RM+ML: 24. Calculation of the Random Feature Eigenvalue Distribution

The lecture notes for the course can be found at https://rolandspeicher.com/wp-content...
cumulants, random feature model, resolvent expansion

0:00 Recap
3:44 Cumulants of data matrix
14:47 Cumulants of product of matrices
46:58 Calculation of Stieltjes transform for product
1:03:25 Cumulants of non-linear feature matrix
1:34:30 Stieltjes transform for feature matrix

The goal of this lecture series is to cover mathematical interesting aspects of neural networks, in particular, those related to random matrices. In this 24th lecture we use our general theory of cumulants to derive some structural property of the cumulants of the entries of the random feature matrix and indicate how from this one can derive the equation for the Stieltjes transform of the non-linear random feature matrix.