Chenyi Li
Publications
MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures
Automatically constructing well-specified and valuable mathematical conjectures remains a central challenge in AI-assisted mathematical discovery. Many existing open problems and conjectures are often too broad, underspecified, or difficult to connect to plausible proof or refutation strategies. We view a mathematical mechanism as a structure or reasoning principle that connects the assumptions of a candidate problem to its target conclusion, such as an inequality, invariant, decomposition, or reduction to an intermediate claim. We present MECA (MEchanism-centered Conjecture Agent), a multi-agent framework that constructs conjectures by jointly developing candidate statements and their supporting mechanisms. Explorer agents propose mechanisms, test how they apply, and revise the candidate conjecture accordingly, while critic agents assess their mathematical validity and research value. Their feedback guides changes to the assumptions, scope, and conclusion. Through this process, MECA transforms broad research directions into precise conjectures with substantive mathematical support while retaining a clearly identified unresolved core. We evaluate MECA in two complementary settings. First, we compare it with a generate-and-revise baseline on reconstructing preselected target-paper conclusions from target-conditioned but article-blind source materials. Second, we construct 100 semi-open problems from literature-derived seeds and existing open problems and evaluate them through independent proof and refutation attempts by automated provers. Our results indicate that mechanism-centered refinement produces well-specified and research-worthy conjectures that remain challenging for current automated provers.
OptProver: Bridging Olympiad and Optimization through Continual Training in Formal Theorem Proving
Recent advances in formal theorem proving have focused on Olympiad-level mathematics, leaving undergraduate domains largely unexplored. Optimization, fundamental to machine learning, operations research, and scientific computing, remains underserved by existing provers. Its reliance on domain-specific formalisms (convexity, optimality conditions, and algorithmic analysis) creates significant distribution shift, making naive domain transfer ineffective. We present OptProver, a trained model that achieves robust transfer from Olympiad to undergraduate optimization. Starting from a strong Olympiad-level prover, our pipeline mitigates distribution shift through two key innovations. First, we employ large-scale optimization-focused data curation via expert iteration. Second, we introduce a specialized preference learning objective that integrates perplexity-weighted optimization with a mechanism to penalize valid but non-progressing proof steps. This not only addresses distribution shifts but also guides the search toward efficient trajectories. To enable rigorous evaluation, we construct a novel benchmark in Lean 4 focused on optimization. On this benchmark, OptProver achieves state-of-the-art Pass@1 and Pass@32 among comparably sized models while maintaining competitive performance on general theorem-proving tasks, demonstrating effective domain transfer without catastrophic forgetting.