# Does data interpolation contradict statistical optimality?

arXiv: https://arxiv.org/abs/1806.09471 · HTML: https://mlsanity.com/paper/1806.09471/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2018.

## Built on by (most cited first, 30 of 95)

- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [Extended Unconstrained Features Model for Exploring Deep Neural Collapse](https://mlsanity.com/paper/2202.08087/) (2022)
- [Label-Imbalanced and Group-Sensitive Classification under Overparameterization](https://mlsanity.com/paper/2103.01550/) (2021)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [Asymptotic theory of in-context learning by linear attention](https://mlsanity.com/paper/2405.11751/) (2024)
- [Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data](https://mlsanity.com/paper/2301.00437/) (2023)
- [SGD Generalizes Better Than GD (And Regularization Doesn't Help)](https://mlsanity.com/paper/2102.01117/) (2021)
- [The Implicit Bias of Benign Overfitting](https://mlsanity.com/paper/2201.11489/) (2022)
- [Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Data](https://mlsanity.com/paper/2309.09725/) (2023)
- [Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting](https://mlsanity.com/paper/2207.06569/) (2022)
- [Perturbation Analysis of Neural Collapse](https://mlsanity.com/paper/2210.16658/) (2022)
- [Benign Overfitting and Grokking in ReLU Networks for XOR Cluster Data](https://mlsanity.com/paper/2310.02541/) (2023)
- [How rotational invariance of common kernels prevents generalization in high dimensions](https://mlsanity.com/paper/2104.04244/) (2021)
- [Generalization Ability of Wide Neural Networks on ℝ](https://mlsanity.com/paper/2302.05933/) (2023)
- [Knowledge Distillation as Semiparametric Inference](https://mlsanity.com/paper/2104.09732/) (2021)
- [On the Impossible Safety of Large AI Models](https://mlsanity.com/paper/2209.15259/) (2022)
- [Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimension](https://mlsanity.com/paper/2305.14077/) (2023)
- [Asymptotics of Random Feature Regression Beyond the Linear Scaling Regime](https://mlsanity.com/paper/2403.08160/) (2024)
- [Nonparametric regression using over-parameterized shallow ReLU neural networks](https://mlsanity.com/paper/2306.08321/) (2023)
- [Six Lectures on Linearized Neural Networks](https://mlsanity.com/paper/2308.13431/) (2023)
- [A Neural Collapse Perspective on Feature Evolution in Graph Neural Networks](https://mlsanity.com/paper/2307.01951/) (2023)
- [The Pitfalls of Memorization: When Memorization Hurts Generalization](https://mlsanity.com/paper/2412.07684/) (2024)
- [Cutting Some Slack for SGD with Adaptive Polyak Stepsizes](https://mlsanity.com/paper/2202.12328/) (2022)
- [Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature model](https://mlsanity.com/paper/2110.11805/) (2021)
- [Trained Transformer Classifiers Generalize and Exhibit Benign Overfitting In-Context](https://mlsanity.com/paper/2410.01774/) (2024)
- [Accelerated, Optimal, and Parallel: Some Results on Model-Based Stochastic Optimization](https://mlsanity.com/paper/2101.02696/) (2021)
- [Memorize to Generalize: on the Necessity of Interpolation in High Dimensional Linear Regression](https://mlsanity.com/paper/2202.09889/) (2022)
- [Implicit Optimization Bias of Next-Token Prediction in Linear Models](https://mlsanity.com/paper/2402.18551/) (2024)

## 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.