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arXiv · 2507.12182

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

Ievgenii Afanasiev·Leonid Berlyand·Mariia Kiyashko
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Abstract

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.

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BibTeXRIS

Ievgenii Afanasiev, Leonid Berlyand, Mariia Kiyashko. 2025-07-16. Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices. https://arxiv.org/abs/2507.12182

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