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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 suggest a novel classification algorithm that is based on local approximations and explain its connections with Artificial Neural Networks (ANNs) and Nearest Neighbour classifiers. We illustrate it on the datasets MNIST and EMNIST of…

Machine Learning · Computer Science 2022-07-19 Eric Setterqvist , Natan Kruglyak , Robert Forchheimer

Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…

Machine Learning · Computer Science 2020-12-17 Bingxin Zhou , Xuebin Zheng , Junbin Gao

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared…

Machine Learning · Computer Science 2019-04-22 Liangchen Luo , Yuanhao Xiong , Yan Liu , Xu Sun

Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable…

Optimization and Control · Mathematics 2024-02-09 Arnulf Jentzen , Adrian Riekert

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

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 first-order optimizers are fundamental tools in deep learning, although they may suffer from poor generalization due to the nonuniform gradient scaling. In this work, we propose AdamL, a novel variant of the Adam optimizer, that…

Machine Learning · Statistics 2023-12-27 Lu Xia , Stefano Massei

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type…

Machine Learning · Computer Science 2024-09-24 Yiming Jiang , Jinlan Liu , Dongpo Xu , Danilo P. Mandic

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

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

The paper presents the formulation, implementation, and evaluation of the ArcGD optimiser. The evaluation is conducted initially on a non-convex benchmark function and subsequently on a real-world ML dataset. The initial comparative study…

Machine Learning · Computer Science 2026-03-25 Nikhil Verma , Joonas Linnosmaa , Leonardo Espinosa-Leal , Napat Vajragupta

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

Deep learning algorithms - typically consisting of a class of deep neural networks trained by a stochastic gradient descent (SGD) optimization method - are nowadays the key ingredients in many artificial intelligence (AI) systems and have…

Machine Learning · Computer Science 2024-07-12 Steffen Dereich , Robin Graeber , Arnulf Jentzen

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

A major contributor to the quality of a deep learning model is the selection of the optimizer. We propose a new dual-joint search space in the realm of neural optimizer search (NOS), along with an integrity check, to automate the process of…

Neural and Evolutionary Computing · Computer Science 2024-04-11 Brandon Morgan , Dean Hougen

AdamZ is an advanced variant of the Adam optimiser, developed to enhance convergence efficiency in neural network training. This optimiser dynamically adjusts the learning rate by incorporating mechanisms to address overshooting and…

Machine Learning · Computer Science 2024-11-26 Ilia Zaznov , Atta Badii , Alfonso Dufour , Julian Kunkel

We present Amos, a stochastic gradient-based optimizer designed for training deep neural networks. It can be viewed as an Adam optimizer with theoretically supported, adaptive learning-rate decay and weight decay. A key insight behind Amos…

Machine Learning · Computer Science 2022-11-22 Ran Tian , Ankur P. Parikh

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Machine Learning · Computer Science 2020-11-25 Mingrui Liu , Wei Zhang , Francesco Orabona , Tianbao Yang

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular…

Machine Learning · Computer Science 2019-03-12 Xiangyi Chen , Sijia Liu , Ruoyu Sun , Mingyi Hong