From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates
A new framework called NSPI has been proposed for automated polynomial inequality proving. This method combines large language models (LLMs) with symbolic computation to enhance scalability and effectiveness. The framework has shown promising results in experiments involving polynomials with up to 10 variables.
- ▪Automated proving of polynomial inequalities is a significant challenge in mathematical reasoning.
- ▪The NSPI framework utilizes LLMs to generate conjectures, which are then refined through symbolic computation.
- ▪Experiments demonstrate the effectiveness of NSPI on challenging benchmarks.
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Computer Science > Artificial Intelligence arXiv:2605.15445 (cs) [Submitted on 14 May 2026] Title:From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates Authors:Ruobing Zuo, Hanrui Zhao, Gaolei He, Zhengfeng Yang, Jianlin Wang View a PDF of the paper titled From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates, by Ruobing Zuo and 4 other authors View PDF HTML (experimental) Abstract:Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability.
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