# DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2407.21176 · HTML: https://mlsanity.com/paper/2407.21176/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 30 of 34)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [Suitability of KANs for Computer Vision: A preliminary investigation](https://mlsanity.com/paper/2406.09087/) (2024)
- [Product Kernel Interpolation for Scalable Gaussian Processes](https://mlsanity.com/paper/1802.08903/) (2018)
- [Thoughts on Massively Scalable Gaussian Processes](https://mlsanity.com/paper/1511.01870/) (2015)

## Built on by (most cited first, 7 of 7)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example](https://mlsanity.com/paper/2408.02743/) (2024)
- [A Causal Graph-Enhanced Gaussian Process Regression for Modeling Engine-out NOx](https://mlsanity.com/paper/2410.18424/) (2024)
- [Bayesian Calibration of Engine-out NOx Models for Engine-to-Engine Transferability](https://mlsanity.com/paper/2511.18178/) (2025)

## Abstract (arXiv)

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth but lack ability to integrate structural characteristics of deep learning architectures with non-parametric flexibility of kernel methods. To address this, deep kernel learning (DKL) was introduced, where inputs to a base kernel are transformed using a deep learning architecture. These kernels can replace standard kernels, allowing both expressive power and scalability. The advent of Kolmogorov-Arnold Networks (KAN) has generated considerable attention and discussion among researchers in scientific domain. In this paper, we introduce a scalable deep kernel using KAN (DKL-KAN) as an effective alternative to DKL using MLP (DKL-MLP). Our approach involves simultaneously optimizing these kernel attributes using marginal likelihood within a Gaussian process framework. We analyze two variants of DKL-KAN for a fair comparison with DKL-MLP: one with same number of neurons and layers as DKL-MLP, and another with approximately same number of trainable parameters. To handle large datasets, we use kernel interpolation for scalable structured Gaussian processes (KISS-GP) for low-dimensional inputs and KISS-GP with product kernels for high-dimensional inputs. The efficacy of DKL-KAN is evaluated in terms of computational training time and test prediction accuracy across a wide range of applications. Additionally, the effectiveness of DKL-KAN is also examined in modeling discontinuities and accurately estimating prediction uncertainty. The results indicate that DKL-KAN outperforms DKL-MLP on datasets with a low number of observations. Conversely, DKL-MLP exhibits better scalability and higher test prediction accuracy on datasets with large number of observations.