Bourbaki: Self-Generated and Goal-Conditioned MDPs for Theorem Proving
Authors: name: Matthieu Zimmer, name: Xiaotong Ji, name: Rasul Tutunov, name: Anthony Bordg, name: Jun Wang, name: Haitham Bou Ammar

Reasoning remains a challenging task for large language models (LLMs),
especially within the logically constrained environment of automated theorem
proving (ATP), due to sparse rewards and the vast scale of proofs. These
challenges are amplified in benchmarks like PutnamBench, which contains
university-level problems requiring complex, multi-step reasoning. To address
this, we introduce self-generated goal-conditioned MDPs (sG-MDPs), a new
framework in which agents generate and pursue their subgoals based on the
evolving proof state. Given this more structured generation of goals, the
resulting problem becomes more amenable to search. We then apply Monte Carlo
Tree Search (MCTS)-like algorithms to solve the sG-MDP, instantiating our
approach in Bourbaki (7B), a modular system that can ensemble multiple 7B LLMs
for subgoal generation and tactic synthesis. On PutnamBench, Bourbaki (7B)
solves 26 problems, achieving new state-of-the-art results with models at this
scale.