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

• URL: http://arxiv.org/abs/2507.12182v1
• Date: Wed, 16 Jul 2025 12:29:23 GMT
• Title: Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
• Authors: Ievgenii Afanasiev, Leonid Berlyand, Mariia Kiyashko,
• Abstract summary: The paper is concerned with deformed Wigner random matrices.<n>The spectrum of such matrices plays a key role in rigorous underpinning of the novel pruning technique.<n>In this paper we develop analysis for the case of growing rank.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The paper is concerned with deformed Wigner random matrices. These matrices are closely connected with 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. Mathematics has been done only for finite-rank matrix $S$. However, in practice rank may grow. In this paper we develop asymptotic analysis for the case of growing rank.

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