Eigenvalue distribution for non linear models of random matrices | Vidéo | Carmin.tv

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Eigenvalue distribution for non linear models of random matrices

By Sandrine Péché

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

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

Date of recording 12/04/2019
Date of publication 09/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

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

Domain(s)

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

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2104/Slides/PecheCirmApril.pdf

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