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[2602.10538] Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models
Summary
This article explores the effectiveness of agentic theorem provers through a statistical provability theory, analyzing their performance and limitations in mathematical reasoning models.
Why It Matters
Understanding the mechanisms behind agentic theorem provers is crucial for advancing AI in mathematical reasoning. This research provides insights into their operational success and potential limitations, which can inform future developments in AI systems and their applications in complex problem-solving.
Key Takeaways
- Agentic theorem provers combine various AI components to enhance mathematical reasoning.
- The study introduces a statistical framework to analyze the success probabilities of these systems.
- Performance gaps are linked to approximation errors and the complexity of problem distributions.
- The research clarifies the conditions under which these provers excel or struggle.
- Insights from this study can guide the future design of AI systems for better performance.
Statistics > Machine Learning arXiv:2602.10538 (stat) [Submitted on 11 Feb 2026 (v1), last revised 12 Feb 2026 (this version, v2)] Title:Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models Authors:Sho Sonoda, Shunta Akiyama, Yuya Uezato View a PDF of the paper titled Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models, by Sho Sonoda and 2 other authors View PDF HTML (experimental) Abstract:Agentic theorem provers -- pipelines that couple a mathematical reasoning model with library retrieval, subgoal-decomposition/search planner, and a proof assistant verifier -- have recently achieved striking empirical success, yet it remains unclear which components drive performance and why such systems work at all despite classical hardness of proof search. We propose a distributional viewpoint and introduce \textbf{statistical provability}, defined as the finite-horizon success probability of reaching a verified proof, averaged over an instance distribution, and formalize modern theorem-proving pipelines as time-bounded MDPs. Exploiting Bellman structure, we prove existence of optimal policies under mild regularity, derive provability certificates via sub-/super-solution inequalities, and bound the performance gap of score-guided planning (greedy/top-\(k\)/beam/rollouts) in terms of approximation error, sequential statistical complexity, representation geometry (metric entropy/doubling stru...
