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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…

Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, offer compact and effective alternatives to full model fine-tuning by introducing low-rank updates to pre-trained weights. However, most existing approaches rely on global low…

Machine Learning · Computer Science 2025-09-25 Babak Barazandeh , Subhabrata Majumdar , Om Rajyaguru , George Michailidis

This paper explores how theory can guide and enhance practical algorithms, using Low-Rank Adaptation (LoRA, Hu et al. 2022) in large language models as a case study. We rigorously prove that, under gradient descent, LoRA adapters align with…

Machine Learning · Statistics 2025-06-24 Yuanhe Zhang , Fanghui Liu , Yudong Chen

Low-rank approximation techniques have become the de facto standard for fine-tuning Large Language Models (LLMs) due to their reduced computational and memory requirements. This paper investigates the effectiveness of these methods in…

Machine Learning · Computer Science 2024-05-30 Saswat Das , Marco Romanelli , Cuong Tran , Zarreen Reza , Bhavya Kailkhura , Ferdinando Fioretto

Low-rank adaptation (LoRA) has become a widely used paradigm for parameter-efficient fine-tuning of large language models, yet its representational capacity often lags behind full fine-tuning. Within the context of LoRA, a key open question…

Machine Learning · Computer Science 2025-11-04 Xin Yu , Cong Xie , Ziyu Zhao , Tiantian Fan , Lingzhou Xue , Zhi Zhang

We explore the low-rank structure of the weight matrices in neural networks at the stationary points (limiting solutions of optimization algorithms) with $L2$ regularization (also known as weight decay). We show several properties of such…

Machine Learning · Computer Science 2025-08-21 Ilja Kuzborskij , Yasin Abbasi Yadkori

While overparameterization in machine learning models offers great benefits in terms of optimization and generalization, it also leads to increased computational requirements as model sizes grow. In this work, we show that by leveraging the…

Machine Learning · Computer Science 2026-02-16 Can Yaras , Peng Wang , Laura Balzano , Qing Qu

Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer,…

Computation and Language · Computer Science 2025-02-04 Ignacio Hounie , Charilaos Kanatsoulis , Arnuv Tandon , Alejandro Ribeiro

Low-Rank Adaptation (LoRA) is the bread and butter of Large Language Model (LLM) finetuning. LoRA learns an additive low-rank perturbation, $AB$, of a pretrained matrix parameter $W$ to align the model to a new task or dataset with $W+AB$.…

Machine Learning · Computer Science 2024-10-15 Hai Huang , Randall Balestriero

Fine-tuning large language models (LLMs) is computationally expensive, and Low-Rank Adaptation (LoRA) provides a cost-effective solution by approximating weight updates through low-rank matrices. In real-world scenarios, LLMs are fine-tuned…

Machine Learning · Computer Science 2025-06-03 Jinda Liu , Yi Chang , Yuan Wu

Low-rank adaption (LoRA) is a prominent method that adds a small number of learnable parameters to the frozen pre-trained weights for parameter-efficient fine-tuning. Prompted by the question, ``Can we make its representation enough with…

Computer Vision and Pattern Recognition · Computer Science 2024-06-14 Injoon Hwang , Haewon Park , Youngwan Lee , Jooyoung Yang , SunJae Maeng

Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the actual updates to the weights depends on…

Machine Learning · Computer Science 2025-07-18 Jui-Nan Yen , Si Si , Zhao Meng , Felix Yu , Sai Surya Duvvuri , Inderjit S. Dhillon , Cho-Jui Hsieh , Sanjiv Kumar

In deep learning, it is common to use more network parameters than training points. In such scenarioof over-parameterization, there are usually multiple networks that achieve zero training error so that thetraining algorithm induces an…

Machine Learning · Computer Science 2023-08-22 Hung-Hsu Chou , Carsten Gieshoff , Johannes Maly , Holger Rauhut

While Large Language Models (LLMs) have revolutionized artificial intelligence, fine-tuning LLMs is extraordinarily computationally expensive, preventing smaller businesses and research teams with limited GPU resources from engaging with…

Machine Learning · Computer Science 2025-08-26 Daniel Frees , Aditri Bhagirath , Moritz Bolling

It is a common practice in natural language processing to pre-train a single model on a general domain and then fine-tune it for downstream tasks. However, when it comes to Large Language Models, fine-tuning the entire model can be…

Artificial Intelligence · Computer Science 2024-10-29 Cristian Meo , Ksenia Sycheva , Anirudh Goyal , Justin Dauwels

The success of gradient descent in ML and especially for learning neural networks is remarkable and robust. In the context of how the brain learns, one aspect of gradient descent that appears biologically difficult to realize (if not…

Neural and Evolutionary Computing · Computer Science 2022-04-12 Shivam Garg , Santosh S. Vempala

Low-rank adaptation (LoRA) and its variants have recently gained much interest due to their ability to avoid excessive inference costs. However, LoRA still encounters the following challenges: (1) Limitation of low-rank assumption; and (2)…

Computation and Language · Computer Science 2024-09-26 Qibin Wang , Xiaolin Hu , Weikai Xu , Wei Liu , Jian Luan , Bin Wang

An important paradigm of natural language processing consists of large-scale pre-training on general domain data and adaptation to particular tasks or domains. As we pre-train larger models, full fine-tuning, which retrains all model…

Computation and Language · Computer Science 2021-10-19 Edward J. Hu , Yelong Shen , Phillip Wallis , Zeyuan Allen-Zhu , Yuanzhi Li , Shean Wang , Lu Wang , Weizhu Chen

Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and…

Machine Learning · Computer Science 2026-02-25 Yilang Zhang , Bingcong Li , Georgios B. Giannakis

With the breakthrough of Transformer-based pre-trained models, the demand for fine-tuning (FT) to adapt the base pre-trained models to downstream applications continues to grow, so it is essential for service providers to reduce the cost of…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-03 Sheng Lin , Fangcheng Fu , Haoyang Li , Hao Ge , Xuanyu Wang , Jiawen Niu , Yaofeng Tu , Bin Cui
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