# Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

arXiv: https://arxiv.org/abs/2405.07200 · HTML: https://mlsanity.com/paper/2405.07200/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 12 May 2024.

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

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Geometry and Dynamics of LayerNorm](https://mlsanity.com/paper/2405.04134/) (2024)

## Built on by (most cited first, 30 of 118)

- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [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)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.17611/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (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)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting](https://mlsanity.com/paper/2502.06910/) (2025)
- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions](https://mlsanity.com/paper/2407.04149/) (2024)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster](https://mlsanity.com/paper/2409.14248/) (2024)
- [KANICE: Kolmogorov-Arnold Networks with Interactive Convolutional Elements](https://mlsanity.com/paper/2410.17172/) (2024)
- [SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.06286/) (2024)
- [Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures](https://mlsanity.com/paper/2501.00016/) (2024)
- [Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs](https://mlsanity.com/paper/2505.03595/) (2025)
- [Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology](https://mlsanity.com/paper/2504.07379/) (2025)
- [Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.14026/) (2025)
- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs](https://mlsanity.com/paper/2506.07958/) (2025)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2411.15111/) (2024)
- [Are KANs Effective for Multivariate Time Series Forecasting?](https://mlsanity.com/paper/2408.11306/) (2024)

## Abstract (arXiv)

Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently capture intricate patterns and irregularities present in high-dimensional functions. This paper presents the Chebyshev Kolmogorov-Arnold Network (Chebyshev KAN), a new neural network architecture inspired by the Kolmogorov-Arnold representation theorem, incorporating the powerful approximation capabilities of Chebyshev polynomials. By utilizing learnable functions parametrized by Chebyshev polynomials on the network's edges, Chebyshev KANs enhance flexibility, efficiency, and interpretability in function approximation tasks. We demonstrate the efficacy of Chebyshev KANs through experiments on digit classification, synthetic function approximation, and fractal function generation, highlighting their superiority over traditional MLPs in terms of parameter efficiency and interpretability. Our comprehensive evaluation, including ablation studies, confirms the potential of Chebyshev KANs to address longstanding challenges in nonlinear function approximation, paving the way for further advancements in various scientific and engineering applications.