{"slug": "inspire-an-internalize-then-improve-approach-for-example-driven-mathematical", "title": "INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning", "summary": "Researchers propose INSPIRE, an Internalize-Then-Improve approach for example-driven mathematical reasoning in large language models, combining Reference-Guided Student Internalization (RGSI) with stage-wise rubric preference training. Experiments across multiple model scales and families show consistent improvements, even surpassing larger open-source models, with no degradation on out-of-distribution benchmarks.", "body_md": "arXiv:2608.27501v1 Announce Type: new\nAbstract: 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) capability acquisition is progressive, as the model must first learn to adopt this strategy before learning to apply it correctly. Therefore we propose INSPIRE, an Internalize-Then-Improve approach combining Reference-Guided Student Internalization (RGSI), which produces high-quality preference candidates under the policy model's own distribution, with a stage-wise rubric preference training strategy that decomposes learning into method-oriented and correctness-oriented stages. Experiments across multiple model scales and families demonstrate consistent improvements, even surpassing larger open-source models, while evaluations on out-of-distribution benchmarks confirm no degradation in general mathematical reasoning ability.", "url": "https://wpnews.pro/news/inspire-an-internalize-then-improve-approach-for-example-driven-mathematical", "canonical_source": "https://arxiv.org/abs/2608.27501", "published_at": "2026-08-31 04:00:00+00:00", "updated_at": "2026-08-31 04:24:19.345563+00:00", "lang": "en", "topics": ["artificial-intelligence", "large-language-models", "ai-research"], "entities": ["INSPIRE", "Reference-Guided Student Internalization", "RGSI"], "alternates": {"html": "https://wpnews.pro/news/inspire-an-internalize-then-improve-approach-for-example-driven-mathematical", "markdown": "https://wpnews.pro/news/inspire-an-internalize-then-improve-approach-for-example-driven-mathematical.md", "text": "https://wpnews.pro/news/inspire-an-internalize-then-improve-approach-for-example-driven-mathematical.txt", "jsonld": "https://wpnews.pro/news/inspire-an-internalize-then-improve-approach-for-example-driven-mathematical.jsonld"}}