The paper introduces two variance‑adaptive variants of the Muon optimizer—Muon‑NSR and Muon‑VS—for language model pretraining. Both methods incorporate gradient‑variance information into Muon’s orthogonalization process without adding extra hyperparameters, preserving its spectral normalization structure. Experiments on Llama‑style and GPT‑2 models ranging from 125 M to 1.2 B parameters show that these variants outperform well‑tuned Muon baselines and achieve up to a 1.33× step‑to‑target speedup on Llama‑1.2B.
By Jingru Li, Yibo Fan, Huan Li
The paper investigates how different inner optimizers affect replica scaling when training large language models across distributed compute resources. It identifies two key factors—covariance of pseudo-gradients and batch-size impact on noise scale—that influence performance as replicas increase. The authors show that whitening-based pre‑conditioning as an inner optimizer yields strong replica scaling, improving performance relative to DP as model size and data grow.
By Eugene Belilovsky, Stefan Horoi, Edouard Oyallon, Benjamin Th\'erien
arXiv:2602. 03001v2 Announce Type: replace-cross Abstract: To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune.
By Hiroki Naganuma, Shagun Gupta, Youssef Briki, Ioannis Mitliagkas, Irina Rish, Parameswaran Raman, Hao-Jun Michael Shi
arXiv:2602. 09492v2 Announce Type: replace-cross Abstract: Low-rank adaptation (LoRA) is a standard approach for fine-tuning large language models, yet its many variants report conflicting empirical gains, often on the same benchmarks.
By Sangyoon Lee, Jaeho Lee
arXiv:2607. 01487v1 Announce Type: new Abstract: We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law).
By Fabian Schaipp
The paper introduces Power‑Law Entropy Search (PLES), a computational‑cost‑aware acquisition function that uses multi‑fidelity Bayesian optimization to efficiently estimate optimal hyperparameter scaling laws for large language model training. PLES focuses on reducing the overall uncertainty of scaling law estimates rather than optimizing a single objective, selecting configurations that maximize uncertainty reduction per unit computational cost. Experiments on synthetic benchmarks, surrogate models, and real LLM pre‑training runs show that PLES converges to accurate scaling laws using less than one‑tenth of the computational budget required by conventional grid search and other baselines.
By Zhiliang Chen, Sebastian Ament, David Eriksson, Maximilian Balandat, Eytan Bakshy, Jihao Andreas Lin
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
By Naoki Sato, Hiroki Naganuma, Hideaki Iiduka
MONA is a new optimizer that extends the Muon optimizer by adding a Nesterov‑style acceleration term derived from an exponential moving average of gradient differences. The paper provides a convergence analysis showing that this term offers curvature‑aware corrections while maintaining Muon’s spectral‑norm regularization. Empirical results demonstrate that MONA outperforms both Muon and AdamW on Mixture‑of‑Experts pretraining across models ranging from 1 B to 68 B parameters, and achieves state‑of‑the‑art performance on downstream benchmarks after fine‑tuning the largest model.
By Jiacheng Li, Jianchao Tan, Hongtao Xu, Jiaqi Zhang, Yifan Lu, Yerui Sun, Yuchen Xie, Xunliang Cai
arXiv:2606. 17526v1 Announce Type: new Abstract: Efficient optimization is essential for training large language models.
By Da Chang, Ganzhao Yuan
The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.
By Xiaodong Wu, Wenyi Yu, Chao Zhang, Philip Woodland
The study investigates whether switching optimizers between pretraining and subsequent training stages of large language models (LLMs) incurs a performance penalty. By pretraining 1.2B Llama‑3 models with varying proportions of AdamW and Muon updates, and interpolating between the two during continued pretraining and supervised fine‑tuning (SFT), the authors find little evidence of a meaningful optimizer mismatch penalty. The results show that final performance is largely determined by the independent effects of the pretraining and post‑training optimizers, with downstream performance generally improving as the proportion of Muon updates during SFT increases, and that Muon remains competitive with AdamW even for task‑general SFT on larger models.
By Xinyu Zhao, Davis Wertheimer, Ashutosh Sharma, Rameswar Panda, Paul Pu Liang
arXiv:2606. 16899v1 Announce Type: new Abstract: Matrix based optimizers such as Muon can substantially speed up language model pretraining, but their gains over AdamW are observed to shrink as model size and data scale grow when using standard constant decoupled weight decay.
By Kaiyue Wen, Xingyu Dang, Kaifeng Lyu, Tengyu Ma, Percy Liang