mlsanityData to 14 Oct 2026

Feature maps for the Laplacian kernel and its generalizations

arXiv 2502.15575 ↗First posted 21 Feb 2025stat.ML cs.AI cs.LGcited by 1

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Abstract (arXiv)

Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being equivalent to that of the neural tangent kernel of deep fully connected networks. However, unlike the Gaussian kernel, the Laplacian kernel is not separable. This poses challenges for techniques to approximate it, especially via the random Fourier features (RFF) methodology and its variants. In this work, we provide random features for the Laplacian kernel and its two generalizations: Mat'ern kernel and the Exponential power kernel. We provide efficiently implementable schemes to sample weight matrices so that random features approximate these kernels. These weight matrices have a weakly coupled heavy-tailed randomness. Via numerical experiments on real datasets we demonstrate the efficacy of these random feature maps.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 30 of its 58 references that are in the map. First posted on arXiv 21 Feb 2025.

Builds on

30 of 58 references.

References · 30

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2017Deep Neural Networks as Gaussian Processescited by 622
  3. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 413
  4. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 317
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  6. 2018To understand deep learning we need to understand kernel learningcited by 187
  7. 2019Linearized two-layers neural networks in high dimensioncited by 155
  8. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 138
  9. 2020Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyondcited by 109
  10. 2016Orthogonal Random Featurescited by 91
  11. 2015On the Error of Random Fourier Featurescited by 76
  12. 2020On the Similarity between the Laplace and Neural Tangent Kernelscited by 76
18 more
  1. 2014Fastfood: Approximate Kernel Expansions in Loglinear Timecited by 74
  2. 2020Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHScited by 74
  3. 2017The Unreasonable Effectiveness of Structured Random Orthogonal Embeddingscited by 45
  4. 2018Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenoncited by 44
  5. 2024Emergence in non-neural models: grokking modular arithmetic via average gradient outer productcited by 28
  6. 2018Quadrature-based features for kernel approximationcited by 26
  7. 2024Average gradient outer product as a mechanism for deep neural collapsecited by 22
  8. 2017Gaussian Quadrature for Kernel Featurescited by 21
  9. 2022On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensionscited by 13
  10. 2023Toward Large Kernel Modelscited by 13
  11. 2022Improved Random Features for Dot Product Kernelscited by 12
  12. 2016Recycling Randomness with Structure for Sublinear time Kernel Expansionscited by 9
  13. 2022A Universal Trade-off Between the Model Size, Test Loss, and Training Loss of Linear Predictorscited by 7
  14. 2016Structured adaptive and random spinners for fast machine learning computationscited by 6
  15. 2024The fast committor machine: Interpretable prediction with kernelscited by 5
  16. 2018Kernel Machines Beat Deep Neural Networks on Mask-based Single-channel Speech Enhancementcited by 3
  17. 2023Orthogonal Random Features: Explicit Forms and Sharp Inequalitiescited by 1
  18. 2024Correspondence of NNGP Kernel and the Matern Kernelcited by 1

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Citing papers per year: 2026: 1.

1 paper.

  1. 2026Lipschitz bounds for integral kernelscited by 0