MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training

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.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2605.26842 [cs.LG]

(or arXiv:2605.26842v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.26842 Focus to learn more arXiv-issued DOI via DataCite

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