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Wav-KAN: Wavelet Kolmogorov-Arnold Networks

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arxiv 2405.12832 v2 pith:GCMWHSZT submitted 2024-05-21 cs.LG cs.AIeess.SPstat.ML

Zavareh Bozorgasl , Hao Chen This is my paper
classification cs.LGcs.AIeess.SPstat.ML
keywords wav-kanwaveletdatakolmogorov-arnoldnetworknetworksstructurefunctions
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 18 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kolmogorov--Arnold Networks for Small Language Models

    cs.LG 2026-07 conditional novelty 7.0 of 10

    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.

  2. A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains

    cs.CE 2025-07 conditional novelty 7.0 of 10

    A boundary-only holomorphic KAN framework solves Laplace, Helmholtz, and elasticity problems on simply and multiply connected 2D domains, outperforming standard PINNs in the tested cases.

  3. Improving Memory Efficiency for Training KANs via Meta Learning

    cs.LG 2025-06 conditional novelty 6.0 of 10

    MetaKANs generates each KAN activation function from a shared prompt-conditioned meta-learner, cutting trainable parameters toward MLP level while retaining comparable or better accuracy on tested benchmarks.

  4. Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States

    quant-ph 2025-06 conditional novelty 6.0 of 10

    SineKAN, a Kolmogorov-Arnold network with sinusoidal activations, accurately represents ground states of 1D spin chains and outperforms RBM, LSTM, and MLP neural quantum states in the J1-J2 model.

  5. GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions

    cs.LG 2025-12 conditional novelty 5.0 of 10

    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.

  6. ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

    cs.LG 2025-12 unverdicted novelty 5.0 of 10

    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...

  7. Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks

    quant-ph 2025-09 reject novelty 5.0 of 10

    QKANs show strong empirical performance on regression, vision, and language tasks, but the claimed exponential parameter reduction is not rigorously established.

  8. Toroidal area-preserving parameterizations of genus-one closed surfaces

    math.NA 2025-08 unverdicted novelty 5.0 of 10

    Four Riemannian optimization algorithms (projected/Riemannian gradient and conjugate gradient) are proposed to compute toroidal area-preserving parameterizations by minimizing stretch energy on a power manifold of ring tori.

  9. Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

    physics.comp-ph 2025-07 conditional novelty 5.0 of 10

    MR-PIKAN, a multi-resolution training schedule that alternates coarse and fine collocation grids, cuts training time while keeping accuracy on multi-scale forward and inverse PDE problems.

  10. Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs

    cs.LG 2025-06 conditional novelty 5.0 of 10

    The first NTK analysis of cPIKANs finds their kernel spectra stay stable during training, correlating with large accuracy gains over PINNs, especially when time is split into subdomains.

  11. Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement

    cs.LG 2025-05 conditional novelty 5.0 of 10

    Training in a B-spline KAN basis is equivalent to preconditioned gradient descent on a multichannel ReLU MLP, and geometric refinement plus trainable knots accelerate and improve training.

  12. Degree-Optimized Cumulative Polynomial Kolmogorov-Arnold Networks

    cs.LG 2025-05 conditional novelty 5.0 of 10

    CP-KAN reformulates polynomial degree selection in Chebyshev-based Kolmogorov-Arnold networks as a QUBO optimization problem and shows competitive regression performance with fewer parameters on several benchmarks.

  13. PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

    cs.LG 2026-07 reject novelty 4.0 of 10

    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...

  14. STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting

    cs.LG 2026-07 conditional novelty 4.0 of 10

    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.

  15. SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions

    cs.LG 2026-06 conditional novelty 4.0 of 10

    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.

  16. Adversarial Activation Patching: A Framework for Detecting and Mitigating Emergent Deception in Safety-Aligned Transformers

    cs.LG 2025-07 reject novelty 4.0 of 10

    A framework that borrows activation patching to adversarially induce and measure deception, supported only by an underspecified toy network simulation.

  17. Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony

    cs.LG 2025-06 conditional novelty 4.0 of 10

    Augmenting Kolmogorov-Arnold Networks with prediction exits at each layer improves accuracy and often yields more parsimonious models, and a differentiable learning-to-exit algorithm automates the choice of exit weights.

  18. Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment

    eess.IV 2025-05 conditional novelty 4.0 of 10

    A Taylor-expansion KAN variant outperforms B-spline, orthogonal-polynomial, wavelet, and Fourier KAN variants and MLPs on five authentic BIQA databases, with PCA and shallow layers reducing training cost.

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