Abstract
This paper presents the development and application of Wavelet Kolmogorov-Arnold Networks (Wav-KAN) in federated learning. We implemented Wav-KAN \cite{wav-kan} in the clients. Indeed, we have considered both continuous wavelet transform (CWT) and also discrete wavelet transform (DWT) to enable multiresolution capabaility which helps in heteregeneous data distribution across clients. Extensive experiments were conducted on different datasets, demonstrating Wav-KAN's superior performance in terms of interpretability, computational speed, training and test accuracy. Our federated learning algorithm integrates wavelet-based activation functions, parameterized by weight, scale, and translation, to enhance local and global model performance. Results show significant improvements in computational efficiency, robustness, and accuracy, highlighting the effectiveness of wavelet selection in scalable neural network design.