AdaR: A Framework for Equipping LLMs with Adaptive Reasoning

Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures in robustness and generalization. This paper attributes these deficiencies to spurious reasoning, wherein generated reasoning traces are driven by superficial correlations, leading models to blindly reproduce memorized patterns from the training data. To address this challenge, we propose the AdaR framework to equip LLMs with adaptive reasoning, wherein models establish correct correlations between query templates and reasoning processes. AdaR automatically synthesizes logically equivalent queries by varying variable values and trains models using Reinforcement Learning with Verifiable Rewards (RLVR) to penalize spurious logic while encouraging adaptive logic. To ensure data quality, we extract the problem-solving logic from the original query, generate the corresponding answer through code execution, and then apply a sanity check. Experimental results demonstrate that AdaR achieves substantial improvements in mathematical reasoning while maintaining high data efficiency. Furthermore, even advanced LLMs still exhibit deficiencies in robustness and generalization, which our work effectively mitigates. Our project is available at https://github.com/NJUNLP/AdaR.