Riemannian Optimization for LoRA on the Stiefel Manifold
JuneYoung Park, Minjae Kang, Seongbae Lee, Haegang Lee, Seongwan Kim, Jaeho Lee
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.
BibTeX
@inproceedings{emnlp2025_riemannianoptimi,
title = {Riemannian Optimization for LoRA on the Stiefel Manifold},
author = {JuneYoung Park and Minjae Kang and Seongbae Lee and Haegang Lee and Seongwan Kim and Jaeho Lee},
booktitle = {EMNLP 2025},
year = {2025}
}