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Appearance of Random Matrix Theory in deep learning

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  • Baskerville, Nicholas P.
  • Granziol, Diego
  • Keating, Jonathan P.

Abstract

We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover agreement with Gaussian Orthogonal Ensemble statistics across several network architectures and datasets. These results shed new light on the applicability of Random Matrix Theory to modelling neural networks and suggest a role for it in the study of loss surfaces in deep learning.

Suggested Citation

  • Baskerville, Nicholas P. & Granziol, Diego & Keating, Jonathan P., 2022. "Appearance of Random Matrix Theory in deep learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    • Handle: RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009432
    DOI: 10.1016/j.physa.2021.126742
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    References listed on IDEAS

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    1. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
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    Cited by:

    1. Chinea Manrique de Lara, Alejandro, 2023. "On the theory of deep learning: A theoretical physics perspective (Part I)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    2. Yong Zhou & Xinming Guo & Fujin Hou & Jianqing Wu, 2022. "Review of Intelligent Road Defects Detection Technology," Sustainability, MDPI, vol. 14(10), pages 1-19, May.

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