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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

In recent studies, line search methods have shown significant improvements in the performance of traditional stochastic gradient descent techniques, eliminating the need for a specific learning rate schedule. In this paper, we identify…

Machine Learning · Computer Science 2024-03-28 Philip Kenneweg , Tristan Kenneweg , Barbara Hammer

Learned optimizers are increasingly effective, with performance exceeding that of hand designed optimizers such as Adam~\citep{kingma2014adam} on specific tasks \citep{metz2019understanding}. Despite the potential gains available, in…

Machine Learning · Computer Science 2021-01-20 Luke Metz , C. Daniel Freeman , Niru Maheswaranathan , Jascha Sohl-Dickstein

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous…

Machine Learning · Computer Science 2026-05-13 Pranav Vaidhyanathan , Lucas Schorling , Natalia Ares , Michael A. Osborne

Adam with decoupled weight decay, also known as AdamW, is widely acclaimed for its superior performance in language modeling tasks, surpassing Adam with $\ell_2$ regularization in terms of generalization and optimization. However, this…

Machine Learning · Computer Science 2024-04-09 Shuo Xie , Zhiyuan Li

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

Standard mixed-precision training of neural networks requires many bytes of accelerator memory for each model parameter. These bytes reflect not just the parameter itself, but also its gradient and one or more optimizer state variables.…

Machine Learning · Computer Science 2026-03-13 Jose Javier Gonzalez Ortiz , Abhay Gupta , Christopher Rinard , Davis Blalock

As optimizers are critical to the performances of neural networks, every year a large number of papers innovating on the subject are published. However, while most of these publications provide incremental improvements to existing…

Machine Learning · Computer Science 2021-08-10 Less Wright , Nestor Demeure

Here I present a small update to the bias-correction term in the Adam optimizer that has the advantage of making smaller gradient updates in the first several steps of training. With the default bias-correction, Adam may actually make…

Machine Learning · Computer Science 2021-10-25 John St John

Lion optimizer is a popular learning-based optimization algorithm in machine learning, which shows impressive performance in training many deep learning models. Although convergence property of the Lion optimizer has been studied, its…

Machine Learning · Computer Science 2026-04-17 Feihu Huang , Guanyi Zhang , Songcan Chen

We introduce a new method inspired by Adam that enhances convergence speed and achieves better loss function minima. Traditional optimizers, including Adam, apply uniform or globally adjusted learning rates across neural networks without…

Machine Learning · Computer Science 2024-11-01 Remi Genet , Hugo Inzirillo

Widely used compilers like GCC and LLVM usually have hundreds of optimizations controlled by optimization flags, which are enabled or disabled during compilation to improve runtime performance (e.g., small execution time) of the compiler…

Programming Languages · Computer Science 2023-05-01 Mingxuan Zhu , Dan Hao , Junjie Chen

Deep learning optimizers are optimization algorithms that enable deep neural networks to learn. The effectiveness of learning is highly dependent on the optimizer employed in the training process. Alongside the rapid advancement of deep…

Machine Learning · Computer Science 2025-09-24 Doğay Altınel

We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we…

Optimization and Control · Mathematics 2026-05-14 Yaxin Yu , Long Chen , Minfu Feng

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

Large language models have achieved remarkable success, but their extensive parameter size necessitates substantial memory for training, thereby setting a high threshold. While the recently proposed low-memory optimization (LOMO) reduces…

Machine Learning · Computer Science 2024-06-07 Kai Lv , Hang Yan , Qipeng Guo , Haijun Lv , Xipeng Qiu

Accelerated training algorithms, such as adaptive learning rates (or preconditioning) and various normalization methods, are widely used but not fully understood. When regularization is introduced, standard optimizers like adaptive learning…

Machine Learning · Computer Science 2025-12-30 Qiang Ye

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

This paper proposes an efficient optimizer called AdaPlus which integrates Nesterov momentum and precise stepsize adjustment on AdamW basis. AdaPlus combines the advantages of AdamW, Nadam, and AdaBelief and, in particular, does not…

Machine Learning · Computer Science 2023-12-27 Lei Guan

As deep learning models exponentially increase in size, optimizers such as Adam encounter significant memory consumption challenges due to the storage of first and second moment data. Current memory-efficient methods like Adafactor and CAME…

Machine Learning · Computer Science 2024-03-25 Pengxiang Zhao , Ping Li , Yingjie Gu , Yi Zheng , Stephan Ludger Kölker , Zhefeng Wang , Xiaoming Yuan