Wav-KAN：小波Kolmogorov-Arnold网络
Wav-KAN: Wavelet Kolmogorov-Arnold Networks
AI总结：
本文提出Wav-KAN，一种基于小波函数的Kolmogorov-Arnold网络架构，通过高效捕获高低频成分，提升可解释性、训练速度、鲁棒性和性能，优于Spl-KAN和MLPs。
摘要：
在本文中，我们介绍了Wav-KAN，一种创新的神经网络架构，它利用小波Kolmogorov-Arnold网络（Wav-KAN）框架来增强可解释性和性能。传统的多层感知机（MLPs）以及最近的发展如Spl-KAN在可解释性、训练速度、鲁棒性、计算效率和性能方面面临挑战。Wav-KAN通过将小波函数纳入Kolmogorov-Arnold网络结构来解决这些局限性，使网络能够高效地捕获输入数据的高频和低频成分。基于小波的近似采用正交或半正交基，并在准确表示底层数据结构与避免对噪声过拟合之间保持平衡。虽然连续小波变换（CWT）具有很大潜力，我们也采用了离散小波变换（DWT）进行多分辨率分析，这避免了在查找细节时重新计算先前步骤的需要。类似于水适应其容器形状，Wav-KAN适应数据结构，从而与Spl-KAN和MLPs相比，提高了准确性、加快了训练速度并增强了鲁棒性。我们的结果突出了Wav-KAN作为开发可解释且高性能神经网络的强大工具的潜力，其应用跨越多个领域。这项工作为在PyTorch和TensorFlow等框架中进一步探索和实现Wav-KAN奠定了基础，旨在使KAN中的小波像通用逼近理论（UAT）中的ReLU和sigmoid等激活函数一样普及。用于复现模拟的代码可在https://github.com/zavareh1/Wav-KAN获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
