@inproceedings{park-etal-2025-riemannian,
title = "{R}iemannian Optimization for {L}o{RA} on the Stiefel Manifold",
author = "Park, JuneYoung and
Kang, Minjae and
Lee, Seongbae and
Lee, Haegang and
Kim, Seongwan and
Lee, Jaeho",
editor = "Christodoulopoulos, Christos and
Chakraborty, Tanmoy and
Rose, Carolyn and
Peng, Violet",
booktitle = "Findings of the Association for Computational Linguistics: EMNLP 2025",
month = nov,
year = "2025",
address = "Suzhou, China",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.findings-emnlp.1143/",
pages = "20971--20985",
ISBN = "979-8-89176-335-7",
abstract = "While powerful, large language models (LLMs) present significant fine-tuning challenges due to their size. Parameter-efficient fine-tuning (PEFT) methods like LoRA provide solutions, yet suffer from critical optimizer inefficiencies; notably basis redundancy in LoRA{'}s $B$ matrix when using AdamW, which fundamentally limits performance. We address this by optimizing the $B$ matrix on the Stiefel manifold, imposing explicit orthogonality constraints that achieve near-perfect orthogonality and full effective rank. This geometric approach dramatically enhances parameter efficiency and representational capacity. Our Stiefel optimizer consistently outperforms AdamW across benchmarks with both LoRA and DoRA, demonstrating that geometric constraints are the key to unlocking LoRA{'}s full potential for effective LLM fine-tuning."
}<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="park-etal-2025-riemannian">
<titleInfo>
<title>Riemannian Optimization for LoRA on the Stiefel Manifold</title>
</titleInfo>
<name type="personal">
<namePart type="given">JuneYoung</namePart>
<namePart type="family">Park</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Minjae</namePart>
<namePart type="family">Kang</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Seongbae</namePart>
<namePart type="family">Lee</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Haegang</namePart>
<namePart type="family">Lee</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Seongwan</namePart>
<namePart type="family">Kim</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jaeho</namePart>
<namePart type="family">Lee</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<originInfo>
<dateIssued>2025-11</dateIssued>
</originInfo>
<typeOfResource>text</typeOfResource>
<relatedItem type="host">
<titleInfo>
<title>Findings of the Association for Computational Linguistics: EMNLP 2025</title>
</titleInfo>
<name type="personal">
<namePart type="given">Christos</namePart>
<namePart type="family">Christodoulopoulos</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Tanmoy</namePart>
<namePart type="family">Chakraborty</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Carolyn</namePart>
<namePart type="family">Rose</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Violet</namePart>
<namePart type="family">Peng</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<originInfo>
<publisher>Association for Computational Linguistics</publisher>
<place>
<placeTerm type="text">Suzhou, China</placeTerm>
</place>
</originInfo>
<genre authority="marcgt">conference publication</genre>
<identifier type="isbn">979-8-89176-335-7</identifier>
</relatedItem>
<abstract>While powerful, large language models (LLMs) present significant fine-tuning challenges due to their size. Parameter-efficient fine-tuning (PEFT) methods like LoRA provide solutions, yet suffer from critical optimizer inefficiencies; notably basis redundancy in LoRA’s B matrix when using AdamW, which fundamentally limits performance. We address this by optimizing the B matrix on the Stiefel manifold, imposing explicit orthogonality constraints that achieve near-perfect orthogonality and full effective rank. This geometric approach dramatically enhances parameter efficiency and representational capacity. Our Stiefel optimizer consistently outperforms AdamW across benchmarks with both LoRA and DoRA, demonstrating that geometric constraints are the key to unlocking LoRA’s full potential for effective LLM fine-tuning.</abstract>
<identifier type="citekey">park-etal-2025-riemannian</identifier>
<location>
<url>https://aclanthology.org/2025.findings-emnlp.1143/</url>
</location>
<part>
<date>2025-11</date>
<extent unit="page">
<start>20971</start>
<end>20985</end>
</extent>
</part>
</mods>
</modsCollection>
%0 Conference Proceedings
%T Riemannian Optimization for LoRA on the Stiefel Manifold
%A Park, JuneYoung
%A Kang, Minjae
%A Lee, Seongbae
%A Lee, Haegang
%A Kim, Seongwan
%A Lee, Jaeho
%Y Christodoulopoulos, Christos
%Y Chakraborty, Tanmoy
%Y Rose, Carolyn
%Y Peng, Violet
%S Findings of the Association for Computational Linguistics: EMNLP 2025
%D 2025
%8 November
%I Association for Computational Linguistics
%C Suzhou, China
%@ 979-8-89176-335-7
%F park-etal-2025-riemannian
%X While powerful, large language models (LLMs) present significant fine-tuning challenges due to their size. Parameter-efficient fine-tuning (PEFT) methods like LoRA provide solutions, yet suffer from critical optimizer inefficiencies; notably basis redundancy in LoRA’s B matrix when using AdamW, which fundamentally limits performance. We address this by optimizing the B matrix on the Stiefel manifold, imposing explicit orthogonality constraints that achieve near-perfect orthogonality and full effective rank. This geometric approach dramatically enhances parameter efficiency and representational capacity. Our Stiefel optimizer consistently outperforms AdamW across benchmarks with both LoRA and DoRA, demonstrating that geometric constraints are the key to unlocking LoRA’s full potential for effective LLM fine-tuning.
%U https://aclanthology.org/2025.findings-emnlp.1143/
%P 20971-20985
Markdown (Informal)
[Riemannian Optimization for LoRA on the Stiefel Manifold](https://aclanthology.org/2025.findings-emnlp.1143/) (Park et al., Findings 2025)
ACL
- JuneYoung Park, Minjae Kang, Seongbae Lee, Haegang Lee, Seongwan Kim, and Jaeho Lee. 2025. Riemannian Optimization for LoRA on the Stiefel Manifold. In Findings of the Association for Computational Linguistics: EMNLP 2025, pages 20971–20985, Suzhou, China. Association for Computational Linguistics.