Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Collection Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Organizer(s) Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken
Date(s) 08/04/2019 - 12/04/2019
linked URL https://www.chairejeanmorlet.com/2104.html
00:00:00 / 00:00:00
18 22

Eigenvalue distribution for non linear models of random matrices

By Sandrine Péché

The talk concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M= \frac{1}{m} YY^²$ with $Y=f(WX)$ where W and X are random rectangular matrices with i.i.d. centered entries. The function f is applied pointwise and can be seen as an activation function in (random) neural networks. We compute the asymptotic empirical distribution of this ensemble in the case where W and X have subGaussian tails and f is smooth. This extends a result of [PW17] where the case of Gaussian matrices W and X is considered. We also investigate the same questions in the multi-layer case, regarding neural network applications.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19518103
  • Cite this video Péché, Sandrine (12/04/2019). Eigenvalue distribution for non linear models of random matrices. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19518103
  • URL https://dx.doi.org/10.24350/CIRM.V.19518103

Bibliography

  • Benigni, L., & Péché, S. (2019). Eigenvalue distribution of nonlinear models of random matrices. arXiv preprint arXiv:1904.03090. - https://arxiv.org/abs/1904.03090

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback