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[2507.12182] Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices
Summary
This paper explores the asymptotic behavior of eigenvalues in large random matrices, particularly focusing on the impact of rank perturbations, which are relevant to deep neural networks.
Why It Matters
Understanding the eigenvalue distribution in large random matrices is crucial for advancements in machine learning, especially in optimizing neural network architectures. This research contributes to the theoretical foundation for pruning techniques in deep learning, potentially improving model efficiency and performance.
Key Takeaways
- The study focuses on large rank perturbations of random matrices.
- Eigenvalues play a significant role in the performance of deep neural networks.
- The paper provides an asymptotic analysis relevant for understanding complex spectra.
- Insights from this research can inform pruning techniques in neural networks.
- The findings have implications for both theoretical and practical aspects of machine learning.
Mathematical Physics arXiv:2507.12182 (math-ph) [Submitted on 16 Jul 2025 (v1), last revised 20 Feb 2026 (this version, v3)] Title:Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices Authors:Ievgenii Afanasiev, Leonid Berlyand, Mariia Kiyashko View a PDF of the paper titled Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices, by Ievgenii Afanasiev and 2 other authors View PDF HTML (experimental) 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. Comments: Subjects: Mathematical Physics (math-ph); Machine Learning (cs.LG); Probability (math.PR) MSC classes: 60B20, 15B52 Cite as: arXiv:2507.12182 [math-ph] (or arXiv:2507.12182v3 [math-ph] for this version) https://doi.org/10.48550/arXiv.2507.12182 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ievgenii Afanasiev [view email] [v1] Wed, 16 Jul 2025 12:29:23 UTC (42 KB) [v2] Fri, 22 Aug 2025 03:...
