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Reinforcement learning (RL), particularly RL from verifiable reward (RLVR), has become a crucial phase of training large language models (LLMs) and a key focus of current scaling efforts. However, optimization practices in RL largely follow…

Machine Learning · Computer Science 2026-02-25 Sagnik Mukherjee , Lifan Yuan , Pavan Jayasinha , Dilek Hakkani-Tür , Hao Peng

This study explores a novel approach to enhance the performance of Large Language Models (LLMs) through the optimization of input data within prompts. While previous research has primarily focused on refining instruction components and…

Machine Learning · Computer Science 2025-02-18 Sam Lin , Wenyue Hua , Lingyao Li , Zhenting Wang , Yongfeng Zhang

Recent research explores optimization using large language models (LLMs) by either iteratively seeking next-step solutions from LLMs or directly prompting LLMs for an optimizer. However, these approaches exhibit inherent limitations,…

Optimization and Control · Mathematics 2024-03-06 Zeyuan Ma , Hongshu Guo , Jiacheng Chen , Guojun Peng , Zhiguang Cao , Yining Ma , Yue-Jiao Gong

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

Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation. However, existing PEFT methods mainly operate in Euclidean space,…

Machine Learning · Computer Science 2026-02-17 Buze Zhang , Jinkai Tao , Zilang Zeng , Neil He , Ali Maatouk , Menglin Yang , Rex Ying

In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral…

Training large language models (LLMs) relies almost exclusively on dense adaptive optimizers with increasingly sophisticated preconditioners. We challenge this by showing that randomly masking parameter updates can be highly effective, with…

Machine Learning · Computer Science 2026-02-18 Taejong Joo , Wenhan Xia , Cheolmin Kim , Ming Zhang , Eugene Ie

Large language models (LLMs) have demonstrated remarkable performance due to their large parameter counts and extensive training data. However, their scale leads to significant memory bottlenecks during training, especially when using…

Machine Learning · Computer Science 2026-05-14 Ziqing Wen , Jiahuan Wang , Ping Luo , Dongsheng Li , Tao Sun

While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models…

Machine Learning · Computer Science 2026-05-11 Dingzhi Yu , Hongyi Tao , Yuanyu Wan , Luo Luo , Lijun Zhang

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

Large Language Models (LLMs) are currently pre-trained and fine-tuned on large cloud servers. The next frontier is LLM personalization, where a foundation model can be fine-tuned with user/task-specific data. Given the sensitive nature of…

Machine Learning · Computer Science 2025-09-23 Lei Gao , Amir Ziashahabi , Yue Niu , Salman Avestimehr , Murali Annavaram

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

Machine Learning · Computer Science 2026-05-22 Athanasios Glentis , Jiaxiang Li , Andi Han , Mingyi Hong

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks. Typically, LLMs are first pre-trained on large corpora and subsequently fine-tuned on task-specific datasets. However, during fine-tuning,…

Machine Learning · Computer Science 2025-10-21 Yupeng Chen , Senmiao Wang , Yushun Zhang , Zhihang Lin , Haozhe Zhang , Weijian Sun , Tian Ding , Ruoyu Sun

In contrast to single-objective optimization (SOO), multi-objective optimization (MOO) requires an optimizer to find the Pareto frontier, a subset of feasible solutions that are not dominated by other feasible solutions. In this paper, we…

Machine Learning · Computer Science 2024-08-13 Yiyang Zhao , Linnan Wang , Kevin Yang , Tianjun Zhang , Tian Guo , Yuandong Tian

Recent advanced large language models (LLMs) have showcased their emergent capability of in-context learning, facilitating intelligent decision-making through natural language prompts without retraining. This new machine learning paradigm…

Computational Engineering, Finance, and Science · Computer Science 2024-12-12 Xinxin Zhang , Zhuoqun Xu , Guangpu Zhu , Chien Ming Jonathan Tay , Yongdong Cui , Boo Cheong Khoo , Lailai 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

While spectral-based optimizers like Muon operate directly on the spectrum of updates, standard adaptive methods such as AdamW do not account for the spectral structure of weights and gradients, leaving them vulnerable to two empirical…

Machine Learning · Computer Science 2026-05-29 Xiaowen Jiang , Andrei Semenov , Sebastian U. Stich

Prompt engineering, as an efficient and effective way to leverage Large Language Models (LLM), has drawn a lot of attention from the research community. The existing research primarily emphasizes the importance of adapting prompts to…

Computation and Language · Computer Science 2024-07-08 Yuyan Chen , Zhihao Wen , Ge Fan , Zhengyu Chen , Wei Wu , Dayiheng Liu , Zhixu Li , Bang Liu , Yanghua Xiao

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

Optimizers play a decisive role in reducing pre-training times for LLMs and achieving better-performing models. In this study, we compare three major variants: the de-facto standard AdamW, the simpler Lion, developed through an evolutionary…

Machine Learning · Computer Science 2025-07-23 Joel Schlotthauer , Christian Kroos , Chris Hinze , Viktor Hangya , Luzian Hahn , Fabian Küch