@inproceedings{chen-etal-2026-fedsubmuon,
title = "{F}ed{S}ub{M}uon: Communication-Efficient Federated {LLM} Fine-Tuning via Structured Subspace Muon",
author = "Chen, Shaolong and
Tao, Youming and
Chen, Shuzhen and
Dressler, Falko and
Ye, Qingqing and
Wang, Di",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.990/",
pages = "20908--20922",
ISBN = "979-8-89176-462-0",
abstract = "Federated fine-tuning adapts large language models (LLMs) to decentralized client data, but its scalability in cross-device training is often limited by the high communication cost. Muon is an optimizer that improves optimization performance by orthogonalizing momentum for matrix-valued parameters. Existing federated Muon methods demonstrate the benefit of matrix-aware optimization in federated learning, but still require transmitting full layer-size updates and optimizer state. A natural way to reduce communication is to directly apply Muon to LoRA factors, but this changes the optimized object and weakens Muon{'}s matrix-aware update geometry. We propose FedSubMuon, a communication-efficient federated Muon fine-tuning method that optimizes compact coefficient matrices within shared structured subspaces. This design keeps Muon on a single matrix-valued trainable object, while reducing the client upload to compact coefficient matrices. We further introduce FedSubMuon-GT, an accuracy-oriented extension that uses projected gradients to adapt tracked subspace bases toward task-relevant gradient directions. Experiments on instruction tuning and mathematical reasoning show that FedSubMuon-GT achieves the best overall accuracy on four of five dataset{--}model pairs, while FedSubMuon performs best under all matched communication budgets. On Dolly-15K, the closest communication baseline requires $5.5\times$ and $1.4\times$ more total communication on Llama-1B and Qwen-4B, respectively."
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<abstract>Federated fine-tuning adapts large language models (LLMs) to decentralized client data, but its scalability in cross-device training is often limited by the high communication cost. Muon is an optimizer that improves optimization performance by orthogonalizing momentum for matrix-valued parameters. Existing federated Muon methods demonstrate the benefit of matrix-aware optimization in federated learning, but still require transmitting full layer-size updates and optimizer state. A natural way to reduce communication is to directly apply Muon to LoRA factors, but this changes the optimized object and weakens Muon’s matrix-aware update geometry. We propose FedSubMuon, a communication-efficient federated Muon fine-tuning method that optimizes compact coefficient matrices within shared structured subspaces. This design keeps Muon on a single matrix-valued trainable object, while reducing the client upload to compact coefficient matrices. We further introduce FedSubMuon-GT, an accuracy-oriented extension that uses projected gradients to adapt tracked subspace bases toward task-relevant gradient directions. Experiments on instruction tuning and mathematical reasoning show that FedSubMuon-GT achieves the best overall accuracy on four of five dataset–model pairs, while FedSubMuon performs best under all matched communication budgets. On Dolly-15K, the closest communication baseline requires 5.5\times and 1.4\times more total communication on Llama-1B and Qwen-4B, respectively.</abstract>
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%0 Conference Proceedings
%T FedSubMuon: Communication-Efficient Federated LLM Fine-Tuning via Structured Subspace Muon
%A Chen, Shaolong
%A Tao, Youming
%A Chen, Shuzhen
%A Dressler, Falko
%A Ye, Qingqing
%A Wang, Di
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F chen-etal-2026-fedsubmuon
%X Federated fine-tuning adapts large language models (LLMs) to decentralized client data, but its scalability in cross-device training is often limited by the high communication cost. Muon is an optimizer that improves optimization performance by orthogonalizing momentum for matrix-valued parameters. Existing federated Muon methods demonstrate the benefit of matrix-aware optimization in federated learning, but still require transmitting full layer-size updates and optimizer state. A natural way to reduce communication is to directly apply Muon to LoRA factors, but this changes the optimized object and weakens Muon’s matrix-aware update geometry. We propose FedSubMuon, a communication-efficient federated Muon fine-tuning method that optimizes compact coefficient matrices within shared structured subspaces. This design keeps Muon on a single matrix-valued trainable object, while reducing the client upload to compact coefficient matrices. We further introduce FedSubMuon-GT, an accuracy-oriented extension that uses projected gradients to adapt tracked subspace bases toward task-relevant gradient directions. Experiments on instruction tuning and mathematical reasoning show that FedSubMuon-GT achieves the best overall accuracy on four of five dataset–model pairs, while FedSubMuon performs best under all matched communication budgets. On Dolly-15K, the closest communication baseline requires 5.5\times and 1.4\times more total communication on Llama-1B and Qwen-4B, respectively.
%U https://aclanthology.org/2026.findings-emnlp.990/
%P 20908-20922
Markdown (Informal)
[FedSubMuon: Communication-Efficient Federated LLM Fine-Tuning via Structured Subspace Muon](https://aclanthology.org/2026.findings-emnlp.990/) (Chen et al., Findings 2026)
ACL