mlsanityData to 7 Oct 2026

Does data interpolation contradict statistical optimality?

arXiv 1806.09471 ↗First posted 25 Jun 2018stat.ML cs.LG math.STcited by 95

Not on the map. Why?

Abstract (arXiv)

We show that learning methods interpolating the training data can achieve optimal rates for the problems of nonparametric regression and prediction with square loss.

Key facts. Cited by 95 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Jun 2018.

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Citing papers per year: 2020: 1; 2021: 17; 2022: 24; 2023: 22; 2024: 17; 2025: 9; 2026: 5.

95 papers.

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  1. 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
  2. 2021Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolationcited by 130
  3. 2021Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentrationcited by 110
  4. 2022Extended Unconstrained Features Model for Exploring Deep Neural Collapsecited by 101
  5. 2021Label-Imbalanced and Group-Sensitive Classification under Overparameterizationcited by 74
  6. 2021A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learningcited by 54
  7. 2024Asymptotic theory of in-context learning by linear attentioncited by 54
  8. 2023Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Datacited by 40
  9. 2021SGD Generalizes Better Than GD (And Regularization Doesn't Help)cited by 38
  10. 2022The Implicit Bias of Benign Overfittingcited by 38
  11. 2023Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Datacited by 38
  12. 2022Benign, Tempered, or Catastrophic: A Taxonomy of Overfittingcited by 36
38 more
  1. 2022Perturbation Analysis of Neural Collapsecited by 34
  2. 2021How rotational invariance of common kernels prevents generalization in high dimensionscited by 32
  3. 2023Benign Overfitting and Grokking in ReLU Networks for XOR Cluster Datacited by 32
  4. 2021Knowledge Distillation as Semiparametric Inferencecited by 29
  5. 2023Generalization Ability of Wide Neural Networks on ℝcited by 28
  6. 2022On the Impossible Safety of Large AI Modelscited by 27
  7. 2023Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimensioncited by 26
  8. 2023Nonparametric regression using over-parameterized shallow ReLU neural networkscited by 24
  9. 2024Asymptotics of Random Feature Regression Beyond the Linear Scaling Regimecited by 22
  10. 2023A Neural Collapse Perspective on Feature Evolution in Graph Neural Networkscited by 19
  11. 2023Six Lectures on Linearized Neural Networkscited by 19
  12. 2022Cutting Some Slack for SGD with Adaptive Polyak Stepsizescited by 18
  13. 2021Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature modelcited by 17
  14. 2024The Pitfalls of Memorization: When Memorization Hurts Generalizationcited by 16
  15. 2021Accelerated, Optimal, and Parallel: Some Results on Model-Based Stochastic Optimizationcited by 14
  16. 2022Memorize to Generalize: on the Necessity of Interpolation in High Dimensional Linear Regressioncited by 14
  17. 2024Implicit Optimization Bias of Next-Token Prediction in Linear Modelscited by 14
  18. 2024Trained Transformer Classifiers Generalize and Exhibit Benign Overfitting In-Contextcited by 14
  19. 2021SVRG Meets AdaGrad: Painless Variance Reductioncited by 13
  20. 2021Exact Gap between Generalization Error and Uniform Convergence in Random Feature Modelscited by 13
  21. 2022On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensionscited by 13
  22. 2022HARFE: Hard-Ridge Random Feature Expansioncited by 12
  23. 2022Wide and Deep Neural Networks Achieve Optimality for Classificationcited by 12
  24. 2024Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizescited by 12
  25. 2023Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approachcited by 11
  26. 2025Dense Associative Memory with Epanechnikov Energycited by 10
  27. 2022Information bottleneck theory of high-dimensional regression: relevancy, efficiency and optimalitycited by 9
  28. 2023Strong inductive biases provably prevent harmless interpolationcited by 9
  29. 2024On Goodhart's law, with an application to value alignmentcited by 9
  30. 2022Deep Linear Networks can Benignly Overfit when Shallow Ones Docited by 8
  31. 2021Conditioning of Random Feature Matrices: Double Descent and Generalization Errorcited by 7
  32. 2022A Universal Trade-off Between the Model Size, Test Loss, and Training Loss of Linear Predictorscited by 7
  33. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  34. 2021Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolationcited by 6
  35. 2023Rethinking Gauss-Newton for learning over-parameterized modelscited by 6
  36. 2021Nonparametric Regression with Shallow Overparameterized Neural Networks Trained by GD with Early Stoppingcited by 5
  37. 2022Learning Lipschitz Functions by GD-trained Shallow Overparameterized ReLU Neural Networkscited by 5
  38. 2023Interpolation Learning With Minimum Description Lengthcited by 5

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