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Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively…

Machine Learning · Computer Science 2026-03-24 Zehao Li , Tao Ren , Zishi Zhang , Xi Chen , Yijie Peng

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these…

Machine Learning · Computer Science 2025-10-28 Yehonathan Refael , Guy Smorodinsky , Tom Tirer , Ofir Lindenbaum

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the…

Machine Learning · Computer Science 2025-12-15 Haochen Zhang , Junze Yin , Guanchu Wang , Zirui Liu , Lin F. Yang , Tianyi Zhang , Anshumali Shrivastava , Vladimir Braverman

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to…

Machine Learning · Computer Science 2025-12-09 Yehonathan Refael , Jonathan Svirsky , Boris Shustin , Wasim Huleihel , Ofir Lindenbaum

Training efficiency in large-scale models is typically assessed through memory consumption, training time, and model performance. Current methods often exhibit trade-offs among these metrics, as optimizing one generally degrades at least…

Machine Learning · Computer Science 2026-02-03 Tianhao Miao , Zhongyuan Bao , Lejun Zhang

We introduce LDAdam, a memory-efficient optimizer for training large models, that performs adaptive optimization steps within lower dimensional subspaces, while consistently exploring the full parameter space during training. This strategy…

Machine Learning · Computer Science 2025-03-04 Thomas Robert , Mher Safaryan , Ionut-Vlad Modoranu , Dan Alistarh

Learning-to-optimize (L2O) is an emerging research area in large-scale optimization with applications in data science. Recently, researchers have proposed a novel L2O framework called learned mirror descent (LMD), based on the classical…

Optimization and Control · Mathematics 2024-05-13 Hong Ye Tan , Subhadip Mukherjee , Junqi Tang , Carola-Bibiane Schönlieb

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

Machine Learning · Computer Science 2018-08-23 Atilim Gunes Baydin , Robert Cornish , David Martinez Rubio , Mark Schmidt , Frank Wood

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…

Machine Learning · Computer Science 2023-05-23 Min Gan , Xiang-xiang Su , Guang-yong Chen , Jing Chen

Training large language models (LLMs) is constrained by memory requirements, with activations accounting for a substantial fraction of the total footprint. Existing approaches reduce memory using low-rank weight parameterizations or…

Machine Learning · Computer Science 2026-04-13 Sakshi Choudhary , Utkarsh Saxena , Kaushik Roy

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

Machine Learning · Computer Science 2020-11-11 Frithjof Gressmann , Zach Eaton-Rosen , Carlo Luschi

Large language models (LLMs) have recently emerged as powerful tools for tackling many language-processing tasks. Despite their success, training and fine-tuning these models is still far too computationally and memory intensive. In this…

Computer Vision and Pattern Recognition · Computer Science 2024-10-22 Roy Miles , Pradyumna Reddy , Ismail Elezi , Jiankang Deng

We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…

Machine Learning · Computer Science 2022-04-29 Yunfei Teng , Wenbo Gao , Francois Chalus , Anna Choromanska , Donald Goldfarb , Adrian Weller

Continual machine unlearning aims to remove the influence of data that should no longer be retained, while preserving the usefulness of the model on everything else. This setting becomes especially difficult when deletion requests arrive…

Machine Learning · Computer Science 2026-04-15 Yogachandran Rahulamathavan , Nasir Iqbal , Juncheng Hu , Sangarapillai Lambotharan

The performance of a deep neural network is highly dependent on its training, and finding better local optimal solutions is the goal of many optimization algorithms. However, existing optimization algorithms show a preference for descent…

Computer Vision and Pattern Recognition · Computer Science 2019-12-06 Huangxing Lin , Weihong Zeng , Xinghao Ding , Yue Huang , Chenxi Huang , John Paisley

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

Machine Learning · Computer Science 2020-11-19 Giorgos Mamakoukas , Orest Xherija , T. D. Murphey

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

Machine Learning · Computer Science 2026-05-22 Athanasios Glentis , Jiaxiang Li , Andi Han , Mingyi Hong

Fine-tuning Large Language Models (LLMs) has proven effective for a variety of downstream tasks. However, as LLMs grow in size, the memory demands for backpropagation become increasingly prohibitive. Zeroth-order (ZO) optimization methods…

Machine Learning · Computer Science 2025-07-25 Ziming Yu , Pan Zhou , Sike Wang , Jia Li , Mi Tian , Hua Huang

Training large language models (LLMs) is highly resource-intensive due to their massive number of parameters and the overhead of optimizer states. While recent work has aimed to reduce memory consumption, such efforts often entail…

Machine Learning · Computer Science 2025-10-28 Sahar Rajabi , Nayeema Nonta , Sirisha Rambhatla

We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize,…

Machine Learning · Computer Science 2023-11-27 Gilad Yehudai , Alon Cohen , Amit Daniely , Yoel Drori , Tomer Koren , Mariano Schain
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