KAConvNet introduces a Kolmogorov-Arnold Convolutional Layer to build networks competitive with ViTs and CNNs while offering stronger theoretical interpretability.
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Wav-kan: Wavelet kolmogorov-arnold networks
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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.
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.
PU-GKAN applies Shepard normalization to Gaussian bases in KANs, yielding exact constant reproduction, reduced epsilon sensitivity, and better validation accuracy across tested regimes.
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.
Derives generalized formulas for KAN inference complexity using RM, BOP, and NABS metrics across B-spline, GRBF, Chebyshev, and Fourier variants.
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.
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.
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
ATHENA introduces an agentic team framework that autonomously manages the end-to-end computational research lifecycle via a knowledge-driven HENA loop to achieve validation errors of 10^{-14} in scientific computing and machine learning tasks.
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.
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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.