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Related papers: AMO: Adaptive Muon Orthogonalization

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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 Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such…

Machine Learning · Computer Science 2026-02-05 Xianbiao Qi , Marco Chen , Jiaquan Ye , Yelin He , Rong Xiao

Muon improves neural-network training by orthogonalizing matrix-valued updates, but it leaves each layer's update magnitude controlled mostly by a global learning rate. We introduce OrScale, a trust-ratio extension of Muon built on a simple…

Machine Learning · Computer Science 2026-05-11 Yuxuan Lou , Yang You

Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to…

Machine Learning · Computer Science 2020-01-15 Guoqiang Zhang , Kenta Niwa , W. B. Kleijn

Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training…

Machine Learning · Computer Science 2026-03-10 Peng Cheng , Jiucheng Zang , Qingnan Li , Liheng Ma , Yufei Cui , Yingxue Zhang , Boxing Chen , Ming Jian , Wen Tong

Orthonormalized updates accelerate training, improve stability, and enable robust hyperparameter transfer, but existing methods like Muon rely on dense matrix operations that clash with sharded weights in large-scale LLM training, causing…

Machine Learning · Computer Science 2025-09-16 Kwangjun Ahn , Byron Xu , Natalie Abreu , Ying Fan , Gagik Magakyan , Pratyusha Sharma , Zheng Zhan , John Langford

The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…

Machine Learning · Computer Science 2025-05-09 Devan Selvaraj

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

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…

We present Amos, a stochastic gradient-based optimizer designed for training deep neural networks. It can be viewed as an Adam optimizer with theoretically supported, adaptive learning-rate decay and weight decay. A key insight behind Amos…

Machine Learning · Computer Science 2022-11-22 Ran Tian , Ankur P. Parikh

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

We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point…

Machine Learning · Computer Science 2022-03-02 Juhan Bae , Paul Vicol , Jeff Z. HaoChen , Roger Grosse

Matrix-based optimizers have demonstrated immense potential in training Large Language Models (LLMs), however, designing an ideal optimizer remains a formidable challenge. A superior optimizer must satisfy three core desiderata: efficiency,…

Machine Learning · Computer Science 2026-05-06 Jinghui Yuan , Jiaxuan Zou , Shuo Wang , Yong Liu , Feiping Nie

When tuning software configuration for better performance (e.g., latency or throughput), an important issue that many optimizers face is the presence of local optimum traps, compounded by a highly rugged configuration landscape and…

Software Engineering · Computer Science 2024-04-09 Tao Chen , Miqing Li

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of…

Machine Learning · Computer Science 2026-01-21 Jianhao Ma , Yu Huang , Yuejie Chi , Yuxin Chen

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 Post-Optimization Model Edit (POME), a new algorithm that enhances the performance of fine-tuned large language models using only their pretrained and fine-tuned checkpoints, without requiring extra data or further…

Machine Learning · Computer Science 2025-10-09 Yong Liu , Di Fu , Yang Luo , Zirui Zhu , Minhao Cheng , Cho-Jui Hsieh , Yang You

Proximal Policy Optimization (PPO) is a widely used reinforcement learning algorithm that heavily relies on accurate advantage estimates for stable and efficient training. However, raw advantage signals can exhibit significant variance,…

Machine Learning · Computer Science 2025-05-22 Soham Sane

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

While Multi-view Graph Neural Networks (MVGNNs) excel at leveraging diverse modalities for learning object representation, existing methods assume identical local topology structures across modalities that overlook real-world discrepancies.…

Machine Learning · Computer Science 2024-06-05 Peiyu Liang , Hongchang Gao , Xubin He