# BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2406.11173 · HTML: https://mlsanity.com/paper/2406.11173/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [TreeDRNet:A Robust Deep Model for Long Term Time Series Forecasting](https://mlsanity.com/paper/2206.12106/) (2022)
- [Regularized Flexible Activation Function Combinations for Deep Neural Networks](https://mlsanity.com/paper/2007.13101/) (2020)

## Built on by (most cited first, 30 of 46)

- [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)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)
- [SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions](https://mlsanity.com/paper/2407.04149/) (2024)
- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.14026/) (2025)
- [Activation Space Selectable Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2408.08338/) (2024)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2411.15111/) (2024)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [FourierKAN outperforms MLP on Text Classification Head Fine-tuning](https://mlsanity.com/paper/2408.08803/) (2024)
- [Exploring Kolmogorov-Arnold networks for realistic image sharpness assessment](https://mlsanity.com/paper/2409.07762/) (2024)
- [Medical Image Classification with KAN-Integrated Transformers and Dilated Neighborhood Attention](https://mlsanity.com/paper/2502.13693/) (2025)
- [Fast and Accurate Gigapixel Pathological Image Classification with Hierarchical Distillation Multi-Instance Learning](https://mlsanity.com/paper/2502.21130/) (2025)
- [asKAN: Active Subspace embedded Kolmogorov-Arnold Network](https://mlsanity.com/paper/2504.04669/) (2025)
- [Input Convex Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.21208/) (2025)
- [KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example](https://mlsanity.com/paper/2408.02743/) (2024)
- [Exploring Adversarial Transferability between Kolmogorov-arnold Networks](https://mlsanity.com/paper/2503.06276/) (2025)
- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning](https://mlsanity.com/paper/2603.23854/) (2026)
- [GNN-SKAN: Harnessing the Power of SwallowKAN to Advance Molecular Representation Learning with GNNs](https://mlsanity.com/paper/2408.01018/) (2024)
- [KAN v.s. MLP for Offline Reinforcement Learning](https://mlsanity.com/paper/2409.09653/) (2024)
- [P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization](https://mlsanity.com/paper/2410.03801/) (2024)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [TabKAN: Advancing Tabular Data Analysis using Kolmogorov-Arnold Network](https://mlsanity.com/paper/2504.06559/) (2025)
- [Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histograms](https://mlsanity.com/paper/2511.08570/) (2025)

## Abstract (arXiv)

In this paper, we introduce BSRBF-KAN, a Kolmogorov Arnold Network (KAN) that combines B-splines and radial basis functions (RBFs) to fit input vectors during data training. We perform experiments with BSRBF-KAN, multi-layer perception (MLP), and other popular KANs, including EfficientKAN, FastKAN, FasterKAN, and GottliebKAN over the MNIST and Fashion-MNIST datasets. BSRBF-KAN shows stability in 5 training runs with a competitive average accuracy of 97.55% on MNIST and 89.33% on Fashion-MNIST and obtains convergence better than other networks. We expect BSRBF-KAN to open many combinations of mathematical functions to design KANs. Our repo is publicly available at: https://github.com/hoangthangta/BSRBF_KAN.