The double descent and Runge phenomena in overparametrized polynomial interpolation
Not on the map. Why?
Abstract (arXiv)
The Runge phenomenon in polynomial interpolation is often considered a classical analogue of the double descent phenomenon in machine learning. In this note, we explore overparameterized polynomial interpolation in three popular polynomial bases: Monomial, Chebyshev and Legendre basis with coefficients that are minimal in the ℓ2-norm (and, for the monomial basis, also those minimal in the ℓ1-norm). We present our results primarily for equidistant and Chebyshev data points, but many results are independent of the exact form of sampling.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 24 references that are in the map. First posted on arXiv 29 Sep 2026.
Builds on
11 of 24 references.
References · 11
- 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
- 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
- 2019Two models of double descent for weak featurescited by 195
- 2017Spurious Local Minima are Common in Two-Layer ReLU Neural Networkscited by 104
- 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 95
- 2020Representation formulas and pointwise properties for Barron functionscited by 62
- 2019A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamicscited by 49
- 2020A Brief Prehistory of Double Descentcited by 44
- 2020The Slow Deterioration of the Generalization Error of the Random Feature Modelcited by 8
- 2025Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenoncited by 6
- 2023Minimum norm interpolation by perceptra: Explicit regularization and implicit biascited by 3
Built on by
Not cited yet.