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Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…

Machine Learning · Computer Science 2025-10-30 Zhifeng Wang , Longlong Li , Chunyan Zeng

In recent years, stochastic gradient descent (SGD) based techniques has become the standard tools for training neural networks. However, formal theoretical understanding of why SGD can train neural networks in practice is largely missing.…

Machine Learning · Computer Science 2017-11-03 Yuanzhi Li , Yang Yuan

Adaptive gradient optimization methods, such as Adam, are prevalent in training deep neural networks across diverse machine learning tasks due to their ability to achieve faster convergence. However, these methods often suffer from…

Machine Learning · Computer Science 2025-02-12 Abulikemu Abuduweili , Changliu Liu

Matrix factorization (MF) has been widely used in e.g., recommender systems, topic modeling and word embedding. Stochastic gradient descent (SGD) is popular in solving MF problems because it can deal with large data sets and is easy to do…

Machine Learning · Computer Science 2016-11-11 Xiaolong Xie , Wei Tan , Liana L. Fong , Yun Liang

Deep learning at scale is dominated by communication time. Distributing samples across nodes usually yields the best performance, but poses scaling challenges due to global information dissemination and load imbalance across uneven sample…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-22 Shigang Li , Tal Ben-Nun , Giorgi Nadiradze , Salvatore Di Girolamo , Nikoli Dryden , Dan Alistarh , Torsten Hoefler

Can modifying the training data distribution guide optimizers toward solutions with improved generalization when training large language models (LLMs)? In this work, we theoretically analyze an in-context linear regression model with…

Machine Learning · Computer Science 2026-02-03 Tushaar Gangavarapu , Jiping Li , Christopher Vattheuer , Zhangyang Wang , Baharan Mirzasoleiman

Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this…

Neural and Evolutionary Computing · Computer Science 2024-02-07 Ashok Vardhan Makkuva , Marco Bondaschi , Thijs Vogels , Martin Jaggi , Hyeji Kim , Michael C. Gastpar

Optimizer is an essential component for the success of deep learning, which guides the neural network to update the parameters according to the loss on the training set. SGD and Adam are two classical and effective optimizers on which…

Machine Learning · Computer Science 2023-07-04 Yineng Chen , Zuchao Li , Lefei Zhang , Bo Du , Hai Zhao

We introduce two complementary techniques for efficient optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm step size, generalizes AdaGrad-Norm and…

Machine Learning · Computer Science 2025-05-27 Thien Hang Nguyen , Huy Le Nguyen

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

Machine Learning · Computer Science 2022-02-10 Yizhou Wang , Yue Kang , Can Qin , Huan Wang , Yi Xu , Yulun Zhang , Yun Fu

Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

Machine Learning · Computer Science 2018-08-17 Robert Kleinberg , Yuanzhi Li , Yang Yuan

Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have…

Machine Learning · Computer Science 2023-06-14 Aditya Cowsik , Tankut Can , Paolo Glorioso

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

Currently, widely used first-order deep learning optimizers include non-adaptive learning rate optimizers and adaptive learning rate optimizers. The former is represented by SGDM (Stochastic Gradient Descent with Momentum), while the latter…

Machine Learning · Computer Science 2024-09-25 Honglin Qin , Hongye Zheng , Bingxing Wang , Zhizhong Wu , Bingyao Liu , Yuanfang Yang

Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning.…

Machine Learning · Statistics 2022-07-21 Adarsh M. Subramaniam , Akshayaa Magesh , Venugopal V. Veeravalli

Diagonal preconditioners are computationally feasible approximate to second-order optimizers, which have shown significant promise in accelerating training of deep learning models. Two predominant approaches are based on Adam and…

Machine Learning · Computer Science 2025-10-16 Bingbin Liu , Rachit Bansal , Depen Morwani , Nikhil Vyas , David Alvarez-Melis , Sham M. Kakade

Convolutional Neural Networks (CNN) are becoming a common presence in many applications and services, due to their superior recognition accuracy. They are increasingly being used on mobile devices, many times just by porting large models…

Machine Learning · Computer Science 2020-02-21 Valentin Radu , Kuba Kaszyk , Yuan Wen , Jack Turner , Jose Cano , Elliot J. Crowley , Bjorn Franke , Amos Storkey , Michael O'Boyle

1-bit gradient compression and local steps are two representative techniques that enable drastic communication reduction in distributed SGD. Their benefits, however, remain an open question on Adam-based large model pre-training (e.g. BERT…

Machine Learning · Computer Science 2022-05-24 Yucheng Lu , Conglong Li , Minjia Zhang , Christopher De Sa , Yuxiong He

Recent work [4] analyses the local convergence of Adam in a neighbourhood of an optimal solution for a twice-differentiable function. It is found that the learning rate has to be sufficiently small to ensure local stability of the optimal…

Machine Learning · Computer Science 2021-12-14 Guoqiang Zhang , Niwa Kenta , W. Bastiaan Kleijn

Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent in data-driven learning problems as well as in scientific…

Optimization and Control · Mathematics 2025-01-13 Steffen Dereich , Arnulf Jentzen , Adrian Riekert