The effective distribution of user transmit powers is essential for the significant advancements that the emergence of 6G wireless networks brings. In recent studies, Deep Neural Networks (DNNs) have been employed to address this challenge. However, these methods frequently encounter issues regarding fairness and computational inefficiency when making decisions, rendering them unsuitable for future dynamic services that depend heavily on the participation of each individual user. To address this gap, this paper focuses on the challenge of transmit power allocation in wireless networks, aiming to optimize $\alpha$-fairness to balance network utilization and user equity. We introduce a novel approach utilizing Kolmogorov-Arnold Networks (KANs), a class of machine learning models that offer low inference costs compared to traditional DNNs through superior explainability. The study provides a comprehensive problem formulation, establishing the NP-hardness of the power allocation problem. Then, two algorithms are proposed for dataset generation and decentralized KAN training, offering a flexible framework for achieving various fairness objectives in dynamic 6G environments. Extensive numerical simulations demonstrate the effectiveness of our approach in terms of fairness and inference cost. The results underscore the potential of KANs to overcome the limitations of existing DNN-based methods, particularly in scenarios that demand rapid adaptation and fairness.

翻译：用户发射功率的有效分配对于6G无线网络带来的重大进展至关重要。在近期研究中，深度神经网络（DNNs）已被用于应对这一挑战。然而，这些方法在决策时经常面临公平性和计算效率方面的问题，使其难以适用于高度依赖每个用户参与的动态未来服务。为弥补这一不足，本文聚焦于无线网络中的发射功率分配问题，旨在通过优化$\alpha$-公平性来平衡网络利用率与用户公平性。我们提出一种基于Kolmogorov-Arnold网络（KANs）的新方法，该类机器学习模型通过卓越的可解释性，相较于传统DNNs具有更低的推理成本。研究提供了完整的问题建模框架，证明了功率分配问题的NP-hard特性。进而提出了用于数据集生成和分布式KAN训练的两类算法，为动态6G环境中实现多样化公平性目标提供了灵活框架。大量数值仿真验证了所提方法在公平性与推理成本方面的有效性。结果凸显了KANs在克服现有基于DNN方法局限性方面的潜力，特别是在需要快速适应与公平性保障的场景中。