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Adaptive gradient methods like Adagrad and its variants are widespread in large-scale optimization. However, their use of diagonal preconditioning matrices limits the ability to capture parameter correlations. Full-matrix adaptive methods,…

Machine Learning · Computer Science 2025-09-01 Tatyana Matveeva , Aleksandr Katrutsa , Evgeny Frolov

In current deep learning tasks, Adam style optimizers such as Adam, Adagrad, RMSProp, Adafactor, and Lion have been widely used as alternatives to SGD style optimizers. These optimizers typically update model parameters using the sign of…

Machine Learning · Computer Science 2024-10-29 Shuaipeng Li , Penghao Zhao , Hailin Zhang , Xingwu Sun , Hao Wu , Dian Jiao , Weiyan Wang , Chengjun Liu , Zheng Fang , Jinbao Xue , Yangyu Tao , Bin Cui , Di Wang

Adaptive optimization algorithms, particularly Adam and its variant AdamW, are fundamental components of modern deep learning. However, their training dynamics lack comprehensive theoretical understanding, with limited insight into why…

Machine Learning · Computer Science 2024-12-23 Rhys Gould , Hidenori Tanaka

A number of recent adaptive optimizers improve the generalisation performance of Adam by essentially reducing the variance of adaptive stepsizes to get closer to SGD with momentum. Following the above motivation, we suppress the range of…

Machine Learning · Computer Science 2024-07-15 Guoqiang Zhang

Machine learning algorithms aim to find patterns from observations, which may include some noise, especially in robotics domain. To perform well even with such noise, we expect them to be able to detect outliers and discard them when…

Machine Learning · Computer Science 2020-03-04 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Kenji Sugimoto

Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…

Artificial Intelligence · Computer Science 2026-05-07 Yiheng Zhang , Kaiyan Zhao , Shaowu Wu , Yiming Wang , Jiajun Wu , Leong Hou U , Steve Drew , Xiaoguang Niu

We introduce AdamS, a simple yet effective alternative to Adam for large language model (LLM) pretraining and post-training. By leveraging a novel denominator, i.e., the root of weighted sum of squares of the momentum and the current…

Machine Learning · Computer Science 2025-05-23 Huishuai Zhang , Bohan Wang , Luoxin Chen

Large language models (LLMs) are increasingly used in learning algorithms, evaluations, and optimization tasks. Recent studies have shown that using LLM-based optimizers to automatically optimize model prompts, demonstrations, predictions…

Computation and Language · Computer Science 2025-10-23 Guowei Xu , Mert Yuksekgonul , Carlos Guestrin , James Zou

Adaptive optimizers such as Adam (Kingma & Ba, 2015) have been central to the success of large language models. However, they often require to maintain optimizer states throughout training, which can result in memory requirements several…

Machine Learning · Computer Science 2025-02-24 Chao Ma , Wenbo Gong , Meyer Scetbon , Edward Meeds

In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full…

Machine Learning · Computer Science 2025-02-06 Da Chang , Yu Li , Ganzhao Yuan

Despite their popularity in deep learning and machine learning in general, the theoretical properties of adaptive optimizers such as Adagrad, RMSProp, Adam or AdamW are not yet fully understood. In this paper, we develop a novel framework…

Machine Learning · Computer Science 2022-11-09 Han Nguyen , Hai Pham , Sashank J. Reddi , Barnabás Póczos

Hyperparameter tuning is one of the most time-consuming workloads in deep learning. State-of-the-art optimizers, such as AdaGrad, RMSProp and Adam, reduce this labor by adaptively tuning an individual learning rate for each variable.…

Machine Learning · Statistics 2018-02-16 Jian Zhang , Ioannis Mitliagkas

The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to…

Machine Learning · Computer Science 2021-06-22 Zechun Liu , Zhiqiang Shen , Shichao Li , Koen Helwegen , Dong Huang , Kwang-Ting Cheng

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We…

Machine Learning · Statistics 2018-05-23 Ashia C. Wilson , Rebecca Roelofs , Mitchell Stern , Nathan Srebro , Benjamin Recht

Stochastic optimization algorithms using exponential moving averages of the past gradients, such as ADAM, RMSProp and AdaGrad, have been having great successes in many applications, especially in training deep neural networks. ADAM in…

Machine Learning · Computer Science 2026-01-30 Ruiqi Wang , Diego Klabjan

AdamW has become one of the most effective optimizers for training large-scale models. We have also observed its effectiveness in the context of federated learning (FL). However, directly applying AdamW in federated learning settings poses…

Machine Learning · Computer Science 2026-04-21 Junkang Liu , Fanhua Shang , Hongying Liu , Yuxuan Tian , Yuanyuan Liu , Jin Liu , Kewen Zhu , Zhouchen Lin

We propose ActiveLR, an optimization meta algorithm that localizes the learning rate, $\alpha$, and adapts them at each epoch according to whether the gradient at each epoch changes sign or not. This sign-conscious algorithm is aware of…

Machine Learning · Computer Science 2023-01-25 Davood Wadi , Marc Fredette , Sylvain Senecal

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

Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…

Machine Learning · Computer Science 2026-02-19 Akiyoshi Tomihari , Issei Sato

The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the…

Machine Learning · Computer Science 2020-12-15 Lukas Balles , Philipp Hennig