Learning to Reason with Insight for Informal Theorem Proving

2026-04-20 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new framework addresses the primary bottleneck in informal theorem proving by large language models (LLMs): the lack of "insight" or the ability to recognize core problem-solving techniques. Researchers propose DeepInsightTheorem, a hierarchical dataset that explicitly extracts core techniques and proof sketches alongside final proofs for informal mathematical problems. To leverage this dataset, they developed a Progressive Multi-Stage SFT strategy, which mimics human learning by guiding LLMs from basic proof writing to more insightful reasoning. Experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms existing baselines, indicating that teaching models to identify and apply core techniques substantially improves their mathematical reasoning capabilities.

Key takeaway

For AI scientists and machine learning engineers developing advanced reasoning capabilities for LLMs, consider integrating explicit "insight" training. Your models can achieve superior performance in informal theorem proving by structuring training data to highlight core problem-solving techniques and implementing progressive supervised fine-tuning strategies. This approach directly addresses a key limitation in current LLM reasoning, enabling more robust and human-like problem-solving.

Key insights

Teaching LLMs to identify core techniques significantly improves their informal theorem proving capabilities.

Principles

• Insight is critical for complex problem-solving.
• Hierarchical data improves LLM reasoning.
• Progressive learning mimics human cognition.

Method

The proposed method involves creating a hierarchical dataset (DeepInsightTheorem) with explicit core techniques and proof sketches, then training LLMs using a Progressive Multi-Stage SFT strategy to mimic human learning from basic to insightful reasoning.

In practice

• Structure training data with explicit techniques.
• Implement multi-stage supervised fine-tuning.
• Focus on informal reasoning tasks for LLMs.

Topics

• Informal Theorem Proving
• Large Language Models
• DeepInsightTheorem Dataset
• Progressive Multi-Stage SFT
• Mathematical Reasoning

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.