Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget

Zohaib Khan, Omer Tafveez, Zoha Hayat Bhatti


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 (≤1.5B) 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.
Anthology ID:
2026.eacl-srw.37
Volume:
Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 4: Student Research Workshop)
Month:
March
Year:
2026
Address:
Rabat, Morocco
Editors:
Selene Baez Santamaria, Sai Ashish Somayajula, Atsuki Yamaguchi
Venue:
EACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
493–501
Language:
URL:
https://aclanthology.org/2026.eacl-srw.37/
DOI:
Bibkey:
Cite (ACL):
Zohaib Khan, Omer Tafveez, and Zoha Hayat Bhatti. 2026. Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget. In Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 4: Student Research Workshop), pages 493–501, Rabat, Morocco. Association for Computational Linguistics.
Cite (Informal):
Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget (Khan et al., EACL 2026)
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PDF:
https://aclanthology.org/2026.eacl-srw.37.pdf