# Gaussian Process Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2407.18397 · HTML: https://mlsanity.com/paper/2407.18397/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Pooling Methods in Deep Neural Networks, a Review](https://mlsanity.com/paper/2009.07485/) (2020)
- [Deep Gaussian Processes for Regression using Approximate Expectation Propagation](https://mlsanity.com/paper/1602.04133/) (2016)
- [Learning Activation Functions: A new paradigm for understanding Neural Networks](https://mlsanity.com/paper/1906.09529/) (2019)
- [No Routing Needed Between Capsules](https://mlsanity.com/paper/2001.09136/) (2020)

## Built on by (most cited first, 6 of 6)

- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Interpretable Clinical Classification with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.16750/) (2025)
- [Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)](https://mlsanity.com/paper/2512.00260/) (2025)
- [On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2410.08041/) (2024)
- [HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation](https://mlsanity.com/paper/2501.18199/) (2025)
- [Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions](https://mlsanity.com/paper/2602.06737/) (2026)

## Abstract (arXiv)

In this paper, we introduce a probabilistic extension to Kolmogorov Arnold Networks (KANs) by incorporating Gaussian Process (GP) as non-linear neurons, which we refer to as GP-KAN. A fully analytical approach to handling the output distribution of one GP as an input to another GP is achieved by considering the function inner product of a GP function sample with the input distribution. These GP neurons exhibit robust non-linear modelling capabilities while using few parameters and can be easily and fully integrated in a feed-forward network structure. They provide inherent uncertainty estimates to the model prediction and can be trained directly on the log-likelihood objective function, without needing variational lower bounds or approximations. In the context of MNIST classification, a model based on GP-KAN of 80 thousand parameters achieved 98.5% prediction accuracy, compared to current state-of-the-art models with 1.5 million parameters.