English
Related papers

Related papers: NuMuon: Nuclear-Norm-Constrained Muon for Compress…

200 papers

The efficient implementation of large language models (LLMs) is crucial for deployment on resource-constrained devices. Low-rank tensor compression techniques, such as tensor-train (TT) networks, have been widely studied for…

Computation and Language · Computer Science 2025-10-14 Ryan Solgi , Kai Zhen , Rupak Vignesh Swaminathan , Nathan Susanj , Athanasios Mouchtaris , Siegfried Kunzmann , Zheng Zhang

The pursuit of faster optimization algorithms remains an active and important research direction in deep learning. Recently, the Muon optimizer [JJB+24] has demonstrated promising empirical performance, but its theoretical foundation…

Machine Learning · Computer Science 2025-09-30 Lizhang Chen , Jonathan Li , Qiang Liu

The Muon optimizer has demonstrated strong empirical performance in pre-training large language models by performing matrix-level gradient (or momentum) orthogonalization in each layer independently. In this work, we propose TEON, a…

Machine Learning · Computer Science 2026-02-03 Ruijie Zhang , Yequan Zhao , Ziyue Liu , Zhengyang Wang , Dongyang Li , Yupeng Su , Sijia Liu , Zheng Zhang

Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…

Machine Learning · Computer Science 2024-07-24 Aayush Saxena , Arit Kumar Bishwas , Ayush Ashok Mishra , Ryan Armstrong

Conventional wisdom in deep learning optimization dictates updating all layers at every step-a principle followed by all recent state-of-the-art optimizers such as Muon. In this work, we challenge this assumption, showing that full-network…

Machine Learning · Computer Science 2025-10-03 Kaja Gruntkowska , Yassine Maziane , Zheng Qu , Peter Richtárik

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

In recent years, large language models (LLMs) have driven advances in natural language processing. Still, their growing scale has increased the computational burden, necessitating a balance between efficiency and performance. Low-rank…

Computation and Language · Computer Science 2025-02-25 Yixin Ji , Yang Xiang , Juntao Li , Qingrong Xia , Zi Ye , Xinyu Duan , Zhefeng Wang , Kehai Chen , Min Zhang

The majority of parameters in neural networks are naturally represented as matrices. However, most commonly used optimizers treat these matrix parameters as flattened vectors during optimization, potentially overlooking their inherent…

Machine Learning · Statistics 2026-04-15 Wei Shen , Ruichuan Huang , Minhui Huang , Cong Shen , Jiawei Zhang

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…

Machine Learning · Computer Science 2023-12-13 Arnav Chavan , Nahush Lele , Deepak Gupta

The Muon optimizer is consistently faster than Adam in training Large Language Models (LLMs), yet the mechanism underlying its success remains unclear. This paper demystifies this mechanism through the lens of associative memory. By…

Machine Learning · Computer Science 2025-10-07 Shuche Wang , Fengzhuo Zhang , Jiaxiang Li , Cunxiao Du , Chao Du , Tianyu Pang , Zhuoran Yang , Mingyi Hong , Vincent Y. F. Tan

We demonstrate that Muon, the simplest instantiation of a second-order optimizer, explicitly expands the Pareto frontier over AdamW on the compute-time tradeoff. We find that Muon is more effective than AdamW in retaining data efficiency at…

Recommender systems (RecSys) are increasingly emphasizing scaling, leveraging larger architectures and more interaction data to improve personalization. Yet, despite the optimizer's pivotal role in training, modern RecSys pipelines almost…

Information Retrieval · Computer Science 2026-03-03 Rong Shan , Aofan Yu , Bo Chen , Kuo Cai , Qiang Luo , Ruiming Tang , Han Li , Weiwen Liu , Weinan Zhang , Jianghao Lin

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to…

Machine Learning · Computer Science 2026-05-13 Yupeng Su , Ruijie Zhang , Ziyue Liu , Yequan Zhao , Zheng Zhang

In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent method where the update direction is the minimizer of the…

Optimization and Control · Mathematics 2025-06-03 Jiaxiang Li , Mingyi Hong

Memory-efficient optimization is critical for training increasingly large language models (LLMs). A popular strategy involves gradient low-rank projection, storing only the projected optimizer states, with GaLore being a representative…

Machine Learning · Computer Science 2025-10-21 Rui Pan , Yang Luo , Yuxing Liu , Yang You , Tong Zhang

Large Language Models (LLMs) have enabled remarkable progress in natural language processing, yet their high computational and memory demands pose challenges for deployment in resource-constrained environments. Although recent low-rank…

Computation and Language · Computer Science 2026-02-09 Jiayi Tian , Ryan Solgi , Jinming Lu , Yifan Yang , Hai Li , Zheng Zhang

We propose AdaMuon, a novel optimizer that combines element-wise adaptivity with orthogonal updates for large-scale neural network training. AdaMuon incorporates two tightly coupled mechanisms: (1) an element-wise second momentum estimator…

Machine Learning · Computer Science 2025-12-25 Chongjie Si , Debing Zhang , Wei Shen

We present a comprehensive theoretical and empirical study of the Muon optimizer for training transformers only with a small to medium decoder (30M - 200M parameters), with an emphasis on its mathematical foundations, convergence properties…

Machine Learning · Computer Science 2025-09-30 Sushant Mehta , Raj Dandekar , Rajat Dandekar , Sreedath Panat

Large Language Models (LLMs), such as LLaMA and T5, have shown exceptional performance across various tasks through fine-tuning. Although low-rank adaption (LoRA) has emerged to cheaply fine-tune these LLMs on downstream tasks, their…

Machine Learning · Computer Science 2024-08-08 Mingyang Zhang , Hao Chen , Chunhua Shen , Zhen Yang , Linlin Ou , Xinyi Yu , Bohan Zhuang

The rapid expansion of Large Language Models (LLMs) has posed significant challenges regarding the computational resources required for fine-tuning and deployment. Recent advancements in low-rank adapters have demonstrated their efficacy in…

Machine Learning · Computer Science 2025-01-29 J. Pablo Muñoz , Jinjie Yuan , Nilesh Jain