mlsanityData to 14 Oct 2026

Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

arXiv 2009.10683 ↗First posted 22 Sep 2020cs.LG math.ST stat.MLcited by 74

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Abstract (arXiv)

We prove that the reproducing kernel Hilbert spaces (RKHS) of a deep neural tangent kernel and the Laplace kernel include the same set of functions, when both kernels are restricted to the sphere mathbbSd-1. Additionally, we prove that the exponential power kernel with a smaller power (making the kernel less smooth) leads to a larger RKHS, when it is restricted to the sphere mathbbSd-1 and when it is defined on the entire ℝd.

Key facts. Cited by 74 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Sep 2020.

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Citing papers per year: 2021: 18; 2022: 23; 2023: 14; 2024: 9; 2025: 7; 2026: 3.

74 papers.

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  1. 2021Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learningcited by 43
  2. 2021Neural Contextual Bandits without Regretcited by 40
  3. 2022Benign, Tempered, or Catastrophic: A Taxonomy of Overfittingcited by 36
  4. 2021Approximation and Learning with Deep Convolutional Models: a Kernel Perspectivecited by 31
  5. 2023On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domainscited by 31
  6. 2023Generalization in Kernel Regression Under Realistic Assumptionscited by 27
  7. 2021Deep Neural Networks as Point Estimates for Deep Gaussian Processescited by 26
  8. 2023Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimensioncited by 26
  9. 2023Contrastive Learning Is Spectral Clustering On Similarity Graphcited by 25
  10. 2025The Universal Weight Subspace Hypothesiscited by 24
  11. 2022Neural Tangent Kernel: A Surveycited by 23
  12. 2022A Sublinear Adversarial Training Algorithmcited by 22
38 more
  1. 2022Characterizing the Spectrum of the NTK via a Power Series Expansioncited by 22
  2. 2021Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networkscited by 21
  3. 2021A Neural Tangent Kernel Perspective of GANscited by 21
  4. 2021Uniform Generalization Bounds for Overparameterized Neural Networkscited by 21
  5. 2022On the Trade-Off between Actionable Explanations and the Right to be Forgottencited by 20
  6. 2022Regularized Stein Variational Gradient Flowcited by 19
  7. 2022Robustness in deep learning: The good (width), the bad (depth), and the ugly (initialization)cited by 18
  8. 2021Shift Invariance Can Reduce Adversarial Robustnesscited by 16
  9. 2022On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernelscited by 16
  10. 2021Neural Tangent Kernel Maximum Mean Discrepancycited by 15
  11. 2022Bounding the Width of Neural Networks via Coupled Initialization -- A Worst Case Analysiscited by 15
  12. 2022Few-shot Backdoor Attacks via Neural Tangent Kernelscited by 15
  13. 2024Nonparametric Teaching of Implicit Neural Representationscited by 15
  14. 2021Convergence and Alignment of Gradient Descent with Random Backpropagation Weightscited by 14
  15. 2021Learning Curves for Continual Learning in Neural Networks: Self-Knowledge Transfer and Forgettingcited by 14
  16. 2021Understanding Square Loss in Training Overparametrized Neural Network Classifierscited by 14
  17. 2021An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximationcited by 13
  18. 2021FL-NTK: A Neural Tangent Kernel-based Framework for Federated Learning Convergence Analysiscited by 13
  19. 2022A Kernel Perspective of Skip Connections in Convolutional Networkscited by 12
  20. 2022Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descentcited by 11
  21. 2023Benign Overfitting in Deep Neural Networks under Lazy Trainingcited by 10
  22. 2023How many Neurons do we need? A refined Analysis for Shallow Networks trained with Gradient Descentcited by 10
  23. 2024Optimal Convergence Rates for Neural Operatorscited by 8
  24. 2021A spectral-based analysis of the separation between two-layer neural networks and linear methodscited by 7
  25. 2022Approximation results for Gradient Descent trained Shallow Neural Networks in 1dcited by 7
  26. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  27. 2021Random Features for the Neural Tangent Kernelcited by 6
  28. 2021Deep Networks Provably Classify Data on Curvescited by 6
  29. 2022On the Generalization Power of the Overfitted Three-Layer Neural Tangent Kernel Modelcited by 6
  30. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  31. 2023Better NTK Conditioning: A Free Lunch from (ReLU) Nonlinear Activation in Wide Neural Networkscited by 6
  32. 2024Variational Search Distributionscited by 6
  33. 2022Learning Representation from Neural Fisher Kernel with Low-rank Approximationcited by 5
  34. 2022Why Quantization Improves Generalization: NTK of Binary Weight Neural Networkscited by 5
  35. 2023On Statistical Properties of Sharpness-Aware Minimization: Provable Guaranteescited by 5
  36. 2023Adaptation to Misspecified Kernel Regularity in Kernelised Banditscited by 5
  37. 2023Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Spacecited by 5
  38. 2024Laplace-HDC: Understanding the geometry of binary hyperdimensional computingcited by 4

50 most cited of 74 All 74 (JSON)