English
Related papers

Related papers: NorMuon: Making Muon more efficient and scalable

200 papers

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

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 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

Orthogonal momentum gradient updates have emerged to overcome the limitations of vector-based optimizers like Adam. The vector-based optimizer Adam suffers from high memory costs and ill-conditioned momentum gradient updates. However,…

Machine Learning · Computer Science 2025-12-19 Dipan Maity

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 rapid scaling of large language models (LLMs) has made low-precision training essential for reducing memory, improving efficiency, and enabling larger models and datasets. Existing convergence theories for adaptive optimizers, however,…

Machine Learning · Computer Science 2026-03-03 Xuan Tang , Jichu Li , Difan Zou

Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update…

Machine Learning · Computer Science 2026-05-22 Jueun Kim , Baekrok Shin , Jihun Yun , Beomhan Baek , Minhak Song , Chulhee Yun

Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware…

Machine Learning · Computer Science 2026-05-19 Neel Mishra , Kushagara Trivedi , Pawan Kumar

Training large-scale neural networks requires solving nonconvex optimization where the choice of optimizer fundamentally determines both convergence behavior and computational efficiency. While adaptive methods like Adam have long dominated…

Machine Learning · Computer Science 2026-01-30 Chenrui Xu , Wenjing Yan , Ying-Jun Angela Zhang

We introduce Pion, a spectrum-preserving optimizer for large language model (LLM) training based on orthogonal equivalence transformation. Unlike additive optimizers such as Adam and Muon, Pion updates each weight matrix through left and…

Machine Learning · Computer Science 2026-05-13 Kexuan Shi , Hanxuan Li , Zeju Qiu , Yandong Wen , Simon Buchholz , Weiyang Liu

While large language models (LLMs) have emerged as a significant advancement in artificial intelligence, the hardware and computational costs for training LLMs are also significantly burdensome. Among the state-of-the-art optimizers, AdamW…

Machine Learning · Computer Science 2026-02-02 Yufei Gu , Zeke Xie

Recent empirical research has demonstrated that deep learning optimizers based on the linear minimization oracle (LMO) over specifically chosen Non-Euclidean norm balls, such as Muon and Scion, outperform Adam-type methods in the training…

Optimization and Control · Mathematics 2025-12-19 Xun Qian , Hussein Rammal , Dmitry Kovalev , Peter Richtárik

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate…

Machine Learning · Computer Science 2026-05-18 Binghang Lu , Zheyuan Deng , Runyu Zhang , Bing Hu , Yunhan Zhao , Yuan Tian , Changhong Mou , Guang Lin , Xiaomin Li

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

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

The core bottleneck of Federated Learning (FL) lies in the communication rounds. That is, how to achieve more effective local updates is crucial for reducing communication rounds. Existing FL methods still primarily use element-wise local…

Machine Learning · Computer Science 2025-11-03 Junkang Liu , Fanhua Shang , Junchao Zhou , Hongying Liu , Yuanyuan Liu , Jin Liu

With the rapid development of natural language processing technology, large-scale language models (LLM) have achieved remarkable results in a variety of tasks. However, how to effectively train these huge models and improve their…

Artificial Intelligence · Computer Science 2024-12-09 Jiajing Chen , Bingying Liu , Xiaoxuan Liao , Jia Gao , Hongye Zheng , Yue Li

Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…

Machine Learning · Computer Science 2025-12-23 Yiheng Zhang , Shaowu Wu , Yuanzhuo Xu , Jiajun Wu , Shang Xu , Steve Drew , Xiaoguang Niu

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

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