Wahkon combines kernel methods and deep learning with finite-sample guarantees

Wahkon is a deep RKHS superposition network that combines Kolmogorov's superposition principle with reproducing-kernel Hilbert space regularization. Released on arXiv on May 15, 2026, the architecture delivers minimax-optimal convergence rates under mild smoothness assumptions while maintaining finite-sample statistical guarantees that standard deep learning typically lacks.

The method extends the classical spline/Gaussian-process duality to deep compositions. The authors prove that the penalized Wahkon estimator is exactly the maximum a posteriori estimate under a hierarchical Gaussian-process prior, and they establish a finite-dimensional deep representer theorem that makes training tractable. Layerwise complexity control is explicit: the framework clarifies how depth and width trade off with regularity, using metric-entropy arguments to bound generalization error.

Benchmarks

Wahkon outperformed multilayer perceptrons, Neural Tangent Kernels, and Kolmogorov–Arnold Networks across simulation benchmarks and a single-cell CITE-seq study. The results demonstrate that the architecture delivers both accuracy and calibrated uncertainty, addressing a longstanding gap between deep learning's predictive power and RKHS methods' statistical rigor. The preprint does not report wall-clock training times or parameter counts, but the finite-dimensional representer theorem suggests the method scales more favorably than kernel methods that struggle in high dimensions.

The framework targets practitioners who need interpretability and statistical guarantees alongside prediction accuracy, particularly in scientific domains where finite-sample confidence matters.