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Eigenvalue distribution for non linear models of random matrices
Multi angle
Authors : Péché, Sandrine (Author of the conference)
CIRM (Publisher )
60B20 - Random matrices (probabilistic aspects)
15B52 - Random matrices
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/PecheCirmApril.pdf
CIRM (Publisher )
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Abstract :
The talk concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M=
\frac{1}{m} YY^*$ 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.
MSC Codes : \frac{1}{m} YY^*$ 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.
60B20 - Random matrices (probabilistic aspects)
15B52 - Random matrices
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/PecheCirmApril.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/05/2019 Conference Date : 12/04/2019 Subseries : Research talks arXiv category : Probability ; Machine Learning Mathematical Area(s) : Probability & Statistics ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:44:29 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-12_Péché.mp4 
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Information on the Event
Event Title : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataEvent Organizers : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2104.html
Citation Data
DOI : 10.24350/CIRM.V.19518103Cite this video as: Péché, Sandrine (2019). Eigenvalue distribution for non linear models of random matrices. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19518103 URI : http://dx.doi.org/10.24350/CIRM.V.19518103 |
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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
