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 also maintains a balance between
accurately representing the underlying data structure and avoiding overfitting
to the noise. 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, TensorFlow, and also
it makes wavelet in KAN in wide-spread usage like nowadays activation functions
like ReLU, sigmoid in universal approximation theory (UAT).

通过在 Kolmogorov-Arnold 网络结构中引入小波函数，Wav-KAN 提供了一种可解释性和性能得到提升的创新神经网络架构。