Zavareh Bozorgasl

Zavareh Bozorgasl, Hao Chen

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.

Zavareh Bozorgasl, Hao Chen

This paper presents a novel approach to enhance communication efficiency in federated learning through clipped uniform quantization. By leveraging optimal clipping thresholds and client-specific adaptive quantization schemes, the proposed method significantly reduces bandwidth and memory requirements for model weight transmission between clients and the server while maintaining competitive accuracy. We investigate the effects of symmetric clipping and uniform quantization on model performance, emphasizing the role of stochastic quantization in mitigating artifacts and improving robustness. Extensive simulations demonstrate that the method achieves near-full-precision performance with substantial communication savings. Moreover, the proposed approach facilitates efficient weight averaging based on the inverse of the mean squared quantization errors, effectively balancing the trade-off between communication efficiency and model accuracy. Moreover, in contrast to federated averaging, this design obviates the need to disclose client-specific data volumes to the server, thereby enhancing client privacy. Comparative analysis with conventional quantization methods further confirms the efficacy of the proposed scheme.