Learning to Reason with Insight for Informal Theorem Proving

arXiv cs.CL Papers
theorem-proving large-language-models mathematical-reasoning informal-proofs dataset supervised-fine-tuning

Summary

This paper proposes DeepInsightTheorem, a hierarchical dataset and Progressive Multi-Stage SFT training strategy to improve LLMs' informal theorem proving by teaching them to identify and apply core techniques through insight-aware reasoning.

arXiv:2604.16278v1 Announce Type: cross Abstract: Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose DeepInsightTheorem, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.
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# Learning to Reason with Insight for Informal Theorem Proving
Source: https://arxiv.org/abs/2604.16278
Authors: Yunhe Li (https://arxiv.org/search/cs?searchtype=author&query=Li,+Y), Hao Shi (https://arxiv.org/search/cs?searchtype=author&query=Shi,+H), Bowen Deng (https://arxiv.org/search/cs?searchtype=author&query=Deng,+B), Wei Wang (https://arxiv.org/search/cs?searchtype=author&query=Wang,+W), Mengzhe Ruan (https://arxiv.org/search/cs?searchtype=author&query=Ruan,+M), Hanxu Hou (https://arxiv.org/search/cs?searchtype=author&query=Hou,+H), Zhongxiang Dai (https://arxiv.org/search/cs?searchtype=author&query=Dai,+Z), Siyang Gao (https://arxiv.org/search/cs?searchtype=author&query=Gao,+S), Chao Wang (https://arxiv.org/search/cs?searchtype=author&query=Wang,+C), Shuang Qiu (https://arxiv.org/search/cs?searchtype=author&query=Qiu,+S), Linqi Song (https://arxiv.org/search/cs?searchtype=author&query=Song,+L)

View PDF (https://arxiv.org/pdf/2604.16278)

> Abstract: Although most automated theorem-proving approaches rely on formal proof systems, informal theorem proving can better align with large language models' (LLMs) strengths in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving: the lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We introduce $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully leverage this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results show that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning capabilities.

## Submission history

From: Yunhe Li [view email (https://arxiv.org/show-email/b478e370/2604.16278)] **[v1]** Fri, 17 Apr 2026 17:36:21 UTC (3,441 KB)

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