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Wav-KAN: Wavelet Kolmogorov-Arnold Networks
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Wav-KAN: Wavelet Kolmogorov-Arnold Networks
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In this paper, we introduce Wav-KAN, an innovative neural network architecture that leverages the Wavelet Kolmogorov-Arnold Networks (Wav-KAN) framework to enhance interpretability and performance. Traditional multilayer perceptrons (MLPs) and even recent advancements like Spl-KAN face challenges related to interpretability, training speed, robustness, computational efficiency, and performance. Wav-KAN addresses these limitations by incorporating wavelet functions into the Kolmogorov-Arnold network structure, enabling the network to capture both high-frequency and low-frequency components of the input data efficiently. Wavelet-based approximations employ orthogonal or semi-orthogonal basis and maintain a balance between accurately representing the underlying data structure and avoiding overfitting to the noise. While continuous wavelet transform (CWT) has a lot of potentials, we also employed discrete wavelet transform (DWT) for multiresolution analysis, which obviated the need for recalculation of the previous steps in finding the details. Analogous to how water conforms to the shape of its container, Wav-KAN adapts to the data structure, resulting in enhanced accuracy, faster training speeds, and increased robustness compared to Spl-KAN and MLPs. Our results highlight the potential of Wav-KAN as a powerful tool for developing interpretable and high-performance neural networks, with applications spanning various fields. This work sets the stage for further exploration and implementation of Wav-KAN in frameworks such as PyTorch and TensorFlow, aiming to make wavelets in KAN as widespread as activation functions like ReLU and sigmoid in universal approximation theory (UAT). The codes to replicate the simulations are available at https://github.com/zavareh1/Wav-KAN.
Forward citations
Cited by 25 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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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 ...
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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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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...
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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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GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions
GS-KAN shares one learnable B-spline per layer across all edges, cutting parameter counts to MLP levels while beating MLP/KAN baselines in the tested regimes.
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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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ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
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 a...
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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 trad...
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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...
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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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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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