# Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices

arXiv: https://arxiv.org/abs/2507.12182 · HTML: https://mlsanity.com/paper/2507.12182/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Builds on (most cited first, 2 of 2)

- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Enhancing Accuracy in Deep Learning Using Random Matrix Theory](https://mlsanity.com/paper/2310.03165/) (2023)

## Abstract (arXiv)

The paper is concerned with deformed Wigner random matrices. These matrices are closely related to Deep Neural Networks (DNNs): weight matrices of trained DNNs could be represented in the form R + S, where R is random and S is highly correlated. The spectrum of such matrices plays a key role in rigorous underpinning of the novel pruning technique based on Random Matrix Theory. In practice, the spectrum of the matrix S can be rather complicated. In this paper, we develop an asymptotic analysis for the case of full rank S with increasing number of outlier eigenvalues.