Abstract:Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training tractable and provides explicit layerwise complexity control. We show the penalized estimator is exactly the MAP (maximum a posteriori) estimate under a hierarchical Gaussian-process prior, extending the spline/GP duality to deep compositions. Using metric-entropy arguments, we establish minimax-optimal convergence rates under mild smoothness and clarify how depth and width trade off with regularity. Empirically, Wahkon outperforms multilayer perceptrons, Neural Tangent Kernels, and Kolmogorov--Arnold Networks across simulation benchmarks and a single-cell CITE-seq study. By unifying Kolmogorov's superposition principle with RKHS regularization, Wahkon delivers accuracy, interpretability, and statistical rigor in a single framework.
| Subjects: | Methodology (stat.ME); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.14041 [stat.ME] |
| (or arXiv:2605.14041v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.14041 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yongkai Chen [view email]
[v1]
Wed, 13 May 2026 19:01:59 UTC (1,388 KB)