mlsanityData to 14 Oct 2026

Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon

arXiv 1812.11167 ↗First posted 28 Dec 2018stat.ML cs.LG math.STcited by 44

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Abstract (arXiv)

We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on data. The result supports the empirical observation that minimum-norm interpolation (that is, exact fit to training data) in RKHS generalizes well for some high-dimensional datasets, but not for low-dimensional ones.

Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Dec 2018.

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Citing papers per year: 2021: 6; 2022: 8; 2023: 14; 2024: 9; 2025: 5; 2026: 2.

44 papers.

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  1. 2022Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regressioncited by 45
  2. 2022Benign, Tempered, or Catastrophic: A Taxonomy of Overfittingcited by 36
  3. 2023On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domainscited by 31
  4. 2021Towards an Understanding of Benign Overfitting in Neural Networkscited by 30
  5. 2023Generalization Ability of Wide Neural Networks on ℝcited by 30
  6. 2023Benign Overfitting in Linear Classifiers and Leaky ReLU Networks from KKT Conditions for Margin Maximizationcited by 29
  7. 2023Generalization in Kernel Regression Under Realistic Assumptionscited by 27
  8. 2023Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimensioncited by 26
  9. 2023Nonparametric regression using over-parameterized shallow ReLU neural networkscited by 24
  10. 2023Six Lectures on Linearized Neural Networkscited by 20
  11. 2022Sharp Asymptotics of Kernel Ridge Regression Beyond the Linear Regimecited by 19
  12. 2023On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decaycited by 19
32 more
  1. 2023Kernel interpolation generalizes poorlycited by 16
  2. 2023From Tempered to Benign Overfitting in ReLU Neural Networkscited by 16
  3. 2021Harmless interpolation in regression and classification with structured featurescited by 14
  4. 2022On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensionscited by 13
  5. 2022Wide and Deep Neural Networks Achieve Optimality for Classificationcited by 12
  6. 2024Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decaycited by 11
  7. 2023Strong inductive biases provably prevent harmless interpolationcited by 10
  8. 2024The phase diagram of kernel interpolation in large dimensionscited by 9
  9. 2024Overfitting Behaviour of Gaussian Kernel Ridgeless Regression: Varying Bandwidth or Dimensionalitycited by 7
  10. 2021Nonparametric Regression with Shallow Overparameterized Neural Networks Trained by GD with Early Stoppingcited by 5
  11. 2022Learning Lipschitz Functions by GD-trained Shallow Overparameterized ReLU Neural Networkscited by 5
  12. 2023Generalization Ability of Wide Residual Networkscited by 5
  13. 2021Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variationcited by 4
  14. 2022Rates of Convergence for Regression with the Graph Poly-Laplaciancited by 4
  15. 2024On the Consistency of Kernel Methods with Dependent Observationscited by 4
  16. 2022Benign overfitting and adaptive nonparametric regressioncited by 3
  17. 2025Transfer Learning for Benign Overfitting in High-Dimensional Linear Regressioncited by 3
  18. 2023Sobolev Space Regularised Pre Density Modelscited by 2
  19. 2024Spectrally Transformed Kernel Regressioncited by 2
  20. 2024Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learningcited by 2
  21. 2024On the Pinsker bound of inner product kernel regression in large dimensionscited by 2
  22. 2025Beyond Benign Overfitting in Nadaraya-Watson Interpolatorscited by 2
  23. 2021Classification and Adversarial examples in an Overparameterized Linear Model: A Signal Processing Perspectivecited by 1
  24. 2023How many samples are needed to leverage smoothness?cited by 1
  25. 2025Feature maps for the Laplacian kernel and its generalizationscited by 1
  26. 2026On damage of interpolation to adversarial robustness in regressioncited by 1
  27. 2026Harmful Overfitting in Sobolev Spacescited by 1
  28. 2021Fitting Elephantscited by 0
  29. 2024Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Biascited by 0
  30. 2024Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theoriescited by 0
  31. 2025Sobolev norm inconsistency of kernel interpolationcited by 0
  32. 2025L2-Regularized Empirical Risk Minimization Guarantees Small Smooth Calibration Errorcited by 0