# Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)

arXiv: https://arxiv.org/abs/2512.00260 · HTML: https://mlsanity.com/paper/2512.00260/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 29 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Bayesian Kolmogorov Arnold Networks (Bayesian_KANs): A Probabilistic Approach to Enhance Accuracy and Interpretability](https://mlsanity.com/paper/2408.02706/) (2024)
- [Gaussian Process Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.18397/) (2024)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-Aware Flow Field Reconstruction Using SVGP Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2512.22426/) (2025)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) offer a promising alternative to Multi-Layer Perceptron (MLP) by placing learnable univariate functions on network edges, enhancing interpretability. However, standard KANs lack probabilistic outputs, limiting their utility in applications requiring uncertainty quantification. While recent Gaussian Process (GP) extensions to KANs address this, they utilize exact inference methods that scale cubically with data size N, restricting their application to smaller datasets. We introduce the Sparse Variational GP-KAN (SVGP-KAN), an architecture that integrates sparse variational inference with the KAN topology. By employing M inducing points and analytic moment matching, our method reduces computational complexity from O(N3) to O(NM2) or linear in sample size, enabling the application of probabilistic KANs to larger scientific datasets. Furthermore, we demonstrate that integrating a permutation-based importance analysis enables the network to function as a framework for structural identification, identifying relevant inputs and classifying functional relationships.