An Innovative Networks in Federated Learning

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.

Clipped Uniform Quantizers for Communication-Efficient Federated Learning

This paper introduces an approach to employ clipped uniform quantization in federated learning settings, aiming to enhance model efficiency by reducing communication overhead without compromising accuracy. By employing optimal clipping thresholds and adaptive quantization schemes, our method significantly curtails the bit requirements for model weight transmissions between clients and the server. We explore the implications of symmetric clipping and uniform quantization on model performance, highlighting the utility of stochastic quantization to mitigate quantization artifacts and improve model robustness. Through extensive simulations on the MNIST dataset, our results demonstrate that the proposed method achieves near full-precision performance while ensuring substantial communication savings. Specifically, our approach facilitates efficient weight averaging based on quantization errors, effectively balancing the trade-off between communication efficiency and model accuracy. The comparative analysis with conventional quantization methods further confirms the superiority of our technique.

Wav-KAN: Wavelet Kolmogorov-Arnold Networks

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).

Auto-Calibration and 2D-DOA Estimation in UCAs via an Integrated Wideband Dictionary

In this paper, we present a novel auto-calibration scheme for the joint estimation of the two-dimensional (2-D) direction-of-arrival (DOA) and the mutual coupling matrix (MCM) for a signal measured using uniform circular arrays. The method employs an integrated wideband dictionary to mitigate the detrimental effects of the discretization of the continuous parameter space over the considered azimuth and elevation angles. This leads to a reduction of the computational complexity and obtaining of more accurate DOA estimates. Given the more reliable DOA estimates, the method also allows for the estimation of more accurate mutual coupling coefficients. The method utilizes an integrated dictionary in order to iteratively refine the active parameter space, thereby reducing the required computational complexity without reducing the overall performance. The complexity is further reduced by employing only the dominant subspace of the measured signal. Furthermore, the proposed method does not require a constraint on the prior knowledge of the number of nonzero coupling coefficients nor suffer from ambiguity problems. Moreover, a simple formulation for 2-D non-numerical integration is presented. Simulation results show the effectiveness of the proposed method.

Real-Valued 2-D Direction of Arrival Estimation via Sparse Representation

Despite many advantages of direction-of-arrivals (DOAs) in sparse representation domain, they have high computational complexity. This paper presents a new method for real-valued 2-D DOAs estimation of sources in a uniform circular array configuration. This method uses a transformation based on phase mode excitation in uniform circular arrays which called real beamspace L1-SVD (RB-L1SVD). This unitary transformation converts complex manifold matrix to real one, so that the computational complexity is decreased with respect to complex valued computations,its computation, at least, is one,fourth of the complex-valued case; moreover, some benefits from using this transformation are robustness to array imperfections, a better noise suppression because of exploiting an additional real structure, and etc. Numerical results demonstrate the better performance of the proposed approach over previous techniques such as C-L1SVD, RB-ESPRIT, and RB-MUSIC, especially in low signal-to-noise ratios.