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.
Recording during the meeting "Integrability and Randomness in Mathematical Physics and Geometry " the April 12, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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Sandrine Péché: Eigenvalue distribution for non linear models of random matrices amulet meaning | |
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