@inproceedings{lu-etal-2026-representation,
    title = "On the Representation Geometry of {L}o{RA} Model Merging",
    author = "Lu, Chenyang  and
      Li, Jiaru  and
      Zhao, Jinman  and
      Chen, Xinran  and
      Wang, Yining  and
      Cai, Renyi  and
      Li, Yuchen  and
      He, Chao",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.261/",
    pages = "5289--5304",
    ISBN = "979-8-89176-395-1",
    abstract = "Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning, yet merging multiple task-specific LoRA updates without additional training remains challenging. Most existing LoRA merging methods rely on SVD-based alignment, which emphasizes globally shared structure across tasks. In this work, we show that LoRA merging performance can be further improved by combining SVD with CUR decomposition. Through a representation-level analysis, we find that SVD-based decompositions primarily model shared components across tasks, while CUR-based decompositions better preserve task-specific and localized updates. These two perspectives are geometrically misaligned and exhibit complementary advantages, revealing an inherent trade-off between capturing shared structure and preserving task-specific information in LoRA model merging. Guided by this analysis, we propose a training-free merging procedure that explicitly combines the shared structure captured by SVD with the task-specific components preserved by CUR. Experiments on both vision and language benchmarks demonstrate consistent improvements over existing gradient-free LoRA merging methods."
}