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Optimizers play an important role in both pretraining and finetuning stages when training large language models (LLMs). In this paper, we present an observation that full finetuning with the same optimizer as in pretraining achieves a…

Machine Learning · Computer Science 2026-05-08 Yuxing Liu , Jianyu Wang , Tong Zhang

Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting…

Machine Learning · Computer Science 2024-07-03 Clare Lyle , Zeyu Zheng , Khimya Khetarpal , James Martens , Hado van Hasselt , Razvan Pascanu , Will Dabney

Recently, the Muon optimizer based on matrix orthogonalization has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling…

Conventional fine-tuning encounters increasing difficulties given the size of current Pre-trained Language Models, which makes parameter-efficient tuning become the focal point of frontier research. Previous methods in this field add…

Computation and Language · Computer Science 2022-12-12 Wang Qi , Yu-Ping Ruan , Yuan Zuo , Taihao Li

Muon has recently emerged as a strong optimizer for large language model pre-training, orthogonalizing the momentum matrix via Newton--Schulz polar iterations. A natural intuition is that polar iterations, by flattening the singular…

Machine Learning · Computer Science 2026-05-15 Ruijie Zhang , Yequan Zhao , Ziyue Liu , Zhengyang Wang , Yupeng Su , Liyan Tan , 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

Optimizers are crucial for the efficient training of Large Language Models (LLMs). While AdamW is the de facto standard, recent structure-aware optimizers like Muon have emerged, which regularize gradient updates by operating on entire…

Machine Learning · Computer Science 2025-10-07 Zehua Liu , Han Wu , Xiaojin Fu , Shuqi Liu , Xiongwei Han , Tao Zhong , Mingxuan Yuan

Although normalization layers have long been viewed as indispensable components of deep learning architectures, the recent introduction of Dynamic Tanh (DyT) has demonstrated that alternatives are possible. The point-wise function DyT…

Machine Learning · Computer Science 2026-04-01 Mingzhi Chen , Taiming Lu , Jiachen Zhu , Mingjie Sun , Zhuang Liu

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

Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a…

Artificial Intelligence · Computer Science 2026-05-12 Fangzhao Zhang , Sungyoon Kim , Erica Zhang , Yiqi Jiang , Mert Pilanci

This work analyzes the training dynamics of Image Restoration (IR) Transformers and uncovers a critical yet overlooked issue: conventional LayerNorm (LN) drives feature magnitudes to diverge to a million scale and collapses channel-wise…

Computer Vision and Pattern Recognition · Computer Science 2026-02-23 MinKyu Lee , Sangeek Hyun , Woojin Jun , Hyunjun Kim , Jiwoo Chung , Jae-Pil Heo

The choice of optimizer significantly impacts the training efficiency and computational costs of large language models (LLMs). Recently, the Muon optimizer has demonstrated promising results by orthogonalizing parameter updates, improving…

Machine Learning · Computer Science 2025-10-08 Zichong Li , Liming Liu , Chen Liang , Weizhu Chen , Tuo Zhao

MLP is a heavily used backbone in modern deep learning (DL) architectures for supervised learning on tabular data, and AdamW is the go-to optimizer used to train tabular DL models. Unlike architecture design, however, the choice of…

Machine Learning · Computer Science 2026-04-20 Yury Gorishniy , Ivan Rubachev , Dmitrii Feoktistov , Artem Babenko

Training Deep Learning (DL) models require large, high-quality datasets, often assembled with data from different institutions. Federated Learning (FL) has been emerging as a method for privacy-preserving pooling of datasets employing…

Machine Learning · Computer Science 2023-03-21 Bruno Casella , Roberto Esposito , Antonio Sciarappa , Carlo Cavazzoni , Marco Aldinucci

Effectively aligning Large Language Models (LLMs) with human-centric values while preventing the degradation of abilities acquired through Pre-training and Supervised Fine-tuning (SFT) poses a central challenge in Reinforcement Learning…

Computation and Language · Computer Science 2024-05-29 Keming Lu , Bowen Yu , Fei Huang , Yang Fan , Runji Lin , Chang Zhou

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

We demonstrate that the choice of optimizer, neural network architecture, and regularizer significantly affect the adversarial robustness of linear neural networks, providing guarantees without the need for adversarial training. To this…

Machine Learning · Computer Science 2021-06-08 Fartash Faghri , Sven Gowal , Cristina Vasconcelos , David J. Fleet , Fabian Pedregosa , Nicolas Le Roux

Large language models (LLMs) have shown remarkable abilities in diverse natural language processing (NLP) tasks. The LLMs generally undergo supervised fine-tuning (SFT) followed by preference alignment to be usable in downstream…

Computation and Language · Computer Science 2024-06-27 Shiva Kumar Pentyala , Zhichao Wang , Bin Bi , Kiran Ramnath , Xiang-Bo Mao , Regunathan Radhakrishnan , Sitaram Asur , Na , Cheng

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can…

Computation and Language · Computer Science 2026-05-19 Haozhan Tang , Xiuqi Zhu , Xinyin Zhang , Boxun Li , Virginia Smith , Kevin Kuo

Safety alignment for large language models (LLMs) aims to reduce harmful or unsafe behavior while preserving general utility. However, recent findings reveal that alignment effects can be fragile: lightweight post-alignment manipulations,…

Artificial Intelligence · Computer Science 2026-05-29 Zhihao Liu , Yifan Wu , Jian Lou , Di Wang , Yuxi Zhou , Yuke Hu
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