Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks. (arXiv:2201.04753v1 [math.PR])

This paper is concerned with the asymptotic distribution of the largest
eigenvalues for some nonlinear random matrix ensemble stemming from the study
of neural networks. More precisely we consider $M= \frac{1}{m} YY^\top$ with
$Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with i.i.d.
centered entries. This models the data covariance matrix or the Conjugate
Kernel of a single layered random Feed-Forward Neural Network. The function $f$
is applied entrywise and can be seen as the activation function of the …

arxiv kernel math networks neural networks pr