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.
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.
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.
Overprovisioned KANs with sparsification, deep supervision, and depth selection under differentiable MDL yield smaller models with competitive accuracy on benchmarks.
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.