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The Adam optimizer, often used in Machine Learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. This work shows that the classical Adam algorithm…

Computational Engineering, Finance, and Science · Computer Science 2024-09-17 Abhinab Bhattacharjee , Andrey A. Popov , Arash Sarshar , Adrian Sandu

We implement the adaptive step size scheme from the optimization methods AdaGrad and Adam in a novel variant of the Proximal Gradient Method (PGM). Our algorithm, dubbed AdaProx, avoids the need for explicit computation of the Lipschitz…

Optimization and Control · Mathematics 2020-07-06 Peter Melchior , Rémy Joseph , Fred Moolekamp

Running out of GPU memory has become a main bottleneck for large-scale DNN training. How to reduce the memory footprint during training has received intensive research attention. We find that previous gradient accumulation reduces…

Machine Learning · Computer Science 2023-06-01 Yijia Zhang , Yibo Han , Shijie Cao , Guohao Dai , Youshan Miao , Ting Cao , Fan Yang , Ningyi Xu

Gradient descent (GD) based optimization methods are these days the standard tools to train deep neural networks in artificial intelligence systems. In optimization procedures in deep learning the employed optimizer is often not the…

Optimization and Control · Mathematics 2025-09-24 Steffen Dereich , Robin Graeber , Arnulf Jentzen , Adrian Riekert

Deep neural networks are traditionally trained using human-designed stochastic optimization algorithms, such as SGD and Adam. Recently, the approach of learning to optimize network parameters has emerged as a promising research topic.…

Machine Learning · Computer Science 2018-11-26 Shipeng Wang , Jian Sun , Zongben Xu

Since the 21st century, artificial intelligence has been leading a new round of industrial revolution. Under the training framework, the optimization algorithm aims to stably converge high-dimensional optimization to local and even global…

Machine Learning · Computer Science 2025-12-02 Meng Zhu , Quan Xiao , Weidong Min

We present a novel, fast (exponential rate adaption), ab initio (hyper-parameter-free) gradient based optimizer algorithm. The main idea of the method is to adapt the learning rate $\alpha$ by situational awareness, mainly striving for…

Machine Learning · Computer Science 2023-09-13 Alexander Kleinsorge , Stefan Kupper , Alexander Fauck , Felix Rothe

Adaptive optimizers, most notably Adam, have become the default standard for training large-scale neural networks such as Transformers. These methods maintain running estimates of gradient first and second moments, incurring substantial…

Machine Learning · Computer Science 2026-05-12 Yao Lu , Dengdong Fan , Shixun Zhang , Yonghong Tian

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to…

Machine Learning · Computer Science 2025-12-09 Yehonathan Refael , Jonathan Svirsky , Boris Shustin , Wasim Huleihel , Ofir Lindenbaum

This paper introduces EXAdam ($\textbf{EX}$tended $\textbf{Adam}$), a novel optimization algorithm that builds upon the widely-used Adam optimizer. EXAdam incorporates two key enhancements: (1) new debiasing terms for improved moment…

Machine Learning · Computer Science 2025-05-19 Ahmed M. Adly

Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…

Optimization and Control · Mathematics 2020-12-29 Mingrui Liu , Youssef Mroueh , Jerret Ross , Wei Zhang , Xiaodong Cui , Payel Das , Tianbao Yang

The concept of learning to optimize involves utilizing a trainable optimization strategy rather than relying on manually defined full gradient estimations such as ADAM. We present a framework that jointly trains the full gradient estimator…

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

We investigate the role of the optimizer in determining the quality of the model fit for neural networks with a small to medium number of parameters. We study the performance of Adam, an algorithm for first-order gradient-based optimization…

Machine Learning · Computer Science 2022-05-17 John Taylor , Wenyi Wang , Biswajit Bala , Tomasz Bednarz

Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great…

Machine Learning · Computer Science 2025-02-18 Thang Do , Sonja Hannibal , Arnulf Jentzen

The insufficient generalization of adaptive moment estimation (Adam) has hindered its broader application. Recent studies have shown that flat minima in loss landscapes are highly associated with improved generalization. Inspired by the…

Machine Learning · Computer Science 2024-12-18 Long Jin , Han Nong , Liangming Chen , Zhenming Su

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

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

The adaptive moment estimation algorithm Adam (Kingma and Ba) is a popular optimizer in the training of deep neural networks. However, Reddi et al. have recently shown that the convergence proof of Adam is problematic and proposed a variant…

Machine Learning · Computer Science 2019-11-01 Tran Thi Phuong , Le Trieu Phong

Balancing convergence efficiency and robustness under Differential Privacy (DP) is a central challenge in Federated Learning (FL). While AdamW accelerates training and fine-tuning in large-scale models, we find that directly applying it to…

Machine Learning · Computer Science 2026-04-21 Jin Liu , Yinbin Miao , Ning Xi , Junkang Liu

In recent years, large language models (LLMs) have made remarkable progress, with model optimization primarily relying on gradient-based optimizers such as Adam. However, these gradient-based methods impose stringent hardware requirements,…

Artificial Intelligence · Computer Science 2025-10-24 WenTao Liu , Siyu Song , Hao Hao , Aimin Zhou