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Kolmogorov-Arnold Networks are Radial Basis Function Networks
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Kolmogorov-Arnold Networks are Radial Basis Function Networks
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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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Cited by 22 Pith papers
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Kolmogorov--Arnold Networks for Small Language Models
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.
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KANs need curvature: penalties for compositional smoothness
A curvature penalty for KANs, derived to respect compositional effects and equipped with a proven upper bound on full-model curvature, produces smoother activations while preserving accuracy.
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Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting
Temporal autocorrelation reintroduces spectral bias in KANs for time series forecasting, which DCT preprocessing can mitigate.
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In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
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Kolmogorov-Arnold Chemical Reaction Neural Networks for learning pressure-dependent kinetic rate laws
KA-CRNNs learn pressure-dependent and collider-specific kinetic rate laws from data using Kolmogorov-Arnold activations inside a CRNN framework, outperforming interpolative methods by 2.88x in MSE on two proof-of-conc...
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Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms
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.
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Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs
Structural KAN convolutions with shared value functions or wavelet-based adaptive filter shapes match or exceed per-edge KAN accuracy on CIFAR at 0.4M parameters.
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Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks
Adaptive RBF-KAN adds multiple radial basis kernels and LOOCV-based shape initialization to FastKAN, with benchmark tests on 2D functions showing kernel-specific advantages for smooth, discontinuous, and oscillatory cases.
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KAN-MLP-Mixer: A comprehensive investigation of the usage of Kolmogorov-Arnold Networks (KANs) for improving IMU-based Human Activity Recognition
A hybrid KAN-MLP model for IMU-based human activity recognition achieves 5.33% relative macro F1 improvement over pure MLPs on eight datasets by placing KANs at input embedding and classification stages.
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Partition-of-Unity Gaussian Kolmogorov-Arnold Networks
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
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Scale-Parameter Selection in Gaussian Kolmogorov-Arnold Networks
A stable operating interval for the Gaussian scale parameter ε in KANs is ε ∈ [1/(G-1), 2/(G-1)], derived from first-layer feature geometry and validated across multiple approximation and physics-informed problems.
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Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks
Derives generalized formulas for KAN inference complexity using RM, BOP, and NABS metrics across B-spline, GRBF, Chebyshev, and Fourier variants.
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KAN-MLP-Mixer: A comprehensive investigation of the usage of Kolmogorov-Arnold Networks (KANs) for improving IMU-based Human Activity Recognition
A hybrid KAN-MLP architecture with KAN input embedding and specialized LarctanKAN classification layer yields 5.33% average macro F1 gain over pure-MLP baselines in IMU-based human activity recognition.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel...
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Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks
Platform-independent formulas for KAN hardware inference complexity (RM, BOP, NABS) are derived for B-spline, GRBF, Chebyshev, and Fourier variants.
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Optimized Architectures for Kolmogorov-Arnold Networks
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
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...
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STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting
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.
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SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions
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.
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KANLib -- A Modular, Extensible and Fast Kolmogorov-Arnold Network Implementation
KANLib is a unified, extensible KAN framework supporting adaptive grids and basis functions that reproduces reference performance on the California Housing benchmark with competitive speed.
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Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
Hierarchical radial-basis-function Kolmogorov-Arnold networks are introduced with proofs of universal approximation for functions and random fields under Wasserstein-2 distance.
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A Practitioner's Guide to Kolmogorov-Arnold Networks
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a...
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