PiCa: Parameter-Efficient Fine-Tuning with Column Space Projection

Fuente: arXiv
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Main Authors: Hwang, Junseo, Cho, Wonguk, Kim, Taesup
Format: Preprint
Published: 2025
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author Hwang, Junseo
Cho, Wonguk
Kim, Taesup
author_facet Hwang, Junseo
Cho, Wonguk
Kim, Taesup
contents Fine-tuning large foundation models is essential for building expert models tailored to specialized tasks and domains, but fully updating billions of parameters is computationally prohibitive. Reducing the number of trainable parameters using Parameter-Efficient Fine-Tuning (PEFT), such as Low-Rank Adaptation (LoRA), is therefore crucial not only to reduce training costs but also to mitigate storage, caching, and serving overheads during deployment. Prior works, such as Singular Vectors-guided Fine-Tuning (SVFT), have shown that exploiting the geometry of pre-trained weights based on Singular Value Decomposition (SVD) can significantly improve parameter-efficiency, but they lack a solid theoretical foundation. In this paper, we introduce Parameter-Efficient Fine-Tuning with Column Space Projection (PiCa), a novel theoretically grounded PEFT method. We prove that projecting gradients onto the principal column space of pre-trained weights provides an effective inductive bias for adaptation and further enhance parameter efficiency through a novel weight-sharing strategy. Across diverse NLP and vision tasks, PiCa consistently outperforms state-of-the-art baselines under comparable or smaller parameter budgets, demonstrating both theoretical rigor and practical effectiveness.
format Preprint
id arxiv_https___arxiv_org_abs_2505_20211
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle PiCa: Parameter-Efficient Fine-Tuning with Column Space Projection
Hwang, Junseo
Cho, Wonguk
Kim, Taesup
Machine Learning
Artificial Intelligence
Fine-tuning large foundation models is essential for building expert models tailored to specialized tasks and domains, but fully updating billions of parameters is computationally prohibitive. Reducing the number of trainable parameters using Parameter-Efficient Fine-Tuning (PEFT), such as Low-Rank Adaptation (LoRA), is therefore crucial not only to reduce training costs but also to mitigate storage, caching, and serving overheads during deployment. Prior works, such as Singular Vectors-guided Fine-Tuning (SVFT), have shown that exploiting the geometry of pre-trained weights based on Singular Value Decomposition (SVD) can significantly improve parameter-efficiency, but they lack a solid theoretical foundation. In this paper, we introduce Parameter-Efficient Fine-Tuning with Column Space Projection (PiCa), a novel theoretically grounded PEFT method. We prove that projecting gradients onto the principal column space of pre-trained weights provides an effective inductive bias for adaptation and further enhance parameter efficiency through a novel weight-sharing strategy. Across diverse NLP and vision tasks, PiCa consistently outperforms state-of-the-art baselines under comparable or smaller parameter budgets, demonstrating both theoretical rigor and practical effectiveness.
title PiCa: Parameter-Efficient Fine-Tuning with Column Space Projection
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2505.20211