KAConvNet introduces a Kolmogorov-Arnold Convolutional Layer to build networks competitive with ViTs and CNNs while offering stronger theoretical interpretability.
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QKAN is a quantum algorithmic framework using block-encodings and QSVT to implement wide-and-shallow networks for quantum learning and compositional state preparation.
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.
K-U-KAN combines KAN feature lifting, Koopman linear dynamics, and U-KAN refinement with physical and geometric priors to reconstruct 3D dental anatomy from single panoramic radiographs, matching baselines on metrics while improving perceptual quality and halving training time.
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
InfinityKAN is a variational inference method that learns the number of basis functions per layer in KANs during training, matching or exceeding fixed-basis KAN performance across 18 datasets without manual selection.
Derives deterministic distance-aware error bounds for spline networks (including KANs) via bottom-up composition from individual spline neurons under higher-order Lipschitz conditions.
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.
GeoKAN learns a diagonal Riemannian metric to warp inputs for KAN models, enabling task-dependent resolution allocation for sharp and non-uniform regimes.
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 problem.
Platform-independent formulas for KAN hardware inference complexity (RM, BOP, NABS) are derived for B-spline, GRBF, Chebyshev, and Fourier variants.
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.
Automated methods based on Deep Symbolic Regression and Kolmogorov-Arnold Networks discover compact, interpretable path loss models that achieve high accuracy and reduce prediction errors by up to 75% compared to traditional approaches on synthetic and real datasets.
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
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 practitioner's selection guide plus open challenges.
citing papers explorer
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KAConvNet: Kolmogorov-Arnold Convolutional Networks for Vision Recognition
KAConvNet introduces a Kolmogorov-Arnold Convolutional Layer to build networks competitive with ViTs and CNNs while offering stronger theoretical interpretability.
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QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation
QKAN is a quantum algorithmic framework using block-encodings and QSVT to implement wide-and-shallow networks for quantum learning and compositional state preparation.
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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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K-U-KAN: Koopman-Enhanced U-KAN for 3D Dental Reconstruction from a Single Panoramic X-ray Radiograph
K-U-KAN combines KAN feature lifting, Koopman linear dynamics, and U-KAN refinement with physical and geometric priors to reconstruct 3D dental anatomy from single panoramic radiographs, matching baselines on metrics while improving perceptual quality and halving training time.
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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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Variational Kolmogorov-Arnold Network
InfinityKAN is a variational inference method that learns the number of basis functions per layer in KANs during training, matching or exceeding fixed-basis KAN performance across 18 datasets without manual selection.
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Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty
Derives deterministic distance-aware error bounds for spline networks (including KANs) via bottom-up composition from individual spline neurons under higher-order Lipschitz conditions.
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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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Geometric Kolmogorov--Arnold Network (GeoKAN)
GeoKAN learns a diagonal Riemannian metric to warp inputs for KAN models, enabling task-dependent resolution allocation for sharp and non-uniform regimes.
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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 problem.
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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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ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.
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Automated Modeling Method for Pathloss Model Discovery
Automated methods based on Deep Symbolic Regression and Kolmogorov-Arnold Networks discover compact, interpretable path loss models that achieve high accuracy and reduce prediction errors by up to 75% compared to traditional approaches on synthetic and real datasets.
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P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
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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 practitioner's selection guide plus open challenges.
- Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate