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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

Generating adversarial examples (AEs) can be formulated as an optimization problem. Among various optimization-based attacks, the gradient-based PGD and the momentum-based MI-FGSM have garnered considerable interest. However, all these…

Machine Learning · Computer Science 2025-12-17 Wei Tao , Sheng Long , Xin Liu , Wei Li , Qing Tao

Asynchronous methods are widely used in deep learning, but have limited theoretical justification when applied to non-convex problems. We show that running stochastic gradient descent (SGD) in an asynchronous manner can be viewed as adding…

Machine Learning · Statistics 2016-11-28 Ioannis Mitliagkas , Ce Zhang , Stefan Hadjis , Christopher Ré

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

Optimization and Control · Mathematics 2024-11-06 Kexin Jin , Jonas Latz , Chenguang Liu , Alessandro Scagliotti

Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…

Machine Learning · Computer Science 2023-11-20 Slavomír Hanzely

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

Optimization and Control · Mathematics 2026-03-02 Zimeng Wang , Alp Yurtsever

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

We introduce MADGRAD, a novel optimization method in the family of AdaGrad adaptive gradient methods. MADGRAD shows excellent performance on deep learning optimization problems from multiple fields, including classification and…

Machine Learning · Computer Science 2021-08-27 Aaron Defazio , Samy Jelassi

Recent advancements in deep learning optimization have introduced new algorithms, such as Schedule-Free optimizers, AdEMAMix, MARS and Lion which modify traditional momentum mechanisms. In a separate line of work, theoretical acceleration…

Machine Learning · Computer Science 2025-02-05 Depen Morwani , Nikhil Vyas , Hanlin Zhang , Sham Kakade

Gradient descent has been a central training principle for artificial neural networks from the early beginnings to today's deep learning networks. The most common implementation is the backpropagation algorithm for training feed-forward…

Machine Learning · Computer Science 2020-06-09 Stefan Jaeger

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of…

Machine Learning · Computer Science 2020-07-13 Abhinav Venigalla , Atli Kosson , Vitaliy Chiley , Urs Köster

We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum, coined Shuffling Momentum Gradient (SMG), for…

Optimization and Control · Mathematics 2021-06-10 Trang H. Tran , Lam M. Nguyen , Quoc Tran-Dinh

Efficiently exploring complex loss landscapes is key to the performance of deep neural networks. While momentum-based optimizers are widely used in state-of-the-art setups, classical momentum can still struggle with large, misaligned…

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

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

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

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an…

Machine Learning · Computer Science 2021-06-21 Tao Lin , Sai Praneeth Karimireddy , Sebastian U. Stich , Martin Jaggi

Adaptive optimization has achieved notable success for distributed learning while extending adaptive optimizer to federated Learning (FL) suffers from severe inefficiency, including (i) rugged convergence due to inaccurate gradient…

Machine Learning · Computer Science 2023-08-02 Yan Sun , Li Shen , Hao Sun , Liang Ding , Dacheng Tao

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

Machine Learning · Computer Science 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers…

Machine Learning · Computer Science 2025-10-31 Steffen Schotthöfer , Timon Klein , Jonas Kusch