{"ID":2893947,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12182","arxiv_id":"2507.12182","title":"Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices","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.","short_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 underpinn...","url_abs":"https://arxiv.org/abs/2507.12182","url_pdf":"https://arxiv.org/pdf/2507.12182v4","authors":"[\"Ievgenii Afanasiev\",\"Leonid Berlyand\",\"Mariia Kiyashko\"]","published":"2025-07-16T12:29:23Z","proceeding":"math-ph","tasks":"[\"math-ph\",\"cs.LG\",\"math.PR\"]","methods":"[]","has_code":false}