mlsanityData to 7 Oct 2026

Eigenvalue distribution of nonlinear models of random matrices

arXiv 1904.03090 ↗First posted 5 Apr 2019math.PR cs.LGcited by 27

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Abstract (arXiv)

This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider M= frac1m YY^* with Y=f(WX) where W and X are random rectangular matrices with i.i.d. centered entries. The function f is applied pointwise and can be seen as an activation function in (random) neural networks. We compute the asymptotic empirical distribution of this ensemble in the case where W and X have sub-Gaussian tails and f is real analytic. This extends a previous result where the case of Gaussian matrices W and X is considered. We also investigate the same questions in the multi-layer case, regarding neural network applications.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Apr 2019.

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Citing papers per year: 2021: 1; 2022: 8; 2023: 5; 2024: 4; 2025: 5; 2026: 4.

27 papers.

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  1. 2022High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representationcited by 146
  2. 2022Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterizationcited by 36
  3. 2023Deterministic equivalent and error universality of deep random features learningcited by 35
  4. 2022Spectral Evolution and Invariance in Linear-width Neural Networkscited by 30
  5. 2022Homogenization of SGD in high-dimensions: Exact dynamics and generalization propertiescited by 26
  6. 2021Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networkscited by 21
  7. 2022On double-descent in uncertainty quantification in overparametrized modelscited by 15
  8. 2024A Random Matrix Theory Perspective on the Spectrum of Learned Features and Asymptotic Generalization Capabilitiescited by 14
  9. 2024Asymptotics of Learning with Deep Structured (Random) Featurescited by 13
  10. 2022Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networkscited by 12
  11. 2023Fundamental limits of overparametrized shallow neural networks for supervised learningcited by 12
  12. 2023Universality for the global spectrum of random inner-product kernel matrices in the polynomial regimecited by 8
15 more
  1. 2022Overparameterized random feature regression with nearly orthogonal datacited by 6
  2. 2023Deterministic equivalent of the Conjugate Kernel matrix associated to Artificial Neural Networkscited by 5
  3. 2024Dataset-learning duality and emergent criticalitycited by 5
  4. 2022Optimal Activation Functions for the Random Features Regression Modelcited by 4
  5. 2023Least Squares Regression Can Exhibit Under-Parameterized Double Descentcited by 4
  6. 2025Low Rank Gradients and Where to Find Themcited by 4
  7. 2025Global law of conjugate kernel random matrices with heavy-tailed weightscited by 3
  8. 2024Generalization for Least Squares Regression With Simple Spiked Covariancescited by 2
  9. 2025Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scalingcited by 2
  10. 2025High-dimensional ridge regression with random features for non-identically distributed data with a variance profilecited by 1
  11. 2025Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrixcited by 0
  12. 2026A Random Matrix Theory of Masked Self-Supervised Regressioncited by 0
  13. 2026Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descentcited by 0
  14. 2026Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholdingcited by 0
  15. 2026Spectral Perturbation of the Empirical Fisher Information Matrix under Weight Quantizationcited by 0