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Kolmogorov-Arnold Networks are Radial Basis Function Networks

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arxiv 2405.06721 v1 pith:HITFLIPW submitted 2024-05-10 cs.LG cs.AI

Ziyao Li This is my paper · ORCID
classification cs.LGcs.AI
keywords basisnetworksradialfunctionkolmogorov-arnoldapproximatedb-splinesdoing
verification ladder T0 review T1 audit T2 compute T3 formal
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This short paper is a fast proof-of-concept that the 3-order B-splines used in Kolmogorov-Arnold Networks (KANs) can be well approximated by Gaussian radial basis functions. Doing so leads to FastKAN, a much faster implementation of KAN which is also a radial basis function (RBF) network.

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Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 39 citations worldwide. 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. A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains

    cs.CE 2025-07 conditional novelty 7.0 of 10

    A boundary-only holomorphic KAN framework solves Laplace, Helmholtz, and elasticity problems on simply and multiply connected 2D domains, outperforming standard PINNs in the tested cases.

  3. Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms

    gr-qc 2026-07 accept novelty 6.0 of 10

    A piecewise MLP surrogate emulates NRSur7dq4 over its full domain at NR-faithful accuracy with ~1 ms GPU latency and a fully differentiable JAX likelihood pipeline.

  4. 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.

  5. Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks

    stat.ML 2025-08 reject novelty 5.0 of 10

    The paper states universal approximation theorems for sine-based Kolmogorov-Arnold networks, but the proof relies on an invalid lemma and an unproven matrix invertibility.

  6. Physics-Informed PointNets for Modeling Electromagnetic Scattering from All-Dielectric Metasurfaces with Inclined Nanopillars

    physics.optics 2025-07 conditional novelty 5.0 of 10

    A physics-informed PointNet that encodes spatially varying permittivity predicts near-field and far-field scattering from metasurfaces with inclined nanopillars, reaching 1.7% MAPE for low-contrast 2D cases.

  7. Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

    physics.comp-ph 2025-07 conditional novelty 5.0 of 10

    MR-PIKAN, a multi-resolution training schedule that alternates coarse and fine collocation grids, cuts training time while keeping accuracy on multi-scale forward and inverse PDE problems.

  8. Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs

    cs.LG 2025-06 conditional novelty 5.0 of 10

    The first NTK analysis of cPIKANs finds their kernel spectra stay stable during training, correlating with large accuracy gains over PINNs, especially when time is split into subdomains.

  9. "KAN you hear me?" Exploring Kolmogorov-Arnold Networks for Spoken Language Understanding

    cs.CL 2025-05 conditional novelty 5.0 of 10

    Placing a KAN layer between two linear layers improves spoken language understanding accuracy over linear-only baselines on several speech-intent datasets.

  10. PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

    cs.LG 2026-07 reject novelty 4.0 of 10

    PG-KINN pairs a KAN trial space with a Petrov–Galerkin test space for forward and inverse PDEs, but the inverse benchmark data is inconsistent with the governing equation and the accuracy claims are not supported by t...

  11. STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting

    cs.LG 2026-07 conditional novelty 4.0 of 10

    STKAN inserts Taylor-polynomial KAN token mixers into spatial and temporal mixing blocks and achieves small but consistent gains over strong baselines on three traffic-flow benchmarks and a tie on a fourth.

  12. SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions

    cs.LG 2026-06 conditional novelty 4.0 of 10

    SechKAN combines sech basis functions with a 1D linear projection to build a KAN-style model whose parameter count matches MLPs and which is competitive or better than several KAN variants on tested benchmarks.

  13. Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony

    cs.LG 2025-06 conditional novelty 4.0 of 10

    Augmenting Kolmogorov-Arnold Networks with prediction exits at each layer improves accuracy and often yields more parsimonious models, and a differentiable learning-to-exit algorithm automates the choice of exit weights.

  14. Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment

    eess.IV 2025-05 conditional novelty 4.0 of 10

    A Taylor-expansion KAN variant outperforms B-spline, orthogonal-polynomial, wavelet, and Fourier KAN variants and MLPs on five authentic BIQA databases, with PCA and shallow layers reducing training cost.

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