INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning
Mathematical reasoning has seen rapid progress in large language models (LLMs), yet existing methods optimize predominantly for final-answer correctness, raising the question whether models truly internalize mathematical concepts or merely memorize solution patterns. In human mathematics education, example-based reasoning such as constructing counterexamples to test theorem boundaries reflects deep conceptual understanding, but remains underdeveloped in current LLMs. Enhancing this capability through preference optimization presents two key challenges: (1) the model's limited example-based reasoning ability makes constructing effective preference pairs inherently difficult; and (2) capabi...
| Authors | Shuai Wang, Jiayi Kuang, Yinghui Li et al. |
|---|---|
| Primary category | cs.CL |
| Published | 27 August 2026 |
| Last updated at source | 4 September 2026 |
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