@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://aclanthology.org/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."
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<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 (łeq1.5\textB) 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.</abstract>
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%0 Conference Proceedings
%T Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget
%A Khan, Zohaib
%A Tafveez, Omer
%A Bhatti, Zoha Hayat
%Y Baez Santamaria, Selene
%Y Somayajula, Sai Ashish
%Y Yamaguchi, Atsuki
%S Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 4: Student Research Workshop)
%D 2026
%8 March
%I Association for Computational Linguistics
%C Rabat, Morocco
%@ 979-8-89176-383-8
%F khan-etal-2026-plasticity
%X Recent advances in mathematical reasoning typically rely on massive scale, yet the question remains: can strong reasoning capabilities be induced in small language models (łeq1.5\textB) 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.
%U https://aclanthology.org/2026.eacl-srw.37/
%P 493-501
Markdown (Informal)
[Plasticity vs. Rigidity: The Impact of Low-Rank Adapters on Reasoning on a Micro-Budget](https://aclanthology.org/2026.eacl-srw.37/) (Khan et al., EACL 2026)
ACL