@inproceedings{khan-etal-2026-plasticity,
    title = "Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget",
    author = "Khan, Zohaib  and
      Tafveez, Omer  and
      Bhatti, Zoha Hayat",
    editor = "Baez Santamaria, Selene  and
      Somayajula, Sai Ashish  and
      Yamaguchi, Atsuki",
    booktitle = "Proceedings of the 19th Conference of the {E}uropean Chapter of the {A}ssociation for {C}omputational {L}inguistics (Volume 4: Student Research Workshop)",
    month = mar,
    year = "2026",
    address = "Rabat, Morocco",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/manual-author-scripts/2026.eacl-srw.37/",
    pages = "493--501",
    ISBN = "979-8-89176-383-8",
    abstract = "Recent advances in mathematical reasoning typically rely on massive scale, yet the question remains: can strong reasoning capabilities be induced in small language models ($\leq1.5\text{B}$) under extreme constraints? We investigate this by training models on a single A40 GPU (48GB) for under 24 hours using Reinforcement Learning with Verifiable Rewards (RLVR) and Low-Rank Adaptation (LoRA). We find that the success of this ``micro-budget'' regime depends critically on the interplay between adapter capacity and model initialization. While low-rank adapters ($r=8$) consistently fail to capture the complex optimization dynamics of reasoning, high-rank adapters ($r=256$) unlock significant plasticity in standard instruction-tuned models. Our best result achieved an impressive 40.0{\%} Pass@1 on AIME 24 (an 11.1{\%} absolute improvement over baseline) and pushed Pass@16 to 70.0{\%}, demonstrating robust exploration capabilities. However, this plasticity is not universal: while instruction-tuned models utilized the budget to elongate their chain-of-thought and maximize reward, heavily math-aligned models suffered performance collapse, suggesting that noisy, low-budget RL updates can act as destructive interference for models already residing near a task-specific optimum."
}