{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://froggit.ai/public/capsules/49a4af01-ea25-40d6-9c41-f7d973966190","identifier":"49a4af01-ea25-40d6-9c41-f7d973966190","url":"https://froggit.ai/public/capsules/49a4af01-ea25-40d6-9c41-f7d973966190","name":"Learning to Reason with Insight for Informal Theorem Proving","text":"# Learning to Reason with Insight for Informal Theorem Proving\n\nSource-backed public reference for arXiv:2604.16278.\n\n**Authors:** Yunhe Li, Hao Shi, Bowen Deng, Wei Wang, Mengzhe Ruan, Hanxu Hou, Zhongxiang Dai, Siyang Gao, Chao Wang, Shuang Qiu, Linqi Song\n**Primary source:** https://arxiv.org/abs/2604.16278\n**Published:** 2026-04-17T17:36:21Z\n**Updated:** 2026-05-29T17:46:02Z\n**Categories:** cs.AI, cs.CL, cs.LG\n\n## Abstract Summary\nAlthough 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 $\\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. Our framework consists of three components: (1) $\\texttt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof; (2) a Progressive Multi-Stage SFT strategy that mimics the human learning process, teaching the model proof writing, planning, and insight identification; and (3) $\\texttt{InsightPO}$, a policy optimization method that assigns structured rewards over this insight hierarchy. 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...\n\n## Public Use Notes\n- This capsule summarizes the paper's arXiv metadata and abstract; it is not an independent replication or endorsement of the paper's claims.\n- Use it as a cited research reference for discovery, retrieval, and agent context.\n- For clinic","keywords":["cs.AI","cs.CL","cs.LG"],"about":[],"citation":["https://arxiv.org/abs/2604.16278"],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://froggit.ai"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://froggit.ai"},"dateCreated":"2026-04-20T06:00:03.165000Z","dateModified":"2026-06-19T03:07:28Z","isBasedOn":"https://arxiv.org/abs/2604.16278","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":100},{"@type":"PropertyValue","name":"verification_status","value":"sources_verified"},{"@type":"PropertyValue","name":"provenance_status","value":"valid"},{"@type":"PropertyValue","name":"evidence_level","value":"primary_source"},{"@type":"PropertyValue","name":"content_hash","value":"a0e86167cda0da91570d4e7d965b26b123b2c6784789bc7085b1c4325fb5e318"}]}