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Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight…

Machine Learning · Computer Science 2026-05-12 Kai Lion , Florian Hübler , Bingcong Li , Antonio Orvieto , Niao He

Zeroth-order (ZO) optimization has become increasingly popular and important in fine-tuning large language models (LLMs), especially on edge devices due to its ability to adjust the model to local data without the need for memory-intensive…

Machine Learning · Computer Science 2026-05-18 Jiahe Chen , Ziye Ma

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

For a long period of time, Adam has served as the ubiquitous default choice for training deep neural networks. Recently, many new optimizers have been introduced, out of which Muon has perhaps gained the highest popularity due to its…

Machine Learning · Computer Science 2026-03-03 Sara Dragutinović , Rajesh Ranganath

Linear Attention (LA) offers a promising paradigm for scaling large language models (LLMs) to long sequences by avoiding the quadratic complexity of self-attention. Recent LA models such as Mamba2 and GDN interpret linear recurrences as…

Machine Learning · Computer Science 2026-05-08 Yulong Huang , Xiang Liu , Hongxiang Huang , Xiaopeng Lin , Zunchang Liu , Xiaowen Chu , Zeke Xie , Bojun Cheng

Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access…

Information Theory · Computer Science 2018-03-06 Lorne Applebaum , Waheed U. Bajwa , Marco F. Duarte , Robert Calderbank

Distributed optimization is essential for training large models on large datasets. Multiple approaches have been proposed to reduce the communication overhead in distributed training, such as synchronizing only after performing multiple…

Machine Learning · Computer Science 2020-02-21 Jianyu Wang , Vinayak Tantia , Nicolas Ballas , Michael Rabbat

Recent developments have shown that Muon-type optimizers based on linear minimization oracles (LMOs) over non-Euclidean norm balls have the potential to get superior practical performance than Adam-type methods in the training of large…

Machine Learning · Computer Science 2026-04-14 Xun Qian , Alexander Gaponov , Grigory Malinovsky , Peter Richtárik

The training efficiency and scalability of language models on massive clusters currently remain a critical bottleneck. Mainstream approaches like ND parallelism are often cumbersome and complex, while flexible alternatives such as the Zero…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-24 Huawei Bai , Yifan Huang , Wenqi Shi , Ansheng You , Feifan Shao , Tengfei Han , Minghui Yu

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental…

Machine Learning · Computer Science 2026-02-10 Wenbo Gong , Javier Zazo , Qijun Luo , Puqian Wang , James Hensman , Chao Ma

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. This…

Machine Learning · Computer Science 2025-11-24 Naoki Sato , Hiroki Naganuma , Hideaki Iiduka

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

Optimization and Control · Mathematics 2015-10-05 Bruce Cox , Anatoli Juditsky , Arkadi Nemirovski

Optimization with matrix gradient orthogonalization has recently demonstrated impressive results in the training of deep neural networks (Jordan et al., 2024; Liu et al., 2025). In this paper, we provide a theoretical analysis of this…

Machine Learning · Computer Science 2025-04-09 Dmitry Kovalev

Automated incident management is critical for microservice reliability. While recent unified frameworks leverage multimodal data for joint optimization, they unrealistically assume perfect data completeness. In practice, network…

Machine Learning · Computer Science 2026-03-30 Wenzhuo Qian , Hailiang Zhao , Ziqi Wang , Zhipeng Gao , Jiayi Chen , Zhiwei Ling , Shuiguang Deng

The optimization of large language models (LLMs) remains a critical challenge, particularly as model scaling exacerbates sensitivity to algorithmic imprecision and training instability. Recent advances in optimizers have improved…

Machine Learning · Computer Science 2025-11-26 Wei He , Kai Han , Hang Zhou , Hanting Chen , Zhicheng Liu , Xinghao Chen , Yunhe Wang

This paper presents a novel neural network training approach for faster convergence and better generalization abilities in deep reinforcement learning. Particularly, we focus on the enhancement of training and evaluation performance in…

Machine Learning · Computer Science 2020-05-26 Mohammed Sharafath Abdul Hameed , Gavneet Singh Chadha , Andreas Schwung , Steven X. Ding

Training large models with distributed data parallelism (DDP) requires frequent communication of gradients across workers, which can saturate bandwidth. Infrequent communication strategies (e.g., Local SGD) reduce this overhead but, when…

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

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…

Optimization and Control · Mathematics 2024-09-27 Ling Liang , Cameron Austin , Haizhao Yang

Learning-to-optimize (L2O) is an emerging research area in large-scale optimization with applications in data science. Recently, researchers have proposed a novel L2O framework called learned mirror descent (LMD), based on the classical…

Optimization and Control · Mathematics 2024-05-13 Hong Ye Tan , Subhadip Mukherjee , Junqi Tang , Carola-Bibiane Schönlieb