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In deep learning, stochastic gradient descent (SGD) and its momentum-based variants are widely used for optimization. However, the internal dynamics of these methods remain underexplored. In this paper, we analyze gradient behavior through…

Machine Learning · Computer Science 2025-03-11 Zhipeng Yao , Rui Yu , Guisong Chang , Ying Li , Yu Zhang , Dazhou Li

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

Adam is known to perform significantly better than Stochastic Gradient Descent (SGD) in language models, a phenomenon for which a number of explanations have been proposed. In this work, we revisit this "optimizer gap" through a series of…

Machine Learning · Computer Science 2025-06-17 Teodora Srećković , Jonas Geiping , Antonio Orvieto

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating…

Machine Learning · Computer Science 2023-12-27 Shuoran Jiang , Qingcai Chen , Youchen Pan , Yang Xiang , Yukang Lin , Xiangping Wu , Chuanyi Liu , Xiaobao Song

Despite the vast empirical evidence supporting the efficacy of adaptive optimization methods in deep learning, their theoretical understanding is far from complete. This work introduces novel SDEs for commonly used adaptive optimizers:…

Machine Learning · Computer Science 2025-03-12 Enea Monzio Compagnoni , Tianlin Liu , Rustem Islamov , Frank Norbert Proske , Antonio Orvieto , Aurelien Lucchi

Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…

Machine Learning · Computer Science 2021-02-23 Leonard Berrada , Andrew Zisserman , M. Pawan Kumar

Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…

Machine Learning · Computer Science 2026-02-26 Jianneng Yu , Alexandre V. Morozov

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

In this paper, we explore techniques centered around periodic sampling of model weights that provide convergence improvements on gradient update methods (vanilla \acs{SGD}, Momentum, Adam) for a variety of vision problems (classification,…

Machine Learning · Computer Science 2020-03-23 Samarth Tripathi , Jiayi Liu , Unmesh Kurup , Mohak Shah , Sauptik Dhar

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

First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…

Machine Learning · Computer Science 2020-02-05 Chih-Hao Fang , Sudhir B Kylasa , Fred Roosta , Michael W. Mahoney , Ananth Grama

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We…

Machine Learning · Statistics 2018-05-23 Ashia C. Wilson , Rebecca Roelofs , Mitchell Stern , Nathan Srebro , Benjamin Recht

Deep learning thrives with large neural networks and large datasets. However, larger networks and larger datasets result in longer training times that impede research and development progress. Distributed synchronous SGD offers a potential…

Computer Vision and Pattern Recognition · Computer Science 2018-05-02 Priya Goyal , Piotr Dollár , Ross Girshick , Pieter Noordhuis , Lukasz Wesolowski , Aapo Kyrola , Andrew Tulloch , Yangqing Jia , Kaiming He

Modern deep learning systems do not generalize well when the test data distribution is slightly different to the training data distribution. While much promising work has been accomplished to address this fragility, a systematic study of…

As deep learning models exponentially increase in size, optimizers such as Adam encounter significant memory consumption challenges due to the storage of first and second moment data. Current memory-efficient methods like Adafactor and CAME…

Machine Learning · Computer Science 2024-03-25 Pengxiang Zhao , Ping Li , Yingjie Gu , Yi Zheng , Stephan Ludger Kölker , Zhefeng Wang , Xiaoming Yuan

The training of diffusion models is often absent in the evaluation of new optimization techniques. In this work, we benchmark recent optimization algorithms for training a diffusion model for denoising flow trajectories. We observe that…

Machine Learning · Computer Science 2025-10-23 Fabian Schaipp

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

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

Machine Learning · Computer Science 2025-12-23 Ansh Nagwekar

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time novel view synthesis. As an explicit representation optimized through gradient propagation among primitives, optimization widely accepted in deep neural networks…

Computer Vision and Pattern Recognition · Computer Science 2026-05-11 Renjie Ding , Yaonan Wang , Min Liu , Jialin Zhu , Jiazheng Wang , Jiahao Zhao , Wenting Shen , Feixiang He , Xiang Chen

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each…

Machine Learning · Computer Science 2018-08-09 Jeremy Bernstein , Yu-Xiang Wang , Kamyar Azizzadenesheli , Anima Anandkumar