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Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously,…

Machine Learning · Computer Science 2026-04-02 Yuhang Li , Donghyun Lee , Ruokai Yin , Priyadarshini Panda

In this paper, we introduce a new post-training compression paradigm for Large Language Models (LLMs) to facilitate their wider adoption. We delve into LLM weight low-rank decomposition, and find that the challenges of this task stem from…

Computation and Language · Computer Science 2025-08-29 Zhihang Yuan , Yuzhang Shang , Yue Song , Dawei Yang , Qiang Wu , Yan Yan , Guangyu Sun

Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…

Machine Learning · Computer Science 2026-01-15 Lin Xv , Xian Gao , Ting Li , Yuzhuo Fu

Supervised Fine-Tuning (SFT) empowers Large Language Models (LLMs) with exceptional performance on specialized tasks, but it yields dense, high-dimensional delta parameters that pose severe storage and distribution challenges. Singular…

Machine Learning · Computer Science 2026-02-17 Boya Xiong , Shuo Wang , Weifeng Ge , Guanhua Chen , Yun Chen

The components underpinning PLMs -- large weight matrices -- were shown to bear considerable redundancy. Matrix factorization, a well-established technique from matrix theory, has been utilized to reduce the number of parameters in PLM.…

Computation and Language · Computer Science 2023-06-27 Siyu Ren , Kenny Q. Zhu

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

Applications · Statistics 2007-09-06 William Rey

Large Language Models (LLMs) are very demanding in terms of their computational resources. Low-rank decompositions of LLM weights, e.g. via Singular Value Decomposition (SVD), is a promising approach for LLM compression, but presents…

Machine Learning · Computer Science 2025-12-04 Roman Rausch , David Jansen , Sukhbinder Singh , Román Orús

The advancements in Large Language Models (LLMs) have been hindered by their substantial sizes, which necessitates LLM compression methods for practical deployment. Singular Value Decomposition (SVD) offers a promising solution for LLM…

Computation and Language · Computer Science 2025-03-18 Xin Wang , Yu Zheng , Zhongwei Wan , Mi Zhang

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…

Machine Learning · Statistics 2019-12-02 Ali Basirat

Large language models (LLMs) have rapidly scaled in size, bringing severe memory and computational challenges that hinder their deployment. Singular Value Decomposition (SVD)-based compression has emerged as an appealing post-training…

Machine Learning · Computer Science 2025-10-07 Zhendong Mi , Bian Sun , Grace Li Zhang , Shaoyi Huang

Personalized text-to-image models such as DreamBooth require fine-tuning large-scale diffusion backbones, resulting in significant storage overhead when maintaining many subject-specific models. We present Delta-SVD, a post-hoc,…

Computer Vision and Pattern Recognition · Computer Science 2025-08-26 Tangyuan Zhang , Shangyu Chen , Qixiang Chen , Jianfei Cai

Large language models (LLMs) have demonstrated remarkable capabilities, yet prohibitive parameter complexity often hinders their deployment. Existing singular value decomposition (SVD) based compression methods simply deem singular values…

Computation and Language · Computer Science 2025-02-24 Dengjie Li , Tiancheng Shen , Yao Zhou , Baisong Yang , Zhongying Liu , Masheng Yang , Bernard Ghanem , Yibo Yang , Yujie Zhong , Ming-Hsuan Yang

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

Numerical Analysis · Mathematics 2016-11-09 Alessandro Alla , J. Nathan Kutz

We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides…

High Energy Physics - Phenomenology · Physics 2020-07-03 Geoffrey T. Bodwin , Hee Sok Chung

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

Information Theory · Computer Science 2013-11-01 Zemin Zhang , Gregory Ely , Shuchin Aeron , Ning Hao , Misha Kilmer

Large language models (LLMs) have achieved remarkable success in natural language processing (NLP) tasks, yet their substantial memory requirements present significant challenges for deployment on resource-constrained devices. Singular…

Computer Vision and Pattern Recognition · Computer Science 2025-09-26 Zhiteng Li , Mingyuan Xia , Jingyuan Zhang , Zheng Hui , Haotong Qin , Linghe Kong , Yulun Zhang , Xiaokang Yang

In the field of large language model (LLM) compression, singular value decomposition (SVD) is a widely studied and adopted low-rank decomposition technique. Since SVD operates exclusively on linear modules, and these modules in LLMs are…

Machine Learning · Computer Science 2025-10-23 Lin Xv , Jingsheng Gao , Xian Gao , Ting Liu , Yuzhuo Fu

Deep neural networks typically impose significant computational loads and memory consumption. Moreover, the large parameters pose constraints on deploying the model on edge devices such as embedded systems. Tensor decomposition offers a…

Computer Vision and Pattern Recognition · Computer Science 2024-08-30 Yaping He , Linhao Jiang , Di Wu

We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary…

Machine Learning · Computer Science 2023-08-16 Boyu Chen , Hanxuan Chen , Jiao He , Fengyu Sun , Shangling Jui

Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet…

Machine Learning · Computer Science 2026-02-04 Ali Abbasi , Chayne Thrash , Haoran Qin , Shansita Sharma , Sepehr Seifi , Soheil Kolouri