@inproceedings{wang-etal-2026-inspire,
title = "{INSPIRE}: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning",
author = "Wang, Shuai and
Kuang, Jiayi and
Li, Yinghui and
Huang, Haojing and
Liang, Xinnian and
Shen, Ying and
Lin, Liang",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1507/",
pages = "34424--34439",
ISBN = "979-8-89176-459-0",
abstract = "Mathematical reasoning has seen rapid progress in large language models (LLMs), yet existing methods optimize predominantly for final-answer correctness, raising the question of 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."
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<abstract>Mathematical reasoning has seen rapid progress in large language models (LLMs), yet existing methods optimize predominantly for final-answer correctness, raising the question of 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.</abstract>
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%0 Conference Proceedings
%T INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning
%A Wang, Shuai
%A Kuang, Jiayi
%A Li, Yinghui
%A Huang, Haojing
%A Liang, Xinnian
%A Shen, Ying
%A Lin, Liang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F wang-etal-2026-inspire
%X Mathematical reasoning has seen rapid progress in large language models (LLMs), yet existing methods optimize predominantly for final-answer correctness, raising the question of 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.
%U https://aclanthology.org/2026.emnlp-main.1507/
%P 34424-34439
Markdown (Informal)
[INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning](https://aclanthology.org/2026.emnlp-main.1507/) (Wang et al., EMNLP 2026)
ACL