@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://preview.aclanthology.org/author-page-yu-wang-polytechnic/2025.findings-emnlp.1143/",
    doi = "10.18653/v1/2025.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."
}