Making Mathematical Reasoning Adaptive
Authors: name: Zhejian Lai, name: Xiang Geng, name: Zhijun Wang, name: Yang Bai, name: Jiahuan Li, name: Rongxiang Weng, name: Jingang Wang, name: Xuezhi Cao, name: Xunliang Cai, name: Shujian Huang

Mathematical reasoning is a primary indicator of large language models (LLMs)
intelligence. However, existing LLMs exhibit failures of robustness and
generalization. This paper attributes these deficiencies to spurious reasoning,
i.e., producing answers from superficial features. To address this challenge,
we propose the AdaR framework to enable adaptive reasoning, wherein models rely
on problem-solving logic to produce answers. AdaR synthesizes logically
equivalent queries by varying variable values, and trains models with RLVR on
these data to penalize spurious logic while encouraging adaptive logic. To
improve data quality, we extract the problem-solving logic from the original
query and generate the corresponding answer by code execution, then apply a
sanity check. Experimental results demonstrate that AdaR improves robustness
and generalization, achieving substantial improvement in mathematical reasoning
while maintaining high data efficiency. Analysis indicates that data synthesis
and RLVR function in a coordinated manner to enable adaptive reasoning in LLMs.
Subsequent analyses derive key design insights into the effect of critical
factors and the applicability to instruct LLMs. Our project is available at
https://github.com/LaiZhejian/AdaR