# Wahkon: A Statistically Principled Deep RKHS Superposition Network

arXiv: https://arxiv.org/abs/2605.14041 · HTML: https://mlsanity.com/paper/2605.14041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 5 of 5)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)

## Abstract (arXiv)

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.