# Timely Parameter Updating in Over-the-Air Federated Learning

arXiv: https://arxiv.org/abs/2512.19103 · HTML: https://mlsanity.com/paper/2512.19103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Age-Based Scheduling Policy for Federated Learning in Mobile Edge Networks](https://mlsanity.com/paper/1910.14648/) (2019)
- [rTop-k: A Statistical Estimation Approach to Distributed SGD](https://mlsanity.com/paper/2005.10761/) (2020)
- [Harnessing Wireless Channels for Scalable and Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2007.01790/) (2020)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Joint Device Selection and Power Control for Wireless Federated Learning](https://mlsanity.com/paper/2205.09306/) (2022)
- [Differentially Private AirComp Federated Learning with Power Adaptation Harnessing Receiver Noise](https://mlsanity.com/paper/2004.06337/) (2020)
- [Federated Learning over Wireless Networks: A Band-limited Coordinated Descent Approach](https://mlsanity.com/paper/2102.07972/) (2021)
- [Over-the-Air Aggregation for Federated Learning: Waveform Superposition and Prototype Validation](https://mlsanity.com/paper/2110.14285/) (2021)
- [Distributed Learning over a Wireless Network with Non-coherent Majority Vote Computation](https://mlsanity.com/paper/2209.04692/) (2022)
- [LASER: Linear Compression in Wireless Distributed Optimization](https://mlsanity.com/paper/2310.13033/) (2023)
- [Edge Intelligence Over the Air: Two Faces of Interference in Federated Learning](https://mlsanity.com/paper/2306.10299/) (2023)
- [A Demonstration of Over-the-Air Computation for Federated Edge Learning](https://mlsanity.com/paper/2209.09954/) (2022)
- [Over-the-Air Computation for Distributed Systems: Something Old and Something New](https://mlsanity.com/paper/2211.00767/) (2022)

## Abstract (arXiv)

Incorporating over-the-air computations (OAC) into the model training process of federated learning (FL) is an effective approach to alleviating the communication bottleneck in FL systems. Under OAC-FL, every client modulates its intermediate parameters, such as gradient, onto the same set of orthogonal waveforms and simultaneously transmits the radio signal to the edge server. By exploiting the superposition property of multiple-access channels, the edge server can obtain an automatically aggregated global gradient from the received signal. However, the limited number of orthogonal waveforms available in practical systems is fundamentally mismatched with the high dimensionality of modern deep learning models. To address this issue, we propose Freshness Freshness-mAgnItude awaRe top-k (FAIR-k), an algorithm that selects, in each communication round, the most impactful subset of gradients to be updated over the air. In essence, FAIR-k combines the complementary strengths of the Round-Robin and Top-k algorithms, striking a delicate balance between timeliness (freshness of parameter updates) and importance (gradient magnitude). Leveraging tools from Markov analysis, we characterize the distribution of parameter staleness under FAIR-k. Building on this, we establish the convergence rate of OAC-FL with FAIR-k, which discloses the joint effect of data heterogeneity, channel noise, and parameter staleness on the training efficiency. Notably, as opposed to conventional analyses that assume a universal Lipschitz constant across all the clients, our framework adopts a finer-grained model of the data heterogeneity. The analysis demonstrates that since FAIR-k promotes fresh (and fair) parameter updates, it not only accelerates convergence but also enhances communication efficiency by enabling an extended period of local training without significantly affecting overall training efficiency.