@inproceedings{li-etal-2026-mona,
title = "{MONA}: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training",
author = "Li, Jiacheng and
Tan, Jianchao and
Xu, Hongtao and
Zhang, Jiaqi and
Lu, Yifan and
Sun, Yerui and
Xie, Yuchen and
Cai, Xunliang",
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.733/",
pages = "15400--15413",
ISBN = "979-8-89176-462-0",
abstract = "The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present **MONA**, an optimizer that bridges Muon{'}s orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon{'}s gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term enables escape from sharp minima while preserving Muon{'}s spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves **SOTA** performance."
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<abstract>The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present **MONA**, an optimizer that bridges Muon’s orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon’s gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term enables escape from sharp minima while preserving Muon’s spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves **SOTA** performance.</abstract>
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%0 Conference Proceedings
%T MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training
%A Li, Jiacheng
%A Tan, Jianchao
%A Xu, Hongtao
%A Zhang, Jiaqi
%A Lu, Yifan
%A Sun, Yerui
%A Xie, Yuchen
%A Cai, Xunliang
%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 li-etal-2026-mona
%X The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present **MONA**, an optimizer that bridges Muon’s orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon’s gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term enables escape from sharp minima while preserving Muon’s spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves **SOTA** performance.
%U https://aclanthology.org/2026.findings-emnlp.733/
%P 15400-15413
Markdown (Informal)
[MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training](https://aclanthology.org/2026.findings-emnlp.733/) (Li et al., Findings 2026)
ACL
- Jiacheng Li, Jianchao Tan, Hongtao Xu, Jiaqi Zhang, Yifan Lu, Yerui Sun, Yuchen Xie, and Xunliang Cai. 2026. MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 15400–15413, Budapest, Hungary. Association for Computational Linguistics.