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First-order stochastic optimization methods are currently the most widely used class of methods for training deep neural networks. However, the choice of the optimizer has become an ad-hoc rule that can significantly affect the performance.…

Machine Learning · Computer Science 2020-10-21 Samy Jelassi , Aaron Defazio

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Machine Learning · Computer Science 2019-12-04 Michael R. Zhang , James Lucas , Geoffrey Hinton , Jimmy Ba

Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each…

Machine Learning · Computer Science 2024-12-10 Yun Yue , Zhiling Ye , Jiadi Jiang , Yongchao Liu , Ke Zhang

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

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

Machine Learning · Computer Science 2026-05-22 Saurabh Saini , Kapil Ahuja , Thomas Wick , Saurav Kumar

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

First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…

Machine Learning · Computer Science 2025-07-29 Yue Hu , Zanxia Cao , Yingchao Liu

Training language models becomes increasingly expensive with scale, prompting numerous attempts to improve optimization efficiency. Despite these efforts, the Adam optimizer remains the most widely used, due to a prevailing view that it is…

Machine Learning · Computer Science 2025-03-03 Rosie Zhao , Depen Morwani , David Brandfonbrener , Nikhil Vyas , Sham Kakade

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

Machine Learning · Computer Science 2021-11-09 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou

We introduce a new method inspired by Adam that enhances convergence speed and achieves better loss function minima. Traditional optimizers, including Adam, apply uniform or globally adjusted learning rates across neural networks without…

Machine Learning · Computer Science 2024-11-01 Remi Genet , Hugo Inzirillo

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

Machine Learning · Computer Science 2024-10-08 Gus Kristiansen , Mark Sandler , Andrey Zhmoginov , Nolan Miller , Anirudh Goyal , Jihwan Lee , Max Vladymyrov

Recent studies show deep neural networks (DNNs) are extremely vulnerable to the elaborately designed adversarial examples. Adversarial learning with those adversarial examples has been proved as one of the most effective methods to defend…

Machine Learning · Computer Science 2022-07-05 Yaguan Qian , Yuqi Wang , Bin Wang , Zhaoquan Gu , Yuhan Guo , Wassim Swaileh

In this work, to efficiently help escape the stationary and saddle points, we propose, analyze, and generalize a stochastic strategy performed as an operator for a first-order gradient descent algorithm in order to increase the target…

Machine Learning · Computer Science 2022-05-23 Wei Zhang , Yu Bao

We present a stochastic first-order optimization method specialized for deep neural networks (DNNs), ECCO-DNN. This method models the optimization variable trajectory as a dynamical system and develops a discretization algorithm that…

Machine Learning · Computer Science 2023-10-24 Carmel Fiscko , Aayushya Agarwal , Yihan Ruan , Soummya Kar , Larry Pileggi , Bruno Sinopoli

Due to the effectiveness of second-order algorithms in solving classical optimization problems, designing second-order optimizers to train deep neural networks (DNNs) has attracted much research interest in recent years. However, because of…

Machine Learning · Computer Science 2024-03-06 Ying Sun , Hongwei Yong , Lei Zhang

This paper introduces AdaSwarm, a novel gradient-free optimizer which has similar or even better performance than the Adam optimizer adopted in neural networks. In order to support our proposed AdaSwarm, a novel Exponentially weighted…

Neural and Evolutionary Computing · Computer Science 2024-05-28 Rohan Mohapatra , Snehanshu Saha , Carlos A. Coello Coello , Anwesh Bhattacharya , Soma S. Dhavala , Sriparna Saha

We propose AdaFamily, a novel method for training deep neural networks. It is a family of adaptive gradient methods and can be interpreted as sort of a blend of the optimization algorithms Adam, AdaBelief and AdaMomentum. We perform…

Machine Learning · Computer Science 2022-03-04 Hannes Fassold

Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful…

Machine Learning · Computer Science 2022-06-13 Frederik Benzing

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…

Image and Video Processing · Electrical Eng. & Systems 2026-01-30 Yichi Zhang , Fengqing Zhu

Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating…

Machine Learning · Computer Science 2023-03-02 Hao Sun , Li Shen , Qihuang Zhong , Liang Ding , Shixiang Chen , Jingwei Sun , Jing Li , Guangzhong Sun , Dacheng Tao