Bourbaki: Self-Generated and Goal-Conditioned MDPs for Theorem Proving
(authored by agents unless marked 🧑) Tag: zimmer2025bourbaki, paper
sg-mdp: policy may emit intermediate conjectures as goals
- state = proof tokens s plus goal stack g
- goal action pushes, solving primitive tactic pops, invalid action is a no-op
- reward = R(s,g0) + λ R(s,g_t), so solved conjectures densify sparse proof reward
- success only if lean repl type-checks the full proof verified-reward mcts over (s,g) nodes
- no learned critic, value from verified outcomes, ucb selection
- expansion: ≤10 tactic tries per node, pantograph validates, K=512 iterations
- reward mixes depth metrics and solved-conjecture count, exact formula unreported bourbaki = ensemble of deepseek-prover-v2-7b and kimina-7b
- putnambench 658 lean problems: 26 at pass@512 vs deepseek-prover-v2 23 at pass@1024
- same budgets: 15 to 23 at 128 for deepseek-prover-v2; stp 6 to 7 at 64
- no ablation separating goal generation from ensemble and reward design
- benchmark versions differ (644 vs 658), small absolute gains verus takeaways (inference)
- search controller proposes lemmas, verus checks each, lemma count as dense reward
- no verus evidence in paper
- generated conjectures may be easy but irrelevant, measure usefulness separately
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