# Interpolation Learning With Minimum Description Length

arXiv: https://arxiv.org/abs/2302.07263 · HTML: https://mlsanity.com/paper/2302.07263/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Classification vs regression in overparameterized regimes: Does the loss function matter?](https://mlsanity.com/paper/2005.08054/) (2020)
- [How much does your data exploration overfit? Controlling bias via information usage](https://mlsanity.com/paper/1511.05219/) (2015)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [Finite-sample Analysis of Interpolating Linear Classifiers in the Overparameterized Regime](https://mlsanity.com/paper/2004.12019/) (2020)
- [Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting](https://mlsanity.com/paper/2106.09276/) (2021)
- [Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression](https://mlsanity.com/paper/2204.10425/) (2022)
- [In Defense of Uniform Convergence: Generalization via derandomization with an application to interpolating predictors](https://mlsanity.com/paper/1912.04265/) (2019)
- [Distributional Generalization: A New Kind of Generalization](https://mlsanity.com/paper/2009.08092/) (2020)

## Built on by (most cited first, 5 of 5)

- [From Tempered to Benign Overfitting in ReLU Neural Networks](https://mlsanity.com/paper/2305.15141/) (2023)
- [Noisy Interpolation Learning with Shallow Univariate ReLU Networks](https://mlsanity.com/paper/2307.15396/) (2023)
- [Provable Tempered Overfitting of Minimal Nets and Typical Nets](https://mlsanity.com/paper/2410.19092/) (2024)
- [Neural Networks Generalize on Low Complexity Data](https://mlsanity.com/paper/2409.12446/) (2024)
- [Beyond Benign Overfitting in Nadaraya-Watson Interpolators](https://mlsanity.com/paper/2502.07480/) (2025)

## Abstract (arXiv)

We prove that the Minimum Description Length learning rule exhibits tempered overfitting. We obtain tempered agnostic finite sample learning guarantees and characterize the asymptotic behavior in the presence of random label noise.