@inproceedings{zhang-etal-2026-geora,
    title = "{G}eo{RA}: Geometry-Aware Low-Rank Adaptation for {RLVR}",
    author = "Zhang, Jiaying  and
      Shi, Lei  and
      Li, Jiguo  and
      Xu, Jun  and
      Gao, Jiuchong  and
      Hao, Jinghua  and
      He, Renqing",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.1110/",
    pages = "24207--24221",
    ISBN = "979-8-89176-390-6",
    abstract = "Reinforcement Learning with Verifiable Rewards (RLVR) is a key paradigm for improving large-scale reasoning models. Unlike supervised fine-tuning (SFT), RLVR exhibits distinct optimization dynamics and are sensitive to the preservation of pre-trained geometric structures. However, existing parameter-efficient methods face key limitations in this regime. Low-rank adaptation methods, such as PiSSA, are primarily designed for Supervised Fine-Tuning (SFT) and do not account for the distinct optimization dynamics and geometric structures of RLVR. Conversely, directly fine-tuning the unstructured sparse parameter subspace favored by RLVR encounters efficiency bottlenecks on modern hardware. To address these challenges, we propose GeoRA (Geometry-Aware Low-Rank Adaptation), a low-rank adaptation method tailored for RLVR. Specifically, GeoRA exploits the anisotropic and compressible structure of RL update subspace, and extracts its principal directions via Singular Value Decomposition (SVD) to initialize low-rank adapters, while freezing residual components as a structural anchor during training. This design preserves the pre-trained structure and enables efficient dense computation. Experiments on Qwen and Llama models from 1.5B to 32B parameters show that GeoRA consistently outperforms strong low-rank baselines across RLVR settings in mathematics, medicine, and coding, while showing stronger generalization and less forgetting on out-of-domain tasks."
}