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rKAN: Rational Kolmogorov-Arnold Networks

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arxiv 2406.14495 v1 pith:27CTY3LO submitted 2024-06-20 cs.LG cs.NAcs.NEmath.NA

Alireza Afzal Aghaei This is my paper · ORCID
classification cs.LGcs.NAcs.NEmath.NA
keywords functionsbasisrationalfunctionkansrkanapproximationdeep
verification ladder T0 review T1 audit T2 compute T3 formal
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The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent complexity posed implementation challenges. Consequently, researchers have explored alternative basis functions such as Wavelets, Polynomials, and Fractional functions. In this research, we explore the use of rational functions as a novel basis function for KANs. We propose two different approaches based on Pade approximation and rational Jacobi functions as trainable basis functions, establishing the rational KAN (rKAN). We then evaluate rKAN's performance in various deep learning and physics-informed tasks to demonstrate its practicality and effectiveness in function approximation.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kolmogorov--Arnold Networks for Small Language Models

    cs.LG 2026-07 conditional novelty 7.0 of 10

    In small language models, KAN feed-forward blocks are auditable and pruneable, but on standardized benchmarks and scale tests they show no consistent accuracy, quality, or latency advantage over MLP baselines.

  2. Improving Memory Efficiency for Training KANs via Meta Learning

    cs.LG 2025-06 conditional novelty 6.0 of 10

    MetaKANs generates each KAN activation function from a shared prompt-conditioned meta-learner, cutting trainable parameters toward MLP level while retaining comparable or better accuracy on tested benchmarks.

  3. Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States

    quant-ph 2025-06 conditional novelty 6.0 of 10

    SineKAN, a Kolmogorov-Arnold network with sinusoidal activations, accurately represents ground states of 1D spin chains and outperforms RBM, LSTM, and MLP neural quantum states in the J1-J2 model.

  4. On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators

    cs.LG 2025-09 reject novelty 5.0 of 10

    The paper claims spline-parameterized KAN least-squares estimators achieve the minimax univariate regression rate O(n^{-2r/(2r+1)}) for additive and multiplicative KAN structures, independent of dimension.

  5. Toroidal area-preserving parameterizations of genus-one closed surfaces

    math.NA 2025-08 unverdicted novelty 5.0 of 10

    Four Riemannian optimization algorithms (projected/Riemannian gradient and conjugate gradient) are proposed to compute toroidal area-preserving parameterizations by minimizing stretch energy on a power manifold of ring tori.

  6. Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective

    cs.LG 2025-07 conditional novelty 4.0 of 10

    On ten KEEL datasets, KANs outperform MLPs on raw imbalanced data but resampling and focal loss degrade KANs while MLPs with those techniques match KAN performance at far lower cost.

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