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Neural Teleportation

Author

Listed:
  • Marco Armenta

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
    Department of Mathematics, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
    These authors contributed equally to this work.)

  • Thierry Judge

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
    These authors contributed equally to this work.)

  • Nathan Painchaud

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada)

  • Youssef Skandarani

    (Department of Computer Science, Université de Bourgogne Franche-Comte, 21000 Dijon, France)

  • Carl Lemaire

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada)

  • Gabriel Gibeau Sanchez

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada)

  • Philippe Spino

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada)

  • Pierre-Marc Jodoin

    (Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada)

Abstract

In this paper, we explore a process called neural teleportation, a mathematical consequence of applying quiver representation theory to neural networks. Neural teleportation teleports a network to a new position in the weight space and preserves its function. This phenomenon comes directly from the definitions of representation theory applied to neural networks and it turns out to be a very simple operation that has remarkable properties. We shed light on the surprising and counter-intuitive consequences neural teleportation has on the loss landscape. In particular, we show that teleportation can be used to explore loss level curves, that it changes the local loss landscape, sharpens global minima and boosts back-propagated gradients at any moment during the learning process.

Suggested Citation

  • Marco Armenta & Thierry Judge & Nathan Painchaud & Youssef Skandarani & Carl Lemaire & Gabriel Gibeau Sanchez & Philippe Spino & Pierre-Marc Jodoin, 2023. "Neural Teleportation," Mathematics, MDPI, vol. 11(2), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:480-:d:1037552
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