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

Published: July 16, 2025 | arXiv ID: 2507.12182v2

By: Ievgenii Afanasiev, Leonid Berlyand, Mariia Kiyashko

Potential Business Impact:

Makes smart computer programs learn better.

Business Areas:
Big Data Data and Analytics

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.

Page Count
15 pages

Category
Physics:
Mathematical Physics