TLDR: Bourbaki introduces a novel framework called self-generated goal-conditioned Markov Decision Processes (sG-MDPs) to enhance automated theorem proving by allowing AI agents to dynamically generate and pursue intermediate subgoals. This approach, combined with Monte Carlo Tree Search, enables the Bourbaki (7B) system to achieve state-of-the-art results on the challenging PutnamBench dataset, solving 26 problems and significantly outperforming previous 7B models by improving proof success rates, diversity, and sample efficiency.
Large Language Models (LLMs) have shown impressive capabilities in various domains, but they often struggle with complex logical reasoning, especially in automated theorem proving (ATP). This field, which involves automatically generating formal proofs for mathematical statements, presents significant challenges due to the sparse nature of rewards (feedback is only received upon completing a full proof) and the immense number of possible proof steps. Benchmarks like PutnamBench, featuring university-level math problems, highlight these difficulties, as they demand intricate, multi-step reasoning.
To overcome these hurdles, researchers have introduced a novel framework called self-generated goal-conditioned MDPs (sG-MDPs). This innovative approach allows AI agents to dynamically create and pursue their own intermediate subgoals based on the current state of the proof. By structuring the problem in this way, the path to a solution becomes more manageable and amenable to systematic search methods.
The new system, named Bourbaki (7B), is a modular framework that leverages this sG-MDP concept. Inspired by the rigorous approach of the pseudonymous group of French mathematicians, Bourbaki integrates multiple 7B LLMs to generate these subgoals and synthesize the necessary tactics (proof steps). It applies Monte Carlo Tree Search (MCTS)-like algorithms to navigate the complex landscape of possible proof trajectories, enhancing the search process by providing denser feedback signals through verifiable intermediate conjectures.
Bourbaki (7B) has demonstrated remarkable success on the challenging PutnamBench dataset. It successfully solved 26 problems, setting a new state-of-the-art for models of its scale. This significantly outperforms previous 7B models, such as Kimina-7B, which solved only 10 problems. The system’s ability to generate and pursue subgoals not only leads to solving more problems but also enhances the diversity of the generated proofs and improves sample efficiency, meaning it achieves better results with fewer attempts.
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This breakthrough signifies a major step forward in automated theorem proving. By mimicking how human mathematicians break down complex problems into smaller, more manageable steps, Bourbaki provides a more structured and effective way for AI to tackle advanced mathematical reasoning. This research paves the way for more robust and reliable AI systems capable of complex logical deduction. You can read the full research paper here.
