The double descent and Runge phenomena in overparametrized polynomial interpolation

Jason Wein; Stephan Wojtowytsch

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arXiv · 2609.37657

The double descent and Runge phenomena in overparametrized polynomial interpolation

Jason Wein·Stephan Wojtowytsch

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Abstract

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 $\ell^2$-norm (and, for the monomial basis, also those minimal in the $\ell^1$-norm). We present our results primarily for equidistant and Chebyshev data points, but many results are independent of the exact form of sampling.

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Jason Wein, Stephan Wojtowytsch. 2026-09-29. The double descent and Runge phenomena in overparametrized polynomial interpolation. https://arxiv.org/abs/2609.37657

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