Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks

Understand

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.