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Adam is shown not being able to converge to the optimal solution in certain cases. Researchers recently propose several algorithms to avoid the issue of non-convergence of Adam, but their efficiency turns out to be unsatisfactory in…

Machine Learning · Computer Science 2019-06-25 Zhiming Zhou , Qingru Zhang , Guansong Lu , Hongwei Wang , Weinan Zhang , Yong Yu

The success of the Adam optimizer on a wide array of architectures has made it the default in settings where stochastic gradient descent (SGD) performs poorly. However, our theoretical understanding of this discrepancy is lagging,…

Machine Learning · Computer Science 2023-04-28 Frederik Kunstner , Jacques Chen , Jonathan Wilder Lavington , Mark Schmidt

Synchronous mini-batch SGD is state-of-the-art for large-scale distributed machine learning. However, in practice, its convergence is bottlenecked by slow communication rounds between worker nodes. A natural solution to reduce communication…

Machine Learning · Computer Science 2019-04-26 Kumar Kshitij Patel , Aymeric Dieuleveut

Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI)…

Optimization and Control · Mathematics 2025-11-11 Steffen Dereich , Thang Do , Arnulf Jentzen , Philippe von Wurstemberger

Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion…

Machine Learning · Computer Science 2017-12-21 Nitish Shirish Keskar , Richard Socher

In contrast to SGD, adaptive gradient methods like Adam allow robust training of modern deep networks, especially large language models. However, the use of adaptivity not only comes at the cost of extra memory but also raises the…

Machine Learning · Computer Science 2022-07-20 Zhiyuan Li , Srinadh Bhojanapalli , Manzil Zaheer , Sashank J. Reddi , Sanjiv Kumar

Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to excellent scalability properties of this algorithm, and to its efficiency in the context of training deep neural networks.…

Machine Learning · Computer Science 2017-12-07 Dan Alistarh , Demjan Grubic , Jerry Li , Ryota Tomioka , Milan Vojnovic

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

Machine Learning · Computer Science 2026-05-29 Sakshi Kumari , Shyam Kumar M , Sushmitha P

In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge.…

Optimization and Control · Mathematics 2025-04-28 Dmitry Bylinkin , Aleksandr Beznosikov

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of…

Optimization and Control · Mathematics 2021-06-25 Mher Safaryan , Peter Richtárik

In this paper, we present a distributed variant of adaptive stochastic gradient method for training deep neural networks in the parameter-server model. To reduce the communication cost among the workers and server, we incorporate two types…

Machine Learning · Computer Science 2021-06-16 Congliang Chen , Li Shen , Haozhi Huang , Wei Liu

Large language models have achieved major advances across domains, yet training them remains extremely resource-intensive. We revisit Sign-SGD, which serves both as a memory-efficient optimizer for single-node training and as a gradient…

Machine Learning · Computer Science 2026-02-23 Daniil Medyakov , Sergey Stanko , Gleb Molodtsov , Philip Zmushko , Grigoriy Evseev , Egor Petrov , Aleksandr Beznosikov

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep…

Machine Learning · Computer Science 2022-10-14 Mingrui Liu , Zhenxun Zhuang , Yunwei Lei , Chunyang Liao

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Machine Learning · Computer Science 2020-03-04 Achraf Bahamou , Donald Goldfarb

Adam is the default algorithm for training neural networks, including large language models (LLMs). However, \citet{reddi2019convergence} provided an example that Adam diverges, raising concerns for its deployment in AI model training. We…

Machine Learning · Computer Science 2026-03-03 Yushun Zhang , Bingran Li , Congliang Chen , Zhi-Quan Luo , Ruoyu Sun

Full fine-tuning of Large Language Models (LLMs) is notoriously memory-intensive, primarily because conventional optimizers such as SGD or Adam assume access to exact gradients derived from cached activations. Existing solutions either…

Machine Learning · Computer Science 2025-10-28 Jing Yang , Kaitong Cai , Yijia Fan , Yufeng Yang , Keze Wang

The growth of large language models (LLMs) increases challenges of accelerating distributed training across multiple GPUs in different data centers. Moreover, concerns about data privacy and data exhaustion have heightened interest in…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-18 Zhenheng Tang , Zichen Tang , Junlin Huang , Xinglin Pan , Rudan Yan , Yuxin Wang , Amelie Chi Zhou , Shaohuai Shi , Xiaowen Chu , Bo Li

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

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often…

Machine Learning · Computer Science 2022-06-15 Zeke Xie , Xinrui Wang , Huishuai Zhang , Issei Sato , Masashi Sugiyama

Regional energy caps limit the growth of any single data center used for large-scale model training. This single-center training paradigm works when model size remains manageable, but exponential growth in the model size and computational…

Machine Learning · Computer Science 2025-12-18 Rongwei Lu , Jingyan Jiang , Chunyang Li , Xingguang Wei , Zhi Wang