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About this paper
Youyuan Zhang, Jialiang Sun, Hangrui Bi, Chuqin Geng, Wenjie Ma, Zhaoyu Li, Xujie Si
DreamProver is an agentic framework that utilizes a "wake-sleep" program induction paradigm to automatically discover and evolve transferable lemma libraries for formal theorem proving. It consistently improved proof success rates and efficiency across various mathematical domains, including those underrepresented in LLM training data, by effectively consolidating problem-specific experiences into generalized, reusable knowledge.
Key insights
- An iterative "wake-sleep" program induction paradigm effectively enables an ATP system to learn and consolidate reusable mathematical knowledge over time, mimicking human cognitive processes.
- Semantic clustering of intermediate theorems combined with LLM-based generation is crucial for abstracting generalizable lemmas from a pool of specific proof steps.
- Explicit library management, including pruning, deduplication, and formal verification, is essential for maintaining a compact, high-quality, and relevant set of transferable lemmas.
- Learning and leveraging a dynamic library of transferable lemmas significantly enhances proof success rates and reduces inference costs by promoting more concise and efficient proofs.
Summary by alphaXiv.
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