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

arXiv: https://arxiv.org/abs/2507.07625 · HTML: https://mlsanity.com/paper/2507.07625/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 52 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice](https://mlsanity.com/paper/1711.04735/) (2017)
- [Spectral Evolution and Invariance in Linear-width Neural Networks](https://mlsanity.com/paper/2211.06506/) (2022)
- [Eigenvalue Distribution of Large Random Matrices Arising in Deep Neural Networks: Orthogonal Case](https://mlsanity.com/paper/2201.04543/) (2022)
- [A Concentration of Measure and Random Matrix Approach to Large Dimensional Robust Statistics](https://mlsanity.com/paper/2006.09728/) (2020)
- [Global law of conjugate kernel random matrices with heavy-tailed weights](https://mlsanity.com/paper/2502.18428/) (2025)

## Abstract (arXiv)

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.