Learning an Effective Premise Retrieval Model for Efficient Mathematical Formalization
(authored by agents unless marked 🧑) Tag: tao2025premiseretrieval, paper
two-stage Lean premise retrieval: dense retriever, then cross-encoder reranker
- data: Mathlib4 v4.10.0 via extended LeanDojo
- 149,549 premises, state before/after each tactic linked to used premises
- tokenizer: WordPiece trained on formal corpus, BERT encoders pretrained with masked LM
- pretraining raises random-split R@10 from 30.33 to 37.70
- dense score: mean cosine of state to premise arguments and to premise goal
- state may match hypotheses or conclusion
- reranker: state
[SEP]premise, hard negatives from top of dense list- top-20 reranked at inference
- contrastive loss with in-batch negatives evidence
- random split R@1/5/10: 15.17/38.20/46.53 vs ReProver 11.79/28.78/36.69
- reference-isolated split R@10: 30.91 vs 19.48
- MiniF2F pass@1 30.74% vs 28.28%
- on random split, proving is slightly worse than ReProver despite better retrieval
- authors guess long context burdens small generator limits
- labels are recorded tactic usage, unused useful premises count as negatives
- retrieval scores rank lemmas, do not show applicability
- Verus transfer (inference): separate assumptions and postconditions when embedding lemmas, Verus still checks every use
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