IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v610y2023ics0378437122009591.html
   My bibliography  Save this article

Emergent scale invariance in neural networks

Author

Listed:
  • Katsnelson, M.I.
  • Vanchurin, V.
  • Westerhout, T.

Abstract

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a scale-invariant state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales.

Suggested Citation

  • Katsnelson, M.I. & Vanchurin, V. & Westerhout, T., 2023. "Emergent scale invariance in neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    • Handle: RePEc:eee:phsmap:v:610:y:2023:i:c:s0378437122009591
    DOI: 10.1016/j.physa.2022.128401
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122009591
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.128401?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Menesse, Gustavo & Marin, Bóris & Girardi-Schappo, Mauricio & Kinouchi, Osame, 2022. "Homeostatic criticality in neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:eee:phsmap:v:610:y:2023:i:c:s0378437122009591. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

      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.