New Framework Enhances LLMs' Informal Theorem Proving Through Insight Cultivation
A new framework tackles a significant challenge in informal theorem proving using large language models (LLMs): the deficiency in understanding required to pinpoint essential techniques for tackling intricate issues. The method, outlined in arXiv preprint 2604.16278v1, presents DeepInsightTheorem, a hierarchical dataset that organizes informal proofs by clearly extracting fundamental techniques and proof sketches alongside the final proofs. To utilize this dataset, researchers developed a Progressive Multi-Stage Supervised Fine-Tuning (SFT) approach that simulates human learning, progressing models from basic proof composition to deeper reasoning. This research suggests that informal theorem proving aligns more closely with the natural language processing capabilities of LLMs than traditional proof systems. Experiments were performed on complex mathematical problems to assess the framework's ability to enhance critical reasoning skills.
Key facts
- arXiv preprint 2604.16278v1 announces a new framework for informal theorem proving with LLMs
- The primary bottleneck identified is a lack of insight in recognizing core techniques for complex problems
- The framework proposes cultivating reasoning skills to enable insightful reasoning in LLMs
- DeepInsightTheorem is a hierarchical dataset structuring informal proofs with core techniques and proof sketches
- A Progressive Multi-Stage SFT strategy mimics human learning from basic proof writing to insightful thinking
- Informal theorem proving aligns better with LLMs' natural language processing strengths than formal systems
- Experiments were conducted on challenging math problems
- The work addresses the difficulty LLMs face in identifying required techniques for problem-solving
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- arXiv