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https://github.com/zavareh1/Wav-KAN

This repository contains the codes to replicate the simulations from the paper: "Wav-KAN: Wavelet Kolmogorov-Arnold Networks." It showcases the use of wavelet functions in neural networks to improve interpretability, accuracy, and efficiency.
https://github.com/zavareh1/Wav-KAN

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This repository contains the codes to replicate the simulations from the paper: "Wav-KAN: Wavelet Kolmogorov-Arnold Networks." It showcases the use of wavelet functions in neural networks to improve interpretability, accuracy, and efficiency.

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# Wav-KAN: Wavelet Kolmogorov-Arnold Networks

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!



### Links to the Paper

- Available at: [arXiv](https://arxiv.org/abs/2405.12832)

- Also available at: [SSRN](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4835325)

- Citations at: [Google Scholar](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C13&q=Wav-kan%3A+Wavelet+kolmogorov-arnold+networks&btnG=)



### We applied Wav-KAN to Hyperspectral Image Classification

- Available at: [arXiv](https://arxiv.org/abs/2406.07869)

- Citations at: [Google Scholar](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C13&q=arxiv+%2B+Unveiling+the+Power+of+Wavelets%3A+A+Wavelet-based+Kolmogorov-Arnold+Network+for+Hyperspectral+Image+Classification&btnG=)

### Highlights of Wav-KAN on Social Media

![View on X](Images/wav-kan.jpg) 



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 **discrete wavelet transforms (DWT)** 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:



```bibtex

@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}

}