IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3788-d1533619.html
   My bibliography  Save this article

Imposing Star-Shaped Hard Constraints on the Neural Network Output

Author

Listed:
  • Andrei Konstantinov

    (Higher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, Russia
    These authors contributed equally to this work.)

  • Lev Utkin

    (Higher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, Russia
    These authors contributed equally to this work.)

  • Vladimir Muliukha

    (Higher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 St. Petersburg, Russia
    These authors contributed equally to this work.)

Abstract

A problem of imposing hard constraints on the neural network output can be met in many applications. We propose a new method for solving this problem for non-convex constraints that are star-shaped. A region produced by constraints is called star-shaped when there exists an origin in the region from which every point is visible. Two tasks are considered: to generate points inside the region and on the region boundary. The key idea behind the method is to generate a shift of the origin towards a ray parameterized by the additional layer of the neural network. The largest admissible shift is determined by the differentiable Ray marching algorithm. This allows us to generate points which are guaranteed to satisfy the constraints. A more accurate modification of the algorithm is also studied. The proposed method can be regarded as a generalization of the methods for convex constraints. Numerical experiments illustrate the method by solving machine-learning problems. The code implementing the method is publicly available.

Suggested Citation

  • Andrei Konstantinov & Lev Utkin & Vladimir Muliukha, 2024. "Imposing Star-Shaped Hard Constraints on the Neural Network Output," Mathematics, MDPI, vol. 12(23), pages 1-17, November.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3788-:d:1533619
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3788/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/23/3788/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:12:y:2024:i:23:p:3788-:d:1533619. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.