daVinci-Prover: Agent-Native Mid-Training for Formal Theorem Proving
Wenhong Zhu, Xuefeng Li, Jiashuo Zhang, Yu Chen, Tiantian Mi, Qipeng Guo, Pengfei Liu
原文摘要
Advances in large language models (LLMs) are rapidly transforming formal theorem proving. Yet further progress remains constrained by the lack of a transparent and effective data recipe for systematically improving theorem-proving models. In this work, we argue that effective agentic provers require strong mathematical skill priors to ground theorem proving and agentic trajectories to enable long-horizon, interactive proof construction. To this end, we synthesize an agent-native 33.7B-token mid-training corpus covering decomposition, search, self-verification, and revision, together with verifier-grounded agentic trajectories. We further introduce the daVinci-Prover harness, which enables models to construct proofs and interact with a Lean verifier in an isolated workspace, and use it to collect approximately 36K high-quality agent trajectories for supervised fine-tuning. Our mid-training recipe yields an average improvement of 13.7 points over the matched Qwen3-8B SFT-only baseline across MiniF2F, FATE-M, and ProofNet. When applied to the Qwen3.5 series, our approach also yields strong performance across theorem-proving benchmarks and achieves near-saturating MiniF2F performance with memory compaction. The results highlight agent-native mid-training as an effective foundation for developing stronger interactive theorem-proving agents.
cs.CL