Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

TL;DR

This paper establishes concentration inequalities for non-linear random matrices, providing new tools to analyze spectral properties of neural networks and non-commutative polynomials, with implications for understanding complex random matrix models.

Contribution

It introduces novel concentration inequalities for non-linear random matrices, extending analysis techniques to neural networks and non-commutative polynomial models.

Findings

Derived spectral estimates for neural network conjugate kernels

Established concentration bounds for non-commutative polynomials

Applied results to dependent random matrix models

Abstract

We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly dependent) random matrices.