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Related papers: Superfast Low Rank Approximation

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Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Numerical Analysis · Mathematics 2019-07-12 Jared Tanner , Andrew Thompson , Simon Vary

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

Machine Learning · Computer Science 2024-02-27 Jihao Long , Jiequn Han

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…

Computer Vision and Pattern Recognition · Computer Science 2014-10-24 Xiaowei Zhou , Can Yang , Hongyu Zhao , Weichuan Yu

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

Machine Learning · Statistics 2021-06-03 Alain Durmus , Eric Moulines , Alexey Naumov , Sergey Samsonov , Kevin Scaman , Hoi-To Wai

Low-Rank Adaptation (LoRA) is a popular technique for parameter-efficient fine-tuning of Large Language Models (LLMs). We study how different LoRA modules can be merged to achieve skill composition -- testing the performance of the merged…

Computation and Language · Computer Science 2024-12-03 Akshara Prabhakar , Yuanzhi Li , Karthik Narasimhan , Sham Kakade , Eran Malach , Samy Jelassi

First, we extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Second, We develop a class of fast approximate generalized linear regression algorithms with respect to the spectral norm.…

Numerical Analysis · Computer Science 2015-11-11 Haishan Ye , Zhihua Zhang

Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning of large language models, but it is notably ineffective at removing backdoor behaviors from poisoned pretrained models when fine-tuning on clean dataset. Contrary…

Computation and Language · Computer Science 2026-01-13 Hoang-Chau Luong , Lingwei Chen

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Computer Vision and Pattern Recognition · Computer Science 2018-11-12 Xingyu Xie , Jianlong Wu , Guangcan Liu , Jun Wang

Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…

Numerical Analysis · Mathematics 2026-03-25 Salman Ahmadi-Asl , Malihe Nobakht Kooshkghazi , Valentin Leplat

Large-scale pretraining followed by task-specific finetuning has achieved great success in various NLP tasks. Since finetuning all parameters of large pretrained models poses substantial computational and memory challenges, several…

Computation and Language · Computer Science 2024-03-19 Ruiyi Zhang , Rushi Qiang , Sai Ashish Somayajula , Pengtao Xie

Low-rank adaptation (LoRA) has emerged as the de facto standard for parameter-efficient fine-tuning (PEFT) of foundation models, enabling the adaptation of billion-parameter networks with minimal computational and memory overhead. Despite…

Machine Learning · Computer Science 2026-04-24 Bingcong Li , Yilang Zhang , Georgios B. Giannakis

Low-rank adaptation (LoRA) is one of the most popular task-specific parameter-efficient fine-tuning (PEFT) methods on pre-trained language models for its good performance and computational efficiency. LoRA injects a product of two trainable…

Machine Learning · Computer Science 2024-03-20 Youbang Sun , Zitao Li , Yaliang Li , Bolin Ding

We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is…

Data Structures and Algorithms · Computer Science 2023-11-03 Vincent Cohen-Addad , Chenglin Fan , Suprovat Ghoshal , Euiwoong Lee , Arnaud de Mesmay , Alantha Newman , Tony Chang Wang

The large volume and complexity of medical imaging datasets are bottlenecks for storage, transmission, and processing. To tackle these challenges, the application of low-rank matrix approximation (LRMA) and its derivative, local LRMA…

Image and Video Processing · Electrical Eng. & Systems 2025-02-28 Sisipho Hamlomo , Marcellin Atemkeng , Yusuf Brima , Chuneeta Nunhokee , Jeremy Baxter

Fine-tuning pre-trained large language models in a parameter-efficient manner is widely studied for its effectiveness and efficiency. LoRA is one of the most widely used methods, which assumes that the optimization process is essentially…

Computation and Language · Computer Science 2024-12-16 Changqun Li , Chaofan Ding , Kexin Luan , Xinhan Di

Low-Rank Adaptation (LoRA) is a standard tool for parameter-efficient finetuning of large models. While it induces a small memory footprint, its training dynamics can be surprisingly complex as they depend on several hyperparameters such as…

Machine Learning · Computer Science 2026-02-09 Nan Chen , Soledad Villar , Soufiane Hayou

Continual learning in Neural Machine Translation (NMT) faces the dual challenges of catastrophic forgetting and the high computational cost of retraining. This study establishes Low-Rank Adaptation (LoRA) as a parameter-efficient framework…

Computation and Language · Computer Science 2025-12-11 Salvador Carrión , Francisco Casacuberta

Fine-tuning large language models (LLMs) with high parameter efficiency for downstream tasks has become a new paradigm. Low-Rank Adaptation (LoRA) significantly reduces the number of trainable parameters for fine-tuning. Although it has…

Computation and Language · Computer Science 2024-08-14 Jia-Chen Zhang , Yu-Jie Xiong , He-Xi Qiu , Dong-Hai Zhu , Chun-Ming Xia

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). LoRA essentially describes the projection of an input space into a low-dimensional output space, with the…

Computation and Language · Computer Science 2025-10-28 Shiwei Li , Xiandi Luo , Haozhao Wang , Xing Tang , Ziqiang Cui , Dugang Liu , Yuhua Li , Xiuqiang He , Ruixuan Li

Low rank adaptation (LoRA) has emerged as a prominent technique for fine-tuning large language models (LLMs) thanks to its superb efficiency gains over previous methods. While extensive studies have examined the performance and structural…

Machine Learning · Computer Science 2025-05-20 Zi Liang , Haibo Hu , Qingqing Ye , Yaxin Xiao , Ronghua Li