# Over-the-Air Federated Multi-Task Learning Over MIMO Multiple Access Channels

arXiv: https://arxiv.org/abs/2112.13603 · HTML: https://mlsanity.com/paper/2112.13603/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 27 Dec 2021.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Recent Trends in Deep Learning Based Natural Language Processing](https://mlsanity.com/paper/1708.02709/) (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)
- [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)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing](https://mlsanity.com/paper/2007.07122/) (2020)
- [Federated Learning for 6G Communications: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/2006.02931/) (2020)
- [Reconfigurable Intelligent Surface Enabled Federated Learning: A Unified Communication-Learning Design Approach](https://mlsanity.com/paper/2011.10282/) (2020)
- [Cell-Free Massive MIMO for Wireless Federated Learning](https://mlsanity.com/paper/1909.12567/) (2019)
- [ScaleCom: Scalable Sparsified Gradient Compression for Communication-Efficient Distributed Training](https://mlsanity.com/paper/2104.11125/) (2021)
- [Over-the-Air Decentralized Federated Learning](https://mlsanity.com/paper/2106.08011/) (2021)
- [Temporal-Structure-Assisted Gradient Aggregation for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2103.02270/) (2021)
- [Wireless Federated Learning (WFL) for 6G Networks -- Part II: The Compute-then-Transmit NOMA Paradigm](https://mlsanity.com/paper/2104.12005/) (2021)
- [CSIT-Free Model Aggregation for Federated Edge Learning via Reconfigurable Intelligent Surface](https://mlsanity.com/paper/2102.10749/) (2021)

## Built on by (most cited first, 8 of 8)

- [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)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [Digital Over-the-Air Federated Learning in Multi-Antenna Systems](https://mlsanity.com/paper/2302.14648/) (2023)
- [Random Orthogonalization for Federated Learning in Massive MIMO Systems](https://mlsanity.com/paper/2210.09881/) (2022)
- [Over-the-Air Computation in OFDM Systems with Imperfect Channel State Information](https://mlsanity.com/paper/2307.05357/) (2023)
- [Quantized Analog Beamforming Enabled Multi-task Federated Learning Over-the-air](https://mlsanity.com/paper/2503.17649/) (2025)
- [From Federated Learning to X-Learning: Breaking the Barriers of Decentrality Through Random Walks](https://mlsanity.com/paper/2509.03709/) (2025)

## Abstract (arXiv)

With the explosive growth of data and wireless devices, federated learning (FL) over wireless medium has emerged as a promising technology for large-scale distributed intelligent systems. Yet, the urgent demand for ubiquitous intelligence will generate a large number of concurrent FL tasks, which may seriously aggravate the scarcity of communication resources. By exploiting the analog superposition of electromagnetic waves, over-the-air computation (AirComp) is an appealing solution to alleviate the burden of communication required by FL. However, sharing frequency-time resources in over-the-air computation inevitably brings about the problem of inter-task interference, which poses a new challenge that needs to be appropriately addressed. In this paper, we study over-the-air federated multi-task learning (OA-FMTL) over the multiple-input multiple-output (MIMO) multiple access (MAC) channel. We propose a novel model aggregation method for the alignment of local gradients of different devices, which alleviates the straggler problem in over-the-air computation due to the channel heterogeneity. We establish a communication-learning analysis framework for the proposed OA-FMTL scheme by considering the spatial correlation between devices, and formulate an optimization problem for the design of transceiver beamforming and device selection. To solve this problem, we develop an algorithm by using alternating optimization (AO) and fractional programming (FP), which effectively mitigates the impact of inter-task interference on the FL learning performance. We show that due to the use of the new model aggregation method, device selection is no longer essential, thereby avoiding the heavy computational burden involved in selecting active devices. Numerical results demonstrate the validity of the analysis and the superb performance of the proposed scheme.