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When training neural models, it is common to combine multiple loss terms. The balancing of these terms requires considerable human effort and is computationally demanding. Moreover, the optimal trade-off between the loss term can change as…

Machine Learning · Computer Science 2020-06-29 Itzik Malkiel , Lior Wolf

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed…

Machine Learning · Computer Science 2024-11-06 Ionut-Vlad Modoranu , Mher Safaryan , Grigory Malinovsky , Eldar Kurtic , Thomas Robert , Peter Richtarik , Dan Alistarh

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

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…

Adaptive optimization algorithms such as Adam are widely used in deep learning. The stability of such algorithms is often improved with a warmup schedule for the learning rate. Motivated by the difficulty of choosing and tuning warmup…

Machine Learning · Computer Science 2021-03-23 Jerry Ma , Denis Yarats

The Adam optimizer is a popular choice in contemporary deep learning, due to its strong empirical performance. However we observe that in privacy sensitive scenarios, the traditional use of Differential Privacy (DP) with the Adam optimizer…

Machine Learning · Computer Science 2023-12-25 Qiaoyue Tang , Frederick Shpilevskiy , Mathias Lécuyer

Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…

Machine Learning · Computer Science 2025-03-19 Dayal Singh Kalra , John Kirchenbauer , Maissam Barkeshli , Tom Goldstein

In the training of neural networks, adaptive moment estimation (Adam) typically converges fast but exhibits suboptimal generalization performance. A widely accepted explanation for its defect in generalization is that it often tends to…

Machine Learning · Computer Science 2026-03-10 Tao Shi , Liangming Chen , Long Jin , Mengchu Zhou

Gradient-based first-order adaptive optimization methods such as the Adam optimizer are prevalent in training artificial networks, achieving the state-of-the-art results. This work attempts to answer the question whether it is viable for…

Neural and Evolutionary Computing · Computer Science 2022-12-20 Yukun Yang , Peng Li

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

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence…

Machine Learning · Computer Science 2026-05-12 Kristi Topollai , Anna Choromanska

Recent work by Xia et al. leveraged the continuous-limit of the classical momentum accelerated gradient descent and proposed heavy-ball neural ODEs. While this model offers computational efficiency and high utility over vanilla neural ODEs,…

Machine Learning · Computer Science 2022-07-14 Suneghyeon Cho , Sanghyun Hong , Kookjin Lee , Noseong Park

With the increasing practicality of deep learning applications, practitioners are inevitably faced with datasets corrupted by noise from various sources such as measurement errors, mislabeling, and estimated surrogate inputs/outputs that…

Machine Learning · Computer Science 2023-08-30 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Takamitsu Matsubara

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension…

Machine Learning · Computer Science 2019-10-16 Zhanhong Jiang , Aditya Balu , Sin Yong Tan , Young M Lee , Chinmay Hegde , Soumik Sarkar

Distribution-based search algorithms are an effective approach for evolutionary reinforcement learning of neural network controllers. In these algorithms, gradients of the total reward with respect to the policy parameters are estimated…

Neural and Evolutionary Computing · Computer Science 2020-12-09 Nihat Engin Toklu , Paweł Liskowski , Rupesh Kumar Srivastava

Adaptive moment methods such as Adam use a diagonal, coordinate-wise preconditioner based on exponential moving averages of squared gradients. This diagonal scaling is coordinate-system dependent and can struggle with dense or rotated…

Machine Learning · Computer Science 2026-04-09 Devender Singh , Tarun Sheel

Convolutional neural networks (CNNs) are trained using stochastic gradient descent (SGD)-based optimizers. Recently, the adaptive moment estimation (Adam) optimizer has become very popular due to its adaptive momentum, which tackles the…

Machine Learning · Computer Science 2023-09-12 S. K. Roy , M. E. Paoletti , J. M. Haut , S. R. Dubey , P. Kar , A. Plaza , B. B. Chaudhuri

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient…

Machine Learning · Computer Science 2026-03-09 Zhipeng Yao , Rui Yu , Guisong Chang , Ying Li , Yu Zhang , Dazhou Li

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

Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM…

Optimization and Control · Mathematics 2025-05-29 Arnulf Jentzen , Julian Kranz , Adrian Riekert