Tue, 17 Oct 2023
16:00 - 17:00
Ouns El Harzli

We study the distribution of eigenvalues of kernel random matrices where each element is the empirical covariance between the feature map evaluations of a random fully-connected neural network. We show that, under mild assumptions on the non-linear activation function, namely Lipschitz continuity and measurability, the limiting spectral distribution can be written as successive free multiplicative convolutions between the Marchenko-Pastur law and a nonrandom measure specific to the neural network. The latter has no known analytical expression but can be simulated empirically, separately from the random matrices of interest.

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