KORE: Kolmogorov-Optimal Scaling Laws for Spline Regression
Researchers propose KORE, a method that solves for the optimal spline resolution in closed form rather than relying on hyperparameter search. The approach leverages classical approximation theory to pin squared bias to the Kolmogorov n-width and uses the PRESS identity for leave-one-out error estimation. By balancing these known curves, the algorithm analytically determines the minimizer without exhaustive grid sweeps. KORE extends this calculus to high dimensions by replacing ambient input dimension with interaction order in an ANOVA decomposition. The algorithm fits two pilot resolutions and solves a leverage-calibrated system to evaluate the plug-in resolution with minimal compute. Across additive and sparse pairwise targets up to 80 dimensions, KORE matches exhaustive cross-validation accuracy while fitting roughly eight times fewer models. On 36 real tabular datasets, it ranked first among 21 methods in accuracy per unit of compute.