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Fully connected layers are a primary source of memory and computational overhead in deep neural networks due to their dense, often redundant parameterization. While various compression techniques exist, they frequently introduce complex…

Machine Learning · Computer Science 2025-12-16 Maksymilian Szorc

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Optimization and Control · Mathematics 2025-01-27 Vladimir Norkin , Alois Pichler

Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…

Machine Learning · Computer Science 2025-05-22 Naiqi Li , Yuqiu Xie , Peiyuan Liu , Tao Dai , Yong Jiang , Shu-Tao Xia

Low Rank Adaptation (LoRA) has emerged as one of the most widely adopted methods for Parameter Efficient Fine-Tuning (PEFT) of Large Language Models (LLMs). LoRA reduces the number of trainable parameters and memory usage while achieving…

Computation and Language · Computer Science 2024-05-03 Justin Zhao , Timothy Wang , Wael Abid , Geoffrey Angus , Arnav Garg , Jeffery Kinnison , Alex Sherstinsky , Piero Molino , Travis Addair , Devvret Rishi

In recent years, pretrained large language models have demonstrated outstanding performance across various natural language processing tasks. However, full-parameter fine-tuning methods require adjusting all model parameters, leading to…

Computation and Language · Computer Science 2025-03-04 Jiancheng Zhao , Xingda Yu , Yuxiang Zhang , Zhen Yang

Parameter-efficient fine-tuning (PEFT) is essential for reducing the computational overhead of large language models (LLMs). Low-rank family adapters are commonly used to control the parameter size efficiently while maintaining the…

Low-rank adaptation (LoRA) has been prominently employed for parameter-efficient fine-tuning of large language models (LLMs). However, the limited expressive capacity of LoRA, stemming from the low-rank constraint, has been recognized as a…

Computation and Language · Computer Science 2025-03-18 Zhiwei He , Zhaopeng Tu , Xing Wang , Xingyu Chen , Zhijie Wang , Jiahao Xu , Tian Liang , Wenxiang Jiao , Zhuosheng Zhang , Rui Wang

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

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static…

Machine Learning · Computer Science 2026-05-12 Omatharv Bharat Vaidya , Connor T. Jerzak , Nhat Ho , Chandrajit Bajaj

Fine-tuning is a key approach for adapting language models to specific downstream tasks, but updating all model parameters becomes impractical as model sizes increase. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank…

Computation and Language · Computer Science 2025-02-10 Jiayang Yu , Yihang Zhang , Bin Wang , Peiqin Lin , Yongkang Liu , Shi Feng

Low-rank architectures have become increasingly important for efficient large language model (LLM) pre-training, providing substantial reductions in both parameter complexity and memory/computational demands. Despite these advantages,…

Machine Learning · Computer Science 2026-05-14 Boao Kong , Junzhu Liang , Yuxi Liu , Renjia Deng , Kun Yuan

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

Numerical Analysis · Mathematics 2020-08-12 Rishi Advani , Madison Crim , Sean O'Hagan

Fine-tuning large language models (LLMs) is computationally intensive because it requires updating all parameters. Low-Rank Adaptation (LoRA) improves efficiency by modifying only a subset of weights but introduces a trade-off between…

Machine Learning · Computer Science 2024-12-19 Abdessalam Ed-dib , Zhanibek Datbayev , Amine Mohamed Aboussalah

Adapting large-scale pretrained language models to downstream tasks via fine-tuning is the standard method for achieving state-of-the-art performance on NLP benchmarks. However, fine-tuning all weights of models with millions or billions of…

Computation and Language · Computer Science 2021-11-30 Rabeeh Karimi Mahabadi , James Henderson , Sebastian Ruder

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…

Machine Learning · Computer Science 2024-08-13 Jun Lu

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Machine Learning · Computer Science 2013-05-23 Francis Bach

Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…

Machine Learning · Statistics 2026-04-07 Xiao Liang , Shuang Li

We study the computational limits of Low-Rank Adaptation (LoRA) for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient…

Machine Learning · Computer Science 2025-06-09 Jerry Yao-Chieh Hu , Maojiang Su , En-Jui Kuo , Zhao Song , Han Liu

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles…

We propose a neural language modeling system based on low-rank adaptation (LoRA) for speech recognition output rescoring. Although pretrained language models (LMs) like BERT have shown superior performance in second-pass rescoring, the high…