Research
Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
arXiv:2507.12182v4 Announce Type: replace-cross Abstract: The paper is concerned with deformed Wigner random matrices. These matrices are closely related to Deep Neural Networks (DNNs): weight matrice
arXiv:2507.12182v4 Announce Type: replace-cross 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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Source: arXiv cs.LG | 2026-04-21