大模型
arxiv.org ·
MONA：用于可扩展语言模型训练的带 Nesterov 加速的 Muon 优化器
该论文提出 MONA 优化器，在 Muon 的矩阵正交化框架中引入曲率感知加速项，该加速项由梯度差的指数移动平均计算，并给出收敛性分析，表明其在保留 Muon 谱范数正则化的同时引入曲率敏感修正。实验在 1B 至 68B 参数的 MoE 预训练（最大模型 1 万亿 token）上对比 Muon 与 AdamW，报告更好的收敛与下游任务表现；并在 MOE-68B-A3B 上做监督微调，在通用能力、数学推理和代码生成基准上报告 SOTA。
AI推荐理由 arXiv 论文（v2，2026-09-22 修订），提出 MONA 优化器，在 Muon 的正交化梯度处理流程中加入基于梯度差指数移动平均的 Nesterov 加速项，并给出收敛性分析。实验覆盖 1B 至 68B 参数的 MoE 预训练（最大模型 1T token），报告收敛与下游任务优于 Muon 和 AdamW，并在 MOE-68B-A3B 的 SFT 上取得 SOTA。新信息具体、可验证（论文与 DOI 可查），对大规模语言模型训练优化器选择有直接参考价值；局限是结论来自作者自述实验，尚无第三方复现，SOTA 表述需以论文基准为准。
82
正文
Computer Science > Machine Learning
arXiv:2605.26842 (cs)
[Submitted on 26 May 2026 (v1), last revised 22 Sep 2026 (this version, v2)]
Title:MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training
Authors:Jiacheng Li, Jianchao Tan, Hongtao Xu, Jiaqi Zhang, Yifan Lu, Yerui Sun, Yuchen Xie, Xunliang Cai
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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 introduces curvature-sensitive corrections 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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Machine Learning (cs.LG); Computation and Language (cs.CL)
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arXiv:2605.26842 [cs.LG]
(or
arXiv:2605.26842v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.26842
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Submission history
From: Jiacheng Li [view email]
[v1]
Tue, 26 May 2026 10:56:20 UTC (1,624 KB)
[v2]
Tue, 22 Sep 2026 08:02:43 UTC (1,631 KB)
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