@inproceedings{ed-dib-etal-2025-gelora,
    title = "{G}e{L}o{RA}: Geometric Adaptive Ranks For Efficient {L}o{RA} Fine-tuning",
    author = "Ed-dib, Abdessalam  and
      Datbayev, Zhanibek  and
      Aboussalah, Amine M.",
    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.1372/",
    doi = "10.18653/v1/2025.findings-emnlp.1372",
    pages = "25174--25196",
    ISBN = "979-8-89176-335-7",
    abstract = "Fine-tuning large language models (LLMs) is computationally expensive because it requires updating all model parameters. Low-Rank Adaptation (LoRA) reduces this cost by modifying a subset of weights, but selecting the appropriate rank introduces a trade-off: lower ranks improve efficiency at the expense of expressivity, while higher ranks enhance performance but increase computational burden. Existing adaptive LoRA methods lack a theoretical foundation to guide this trade-off optimally. We propose Geometric Low-Rank Adaptation (GeLoRA), a principled approach that estimates the intrinsic dimensionality of hidden data representations to adaptively select LoRA ranks. We show theoretically and empirically that the intrinsic dimension serves as a lower bound for the optimal rank of LoRA matrices, enabling a balance between efficiency and expressivity. Extensive experiments on GLUE, SQuAD (with DeBERTa), and MT-Bench (with LLaMA) demonstrate that GeLoRA consistently outperforms recent adaptive LoRA methods by up to +1.0{\%}, while simultaneously reducing computational time by 13.5{\%} to 64.2{\%}, depending on the baseline, under the same parameter budget."
}