mlsanityData to 7 Oct 2026

On the Spectrum of Random Features Maps of High Dimensional Data

arXiv 1805.11916 ↗First posted 30 May 2018stat.ML cs.LGcited by 27

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Abstract (arXiv)

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gram matrix of these random feature maps, here for Gaussian mixture models of simultaneously large dimension and size. Our results are instrumental to a deeper understanding on the interplay of the nonlinearity and the statistics of the data, thereby allowing for a better tuning of random feature-based techniques.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 May 2018.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 6; 2024: 5; 2025: 1; 2026: 2.

27 papers.

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  1. 2021Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeedcited by 67
  2. 2022Neural networks trained with SGD learn distributions of increasing complexitycited by 50
  3. 2022Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterizationcited by 36
  4. 2023Deterministic equivalent and error universality of deep random features learningcited by 35
  5. 2022Data-driven emergence of convolutional structure in neural networkscited by 29
  6. 2022The dynamics of representation learning in shallow, non-linear autoencoderscited by 27
  7. 2024Dimension-free deterministic equivalents and scaling laws for random feature regressioncited by 23
  8. 2021Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networkscited by 21
  9. 2022On double-descent in uncertainty quantification in overparametrized modelscited by 15
  10. 2023Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernelscited by 13
  11. 2023On the Convergence of Encoder-only Shallow Transformerscited by 13
  12. 2024Asymptotics of Learning with Deep Structured (Random) Featurescited by 13
15 more
  1. 2023Fundamental limits of overparametrized shallow neural networks for supervised learningcited by 12
  2. 2023Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealingcited by 12
  3. 2021Analysis of One-Hidden-Layer Neural Networks via the Resolvent Methodcited by 9
  4. 2021Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clusteringcited by 7
  5. 2021Random matrices in service of ML footprint: ternary random features with no performance losscited by 7
  6. 2021Conditioning of Random Feature Matrices: Double Descent and Generalization Errorcited by 7
  7. 2022Overparameterized random feature regression with nearly orthogonal datacited by 6
  8. 2024Deep Equilibrium Models are Almost Equivalent to Not-so-deep Explicit Models for High-dimensional Gaussian Mixturescited by 6
  9. 2023High-dimensional Asymptotics of VAEs: Threshold of Posterior Collapse and Dataset-Size Dependence of Rate-Distortion Curvecited by 5
  10. 2024Analyzing the Neural Tangent Kernel of Periodically Activated Coordinate Networkscited by 3
  11. 2024"Lossless" Compression of Deep Neural Networks: A High-dimensional Neural Tangent Kernel Approachcited by 3
  12. 2025Global law of conjugate kernel random matrices with heavy-tailed weightscited by 3
  13. 2026Memorisation, convergence and generalisation in generative modelscited by 1
  14. 2022A Generalized Weighted Optimization Method for Computational Learning and Inversioncited by 0
  15. 2026A Random Matrix Theory of Masked Self-Supervised Regressioncited by 0