The double descent and Runge phenomena in overparametrized polynomial interpolation

arXiv:2609.37657 · math.NA, cs.NA, math.CA, stat.ML · Submitted 2026-09-29 · Read on arXiv

math.NA, cs.NA, math.CA, stat.ML

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Regularization — 16× in this paper · explained in 3 episodes
• Chebyshev Polynomials — 7× in this paper · explained in 2 episodes
• Generalization — 7× in this paper · explained in 13 episodes
• Curse of Dimensionality — 3× in this paper · explained in 6 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• A Priori Estimates of the Population Risk for Two-layer Neural Networks
• Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
• Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks
• Mathematical theory of deep learning
• On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime

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