Title: Make Mathematical Reasoning Adaptive
Primary area: foundation or frontier models, including LLMs
Keywords: Synthetic Data, Chain-of-Thought, Mathematical Reasoning

Abstract: 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 adapt to varying variable values when the corresponding problem-solving logic is unchanged. AdaR synthesizes data logically equivalent problems 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 obtain 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 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.