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In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

Machine Learning · Computer Science 2019-03-12 Jiawei Zhang

Gradient descent based optimization methods are the methods of choice to train deep neural networks in machine learning. Beyond the standard gradient descent method, also suitable modified variants of standard gradient descent involving…

Optimization and Control · Mathematics 2025-04-29 Steffen Dereich , Arnulf Jentzen , Adrian Riekert

The performance of deep learning models is critically dependent on sophisticated optimization strategies. While existing optimizers have shown promising results, many rely on first-order Exponential Moving Average (EMA) techniques, which…

Computer Vision and Pattern Recognition · Computer Science 2024-12-10 Roi Peleg , Yair Smadar , Teddy Lazebnik , Assaf Hoogi

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

This paper proposes a new optimizer for deep learning, named d-AmsGrad. In the real-world data, noise and outliers cannot be excluded from dataset to be used for learning robot skills. This problem is especially striking for robots that…

Machine Learning · Computer Science 2021-04-02 Taisuke Kobayashi

LLM-based prompt optimization, that uses LLM-provided "textual gradients" (feedback) to refine prompts, has emerged an effective method for automatic prompt engineering. However, its scalability and stability are unclear when using more…

Computation and Language · Computer Science 2025-11-19 Zixin Ding , Junyuan Hong , Zhan Shi , Jiachen T. Wang , Zinan Lin , Li Yin , Meng Liu , Zhangyang Wang , Yuxin Chen

In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as…

Computer Vision and Pattern Recognition · Computer Science 2019-07-23 Dong Wang , Yicheng Liu , Wenwo Tang , Fanhua Shang , Hongying Liu , Qigong Sun , Licheng Jiao

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear…

Machine Learning · Computer Science 2022-08-02 Tan Nguyen , Richard G. Baraniuk , Robert M. Kirby , Stanley J. Osher , Bao Wang

We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…

Machine Learning · Computer Science 2026-02-03 Aikaterini Karoni , Rajit Rajpal , Benedict Leimkuhler , Gabriel Stoltz

Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…

Machine Learning · Computer Science 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Zhouchen Lin

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

Machine Learning · Computer Science 2020-12-04 Bao Wang , Qiang Ye

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been…

Machine Learning · Computer Science 2024-10-29 Kushal Chakrabarti , Nikhil Chopra

Cardiac anatomy segmentation is useful for clinical assessment of cardiac morphology to inform diagnosis and intervention. Deep learning (DL), especially with motion information, has improved segmentation accuracy. However, existing…

Computer Vision and Pattern Recognition · Computer Science 2025-09-09 Md. Kamrul Hasan , Guang Yang , Choon Hwai Yap

In this paper, we introduce StochGradAdam, a novel optimizer designed as an extension of the Adam algorithm, incorporating stochastic gradient sampling techniques to improve computational efficiency while maintaining robust performance.…

Machine Learning · Computer Science 2025-03-19 Juyoung Yun

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient…

Machine Learning · Computer Science 2020-06-02 Liang Liu , Xiaopeng Luo

Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic…

Machine Learning · Computer Science 2025-05-22 Xianliang Li , Jun Luo , Zhiwei Zheng , Hanxiao Wang , Li Luo , Lingkun Wen , Linlong Wu , Sheng Xu

The development of machine learning is promoting the search for fast and stable minimization algorithms. To this end, we suggest a change in the current gradient descent methods that should speed up the motion in flat regions and slow it…

Machine Learning · Computer Science 2019-06-13 Marco Baiesi

Through theoretical and experimental validation, unlike all existing adaptive methods like Adam which penalize frequently-changing parameters and are only applicable to sparse gradients, we propose the simplest SGD enhanced method,…

Machine Learning · Computer Science 2023-10-04 Gongyue Zhang , Dinghuang Zhang , Shuwen Zhao , Donghan Liu , Carrie M. Toptan , Honghai Liu

This paper presents a novel neural network training approach for faster convergence and better generalization abilities in deep reinforcement learning. Particularly, we focus on the enhancement of training and evaluation performance in…

Machine Learning · Computer Science 2020-05-26 Mohammed Sharafath Abdul Hameed , Gavneet Singh Chadha , Andreas Schwung , Steven X. Ding

An associative memory (AM) enables cue-response recall, and it has recently been recognized as a key mechanism underlying modern neural architectures such as Transformers. In this work, we introduce the concept of distributed dynamic…

Machine Learning · Computer Science 2025-12-01 Bowen Wang , Matteo Zecchin , Osvaldo Simeone