# Prioritizing Gradient Sign Over Modulus: An Importance-Aware Framework for Wireless Federated Learning

arXiv: https://arxiv.org/abs/2603.10763 · HTML: https://mlsanity.com/paper/2603.10763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 49 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Convergence of Update Aware Device Scheduling for Federated Learning at the Wireless Edge](https://mlsanity.com/paper/2001.10402/) (2020)
- [Edge Learning for B5G Networks with Distributed Signal Processing: Semantic Communication, Edge Computing, and Wireless Sensing](https://mlsanity.com/paper/2206.00422/) (2022)
- [Federated Full-Parameter Tuning of Billion-Sized Language Models with Communication Cost under 18 Kilobytes](https://mlsanity.com/paper/2312.06353/) (2023)
- [Design and Analysis of Uplink and Downlink Communications for Federated Learning](https://mlsanity.com/paper/2012.04057/) (2020)
- [Quantized Federated Learning under Transmission Delay and Outage Constraints](https://mlsanity.com/paper/2106.09397/) (2021)
- [Gradient and Channel Aware Dynamic Scheduling for Over-the-Air Computation in Federated Edge Learning Systems](https://mlsanity.com/paper/2212.00491/) (2022)
- [SAFARI: Sparsity enabled Federated Learning with Limited and Unreliable Communications](https://mlsanity.com/paper/2204.02321/) (2022)
- [Knowledge-Guided Learning for Transceiver Design in Over-the-Air Federated Learning](https://mlsanity.com/paper/2203.14753/) (2022)
- [Satellite Federated Edge Learning: Architecture Design and Convergence Analysis](https://mlsanity.com/paper/2404.01875/) (2024)
- [Semi-Federated Learning for Collaborative Intelligence in Massive IoT Networks](https://mlsanity.com/paper/2303.05048/) (2023)
- [Imperfect CSI: A Key Factor of Uncertainty to Over-the-Air Federated Learning](https://mlsanity.com/paper/2307.12793/) (2023)
- [Federated Learning with Erroneous Communication Links](https://mlsanity.com/paper/2201.12991/) (2022)
- [Energy-Efficient Edge Inference in Integrated Sensing, Communication, and Computation Networks](https://mlsanity.com/paper/2503.00298/) (2025)
- [Combating Interference for Over-the-Air Federated Learning: A Statistical Approach via RIS](https://mlsanity.com/paper/2501.16081/) (2025)
- [Edge Large AI Models: Revolutionizing 6G Networks](https://mlsanity.com/paper/2505.00321/) (2025)
- [Edge Large AI Models: Collaborative Deployment and IoT Applications](https://mlsanity.com/paper/2505.03139/) (2025)

## Abstract (arXiv)

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.