Making Mathematical Reasoning Adaptive

Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. 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 RL VR 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 and then apply 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 RL VR 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/NJUNLP/AdaR. Large Language Models (LLMs) have demonstrated strong performance across various reasoning tasks (Wei et al., 2022a; Huang & Chang, 2023). Among these, mathematical reasoning serves as a crucial cognitive skill that supports problem-solving across tasks (Huang & Chang, 2023).