RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis

arXiv:2609.01729 · cs.LG, cs.AI · Submitted 2026-09-01 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-09-01

Updated: 2026-09-01

Comments: 21 pages , 7 figures

Code: https://github.com/ZiyaoLi/fast-kan

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 16× in this paper · explained in 2 episodes
• Accuracy — 13× in this paper · explained in 1 episode
• Chebyshev Polynomials — 10× in this paper · explained in 2 episodes
• Time Series Forecasting — 4× in this paper · explained in 3 episodes
• Interpretability — 3× in this paper · explained in 15 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Activation Function — 2× in this paper · explained in 1 episode
• Adaptivity — 2× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Parameter Efficiency — 1× in this paper · explained in 3 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• KAN: Kolmogorov-Arnold Networks
• KAN 2.0: Kolmogorov-Arnold Networks Meet Science
• Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
• Wav-KAN: Wavelet Kolmogorov-Arnold Networks
• fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions
• Recurrence relations for polynomial sequences via Riordan matrices
• Kolmogorov-Arnold Networks are Radial Basis Function Networks
• ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU
• Kolmogorov-Arnold Networks (KANs) for Time Series Analysis
• Suitability of KANs for Computer Vision: A preliminary investigation
• A Survey on Kolmogorov-Arnold Network
• On the expressiveness and spectral bias of KANs
• Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability
• Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation
• Convolutional Kolmogorov-Arnold Networks
• LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behavior
• PRKAN: Parameter-Reduced Kolmogorov-Arnold Networks
• U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation
• TKAN: Temporal Kolmogorov-Arnold Networks
• GKAN: Graph Kolmogorov-Arnold Networks

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