Make Mathematical Reasoning Adaptive

Zhejian Lai, Xiang Geng, Zhijun Wang, Yang Bai, Jiahuan Li, Rongxiang Weng, Jingang Wang, Xuezhi Cao, Shujian Huang

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 rely on problem-solving logic to produce answers.
AdaR synthesizes logically equivalent queries by varying variable values, and trains models with Reinforcement Learning with Verifiable Rewards (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 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.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 10577