# Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials

arXiv: https://arxiv.org/abs/2406.02583 · HTML: https://mlsanity.com/paper/2406.02583/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 30 May 2024.

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

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (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)
- [Smooth Kolmogorov Arnold networks enabling structural knowledge representation](https://mlsanity.com/paper/2405.11318/) (2024)

## Built on by (most cited first, 30 of 35)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (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)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (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)
- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [Residual Kolmogorov-Arnold Network for Enhanced Deep Learning](https://mlsanity.com/paper/2410.05500/) (2024)
- [Medical Image Classification with KAN-Integrated Transformers and Dilated Neighborhood Attention](https://mlsanity.com/paper/2502.13693/) (2025)
- [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)
- [Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate](https://mlsanity.com/paper/2604.21174/) (2026)
- [Fully analogue in-memory neural computing via quantum tunneling effect](https://mlsanity.com/paper/2510.23638/) (2025)
- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities](https://mlsanity.com/paper/2410.04096/) (2024)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [FunKAN: Functional Kolmogorov-Arnold Network for Medical Image Enhancement and Segmentation](https://mlsanity.com/paper/2509.13508/) (2025)
- [INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstruction](https://mlsanity.com/paper/2510.10188/) (2025)
- [Partition-of-Unity Gaussian Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.23599/) (2026)
- [RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis](https://mlsanity.com/paper/2609.01729/) (2026)
- [On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2410.08041/) (2024)
- [Polynomial, trigonometric, and tropical activations](https://mlsanity.com/paper/2502.01247/) (2025)
- [Degree-Optimized Cumulative Polynomial Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2505.15228/) (2025)
- [Improving KAN with CDF normalization to quantiles](https://mlsanity.com/paper/2507.13393/) (2025)
- [Combinations of Fast Activation and Trigonometric Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2508.11876/) (2025)
- [FI-KAN: Fractal Interpolation Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2603.28288/) (2026)
- [Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches](https://mlsanity.com/paper/2604.16842/) (2026)

## Abstract (arXiv)

This paper presents a comprehensive survey of 18 distinct polynomials and their potential applications in Kolmogorov-Arnold Network (KAN) models as an alternative to traditional spline-based methods. The polynomials are classified into various groups based on their mathematical properties, such as orthogonal polynomials, hypergeometric polynomials, q-polynomials, Fibonacci-related polynomials, combinatorial polynomials, and number-theoretic polynomials. The study aims to investigate the suitability of these polynomials as basis functions in KAN models for complex tasks like handwritten digit classification on the MNIST dataset. The performance metrics of the KAN models, including overall accuracy, Kappa, and F1 score, are evaluated and compared. The Gottlieb-KAN model achieves the highest performance across all metrics, suggesting its potential as a suitable choice for the given task. However, further analysis and tuning of these polynomials on more complex datasets are necessary to fully understand their capabilities in KAN models. The source code for the implementation of these KAN models is available at https://github.com/seydi1370/Basis_Functions .