Dept. of Computer Science, College of Natural Science)

  • Tomoko Ozeki

    (RIKEN, Brain Science Institute)

Abstract

Neural networks provide a good model of learning from statistical data. Multilayer perceptron is regarded as a statistical model in which a nonlinear input-output relation is realized. The set of multilayer perceptrons forms a statistical manifold in which learning and estimation takes place. This is a Riemannian manifold with Fisher information metric. However, such a hierarchical model includes algebraic singularities at which the Fisher information matrix degenerates. This causes various difficulties in learning and statistical estimation. The present paper elucidates the structure of singularities, and how they influence the behavior of learning. The paper describes a new learning algorithm, named the natural gradient method, to overcome such difficulties. Various statistical problems in singular models are discussed, and the models selection criteria (AIC and MDL) are studied in this framework.

Suggested Citation

  • Shun-ichi Amari & Hyeyoung Park & Tomoko Ozeki, 2004. "Geometry of Learning in Multilayer Perceptrons," Springer Books, in: Jaromir Antoch (ed.), COMPSTAT 2004 — Proceedings in Computational Statistics, pages 49-60, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2656-2_3
    DOI: 10.1007/978-3-7908-2656-2_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-7908-2656-2_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.