# Robust Federated Learning Over the Air: Combating Heavy-Tailed Noise with Median Anchored Clipping

arXiv: https://arxiv.org/abs/2409.15100 · HTML: https://mlsanity.com/paper/2409.15100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 23 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [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)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [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)
- [Threats to Federated Learning: A Survey](https://mlsanity.com/paper/2003.02133/) (2020)
- [Wireless Network Intelligence at the Edge](https://mlsanity.com/paper/1812.02858/) (2018)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Turning Channel Noise into an Accelerator for Over-the-Air Principal Component Analysis](https://mlsanity.com/paper/2104.10095/) (2021)
- [AutoClip: Adaptive Gradient Clipping for Source Separation Networks](https://mlsanity.com/paper/2007.14469/) (2020)
- [Taming Fat-Tailed ("Heavier-Tailed'' with Potentially Infinite Variance) Noise in Federated Learning](https://mlsanity.com/paper/2210.00690/) (2022)
- [Over-The-Air Computation in Correlated Channels](https://mlsanity.com/paper/2101.04690/) (2021)
- [Edge Intelligence Over the Air: Two Faces of Interference in Federated Learning](https://mlsanity.com/paper/2306.10299/) (2023)
- [Resource Consumption for Supporting Federated Learning in Wireless Networks](https://mlsanity.com/paper/2204.03850/) (2022)
- [Over-the-Air Consensus for Distributed Vehicle Platooning Control (Extended version)](https://mlsanity.com/paper/2211.06225/) (2022)

## Built on by (most cited first, 3 of 3)

- [Federated learning over physical channels: adaptive algorithms with near-optimal guarantees](https://mlsanity.com/paper/2509.02538/) (2025)
- [Timely Parameter Updating in Over-the-Air Federated Learning](https://mlsanity.com/paper/2512.19103/) (2025)
- [Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm](https://mlsanity.com/paper/2606.22466/) (2026)

## Abstract (arXiv)

Leveraging over-the-air computations for model aggregation is an effective approach to cope with the communication bottleneck in federated edge learning. By exploiting the superposition properties of multi-access channels, this approach facilitates an integrated design of communication and computation, thereby enhancing system privacy while reducing implementation costs. However, the inherent electromagnetic interference in radio channels often exhibits heavy-tailed distributions, giving rise to exceptionally strong noise in globally aggregated gradients that can significantly deteriorate the training performance. To address this issue, we propose a novel gradient clipping method, termed Median Anchored Clipping (MAC), to combat the detrimental effects of heavy-tailed noise. We also derive analytical expressions for the convergence rate of model training with analog over-the-air federated learning under MAC, which quantitatively demonstrates the effect of MAC on training performance. Extensive experimental results show that the proposed MAC algorithm effectively mitigates the impact of heavy-tailed noise, hence substantially enhancing system robustness.