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INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

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 rea

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