Wireless federated learning (FL) facilitates collaborative training of artificial intelligence (AI) models to support ubiquitous intelligent applications at the wireless edge. However, the inherent constraints of limited wireless resources inevitably lead to unreliable communication, which poses a significant challenge to wireless FL. To overcome this challenge, we propose Sign-Prioritized FL (SP-FL), a novel framework that improves wireless FL by prioritizing the transmission of important gradient information through uneven resource allocation. Specifically, recognizing the importance of descent direction in model updating, we transmit gradient signs in individual packets and allow their reuse for gradient descent if the remaining gradient modulus cannot be correctly recovered. To further improve the reliability of transmission of important information, we formulate a hierarchical resource allocation problem based on the importance disparity at both the packet and device levels, optimizing bandwidth allocation across multiple devices and power allocation between sign and modulus packets. To make the problem tractable, the one-step convergence behavior of SP-FL, which characterizes data importance at both levels in an explicit form, is analyzed. We then propose an alternating optimization algorithm to solve this problem using the Newton-Raphson method and successive convex approximation (SCA). Simulation results confirm the superiority of SP-FL, especially in resource-constrained scenarios, demonstrating up to 9.96\% higher testing accuracy on the CIFAR-10 dataset compared to existing methods.

翻译：无线联邦学习（FL）通过协作训练人工智能（AI）模型，为无线边缘的泛在智能应用提供支持。然而，有限的无线资源这一固有约束不可避免地导致通信不可靠，对无线联邦学习构成重大挑战。为克服这一挑战，本文提出符号优先联邦学习（SP-FL），一种通过非均匀资源分配优先传输重要梯度信息以改进无线联邦学习的新框架。具体而言，基于模型更新中下降方向的重要性认知，我们在独立数据包中传输梯度符号，并允许在剩余梯度模值无法正确恢复时复用这些符号进行梯度下降。为进一步提升重要信息传输的可靠性，我们基于数据包与设备层级的重要性差异，构建了一个分层资源分配问题，优化多设备间的带宽分配以及符号包与模值包间的功率分配。为使问题可解，我们分析了SP-FL的单步收敛行为，以显式形式刻画了两个层级的数据重要性。随后提出一种交替优化算法，结合牛顿-拉弗森方法与逐次凸逼近（SCA）求解该问题。仿真结果验证了SP-FL的优越性，尤其在资源受限场景下，在CIFAR-10数据集上相比现有方法测试精度最高可提升9.96%。