Wav-KAN: Wavelet Kolmogorov-Arnold Networks

June 10, 2025 · View on GitHub

The codes to replicate the simulations of the paper:"Wav-KAN: Wavelet Kolmogorov-Arnold Networks". To see a diverse range of possible applications of Wav-KAN, check "Applications" folder!

  • Available at: arXiv
  • Also available at: SSRN

We applied Wav-KAN to Hyperspectral Image Classification

Highlights of Wav-KAN on Social Media (X, formerly Twitter)

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This image showcases Wav-KAN being highlighted and shared with the community on social media. It reflects the growing interest and engagement around this innovative framework.

Current Contents of the Repository

  • MNIST Training and Testing:
    • The repository currently contains the codes required to replicate MNIST training and testing.
    • More codes and examples will be added in future updates.
  • Possible applications of Wavelet/Wav-KAN

Abstract

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 such as:

  • Interpretability
  • Training speed
  • Robustness
  • Computational efficiency
  • Performance limitations

Wav-KAN addresses these issues by:

  • Incorporating wavelet functions into the Kolmogorov-Arnold network structure.
  • Efficiently capturing both high-frequency and low-frequency components of input data.
  • Using continuos (dyadic) wavelet transforms for multiresolution analysis, eliminating the need for recalculations in detail extraction.

Key Features:

  • Wavelet-based approximations employ orthogonal or semi-orthogonal bases, balancing data structure representation and noise reduction.
  • Enhanced accuracy, faster training speeds, and increased robustness compared to Spl-KAN and MLPs.
  • Adaptability to the data structure, akin to how water conforms to its container.

Our results highlight the potential of Wav-KAN as a powerful tool for developing interpretable and high-performance neural networks, with applications across various fields. This work paves the way for further exploration and implementation of Wav-KAN in frameworks such as PyTorch and TensorFlow, aspiring to make wavelets in KAN as common as activation functions like ReLU and sigmoid in universal approximation theory (UAT).

Future Updates

  • Additional code implementations and simulations for Wav-KAN.

Stay tuned for updates! Feedback and contributions are welcome. 🚀

Reference

If you find this repository helpful in your research or projects, please consider citing the following paper:

@article{bozorgasl2024wavkan,
  author  = {Zavareh Bozorgasl and Hao Chen},
  title   = {Wav-KAN: Wavelet Kolmogorov-Arnold Networks},
  journal = {arXiv preprint arXiv:2405.12832},
  year    = {2024},
  url     = {https://arxiv.org/abs/2405.12832}
}