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

2025/07/16 by Ievgenii Afanasiev, Afanasiev, Ievgenii, Leonid Berlyand +3 · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2507.12182

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.

Citations

• Enhancing Accuracy in Deep Learning Using Random Matrix Theory
• Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning
• Free probability of type B and asymptotics of finite-rank perturbations of random matrices
• Mesoscopic Perturbations of Large Random Matrices
• Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices
• The largest eigenvalue of small rank perturbations of Hermitian random matrices
• On the Distribution of the Roots of Certain Symmetric Matrices

Cited by

• Spectra of random graphs with discrete scale invariance

Related

• New matrix perturbation bounds with relative norm: Perturbation of eigenspaces
• The largest eigenvalue of small rank perturbations of Hermitian random matrices
• Asymptotic Theory of Eigenvectors for Random Matrices With Diverging Spikes
• Mesoscopic Perturbations of Large Random Matrices
• Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks