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Related papers: Effective Quantization of Muon Optimizer States

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This paper investigates the impact of different optimizers on the grokking phenomenon, where models exhibit delayed generalization. We conducted experiments across seven numerical tasks (primarily modular arithmetic) using a modern…

Machine Learning · Computer Science 2025-04-23 Amund Tveit , Bjørn Remseth , Arve Skogvold

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce…

Optimization and Control · Mathematics 2026-04-03 Zhehang Du , Weijie Su

Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. While Adam uses adaptive moment estimates to promote stability,…

Machine Learning · Computer Science 2026-02-23 Minxin Zhang , Yuxuan Liu , Hayden Schaeffer

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…

Machine Learning · Computer Science 2026-05-27 Jiacheng Li , Jianchao Tan , Hongtao Xu , Jiaqi Zhang , Yifan Lu , Yerui Sun , Yuchen Xie , Xunliang Cai

Orthogonalized-update optimizers such as Muon improve training of matrix-valued parameters, but existing extensions typically either rescale updates after orthogonalization or use heavier whitening-based preconditioners before it. We…

Machine Learning · Computer Science 2026-05-12 Da Chang , Qiankun Shi , Lvgang Zhang , Yu Li , Ruijie Zhang , Yao Lu , Yongxiang Liu , Ganzhao Yuan

Matrix-structured parameters frequently appear in many artificial intelligence models such as large language models. More recently, an efficient Muon optimizer is designed for matrix parameters of large-scale models, and shows markedly…

Machine Learning · Computer Science 2026-05-20 Feihu Huang , Yuning Luo , Songcan Chen

The rapid progress of large language models (LLMs) is increasingly constrained by memory and deployment costs, motivating compression methods for practical deployment. Many state-of-the-art compression pipelines leverage the low-rank…

The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap remains between its practical performance and theoretical understanding.…

Machine Learning · Computer Science 2026-05-12 Da Chang , Yongxiang Liu , Ganzhao Yuan

Muon has recently emerged as a strong optimizer for large language model pre-training, orthogonalizing the momentum matrix via Newton--Schulz polar iterations. A natural intuition is that polar iterations, by flattening the singular…

Machine Learning · Computer Science 2026-05-15 Ruijie Zhang , Yequan Zhao , Ziyue Liu , Zhengyang Wang , Yupeng Su , Liyan Tan , Zheng Zhang

MLP is a heavily used backbone in modern deep learning (DL) architectures for supervised learning on tabular data, and AdamW is the go-to optimizer used to train tabular DL models. Unlike architecture design, however, the choice of…

Machine Learning · Computer Science 2026-04-20 Yury Gorishniy , Ivan Rubachev , Dmitrii Feoktistov , Artem Babenko

DiLoCo is a powerful framework for training large language models (LLMs), enabling larger optimal batch sizes and increased accelerator utilization under networking constraints. However, DiLoCo's performance has been shown to degrade as the…

Machine Learning · Computer Science 2026-02-26 Benjamin Thérien , Xiaolong Huang , Aaron Defazio , Irina Rish , Eugene Belilovsky

Preconditioned adaptive methods have gained significant attention for training deep neural networks, as they capture rich curvature information of the loss landscape. The central challenge in this field lies in balancing preconditioning…

Machine Learning · Computer Science 2026-05-14 Shenyang Deng , Zhuoli Ouyang , Tianyu Pang , Zihang Liu , Ruochen Jin , Shuhua Yu , Yaoqing Yang

Muon has recently emerged as a competitive alternative to AdamW for large-scale pre-training, with orthogonalization via Newton-Schulz (NS) iterations as its core operation. Existing Muon variants apply a uniform NS schedule to all…

Machine Learning · Computer Science 2026-05-19 Xinlin Zhuang , Panyi Ouyang , Yichen Li , Jiangming Shi , Yizhang Chen , Shuman Liu , Ying Qian , Weiyang Liu , Haibo Zhang , Imran Razzak

Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax…

Machine Learning · Computer Science 2026-05-26 Binghui Li , Kaifei Wang , Han Zhong , Pinyan Lu , Liwei Wang

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent benchmark studies of…

Machine Learning · Computer Science 2026-02-02 Yifeng Liu , Angela Yuan , Quanquan Gu

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale…

Machine Learning · Computer Science 2026-05-12 Aditya Ranganath

The Muon optimizer enjoys strong empirical performance and theoretical grounding. However, the super-linear cost of its orthonormalization step introduces increasing overhead with scale. To alleviate this cost, several works have attempted…

Machine Learning · Computer Science 2025-12-22 Kwangjun Ahn , Noah Amsel , John Langford

Optimizers play an important role in both pretraining and finetuning stages when training large language models (LLMs). In this paper, we present an observation that full finetuning with the same optimizer as in pretraining achieves a…

Machine Learning · Computer Science 2026-05-08 Yuxing Liu , Jianyu Wang , Tong Zhang

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is…

Machine Learning · Computer Science 2023-10-30 Bingrui Li , Jianfei Chen , Jun Zhu

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered…

Machine Learning · Computer Science 2025-09-08 Kaiyue Wen , David Hall , Tengyu Ma , Percy Liang