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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

Recent advances in spectral optimization, notably Muon, have demonstrated that constraining update steps to the Stiefel manifold can significantly accelerate training and improve generalization. However, Muon implicitly assumes an isotropic…

Machine Learning · Computer Science 2026-04-02 Yechen Zhang , Shuhao Xing , Junhao Huang , Kai Lv , Yunhua Zhou , Xipeng Qiu , Qipeng Guo , Kai Chen

Quantization-aware training (QAT) is an effective method to drastically reduce the memory footprint of LLMs while keeping performance degradation at an acceptable level. However, the optimal choice of quantization format and bit-width…

Machine Learning · Computer Science 2026-02-18 Sohir Maskey , Constantin Eichenberg , Johannes Messner , Douglas Orr

Post-training quantization (PTQ) is a promising approach to reducing the storage and computational requirements of large language models (LLMs) without additional training cost. Recent PTQ studies have primarily focused on quantizing only…

Machine Learning · Computer Science 2026-02-17 Reena Elangovan , Charbel Sakr , Anand Raghunathan , Brucek Khailany

Quantization is an effective way to reduce the memory cost of large-scale model training. However, most existing methods adopt fixed-precision policies, which ignore the fact that optimizer-state distributions vary significantly across…

Machine Learning · Computer Science 2026-04-10 Minglu Liu , Cunchen Hu , Liangliang Xu , Fengming Tang , Ruijia Wang , Fu Yu

Training large language models with FP8 formats offers significant efficiency gains. However, the reduced numerical precision of FP8 poses challenges for stable and accurate training. Current frameworks preserve training performance using…

Machine Learning · Computer Science 2025-12-08 Yu Zhang , Hui-Ling Zhen , Mingxuan Yuan , Bei Yu

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

Large Language Models (LLMs) have showcased remarkable impacts across a wide spectrum of natural language processing tasks. Fine-tuning these pretrained models on downstream datasets provides further significant performance gains; however,…

Computation and Language · Computer Science 2026-03-19 Zhikai Li , Xiaoxuan Liu , Banghua Zhu , Zhen Dong , Qingyi Gu , Kurt Keutzer

Recently, Muon and related spectral optimizers have demonstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behaviour remains poorly understood. We analyze stochastic spectral…

Optimization and Control · Mathematics 2026-05-12 Elliot Paquette , Noah Marshall , Lucas Benigni , Guangyuan Wang , Atish Agarwala , Courtney Paquette

Spectral optimizers such as Muon have recently shown strong empirical performance in large-scale language model training, but the source and extent of their advantage remain poorly understood. We study this question through the linear…

Machine Learning · Computer Science 2026-04-29 Juno Kim , Eshaan Nichani , Denny Wu , Alberto Bietti , Jason D. Lee

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

There has been many papers in academic literature on quantizing weight tensors in deep learning models to reduce inference latency and memory footprint. TVM also has the ability to quantize weights and support low-bit computations. Although…

Machine Learning · Computer Science 2023-08-23 Mingfei Guo

Large language models (LLMs) are omnipresent, however their practical deployment is challenging due to their ever increasing computational and memory demands. Quantization is one of the most effective ways to make them more compute and…

Machine Learning · Computer Science 2024-09-04 Yelysei Bondarenko , Riccardo Del Chiaro , Markus Nagel

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

Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…

Machine Learning · Computer Science 2025-02-11 Meyer Scetbon , Chao Ma , Wenbo Gong , Edward Meeds

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

The rapid scaling of language models (LMs) has resulted in unprecedented computational, memory, and energy requirements, making their training and deployment increasingly unsustainable. Quantization has emerged as an essential compression…

Large Language Models (LLMs) have shown an impressive capability in code generation. The LLM effectiveness generally increases with its size: The higher the number of LLM's trainable parameters the better its ability to implement code.…

Software Engineering · Computer Science 2026-01-28 Alessandro Giagnorio , Antonio Mastropaolo , Saima Afrin , Massimiliano Di Penta , Gabriele Bavota

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

The growing demand for Large Language Models (LLMs) in applications such as content generation, intelligent chatbots, and sentiment analysis poses considerable challenges for LLM service providers. To efficiently use GPU resources and boost…

Machine Learning · Computer Science 2024-04-17 Yilong Zhao , Chien-Yu Lin , Kan Zhu , Zihao Ye , Lequn Chen , Size Zheng , Luis Ceze , Arvind Krishnamurthy , Tianqi Chen , Baris Kasikci
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