IneqAgent: Revolutionizing Formal Inequality Proving with Lean4-based Agentic Framework
Summary:IneqAgent is a novel agentic framework that revolutionizes formal inequality proving by integrating Large Language Model (LLM) reasoning with symbolic computation. It employs lemma-level Monte Carlo Tree Search to coordinate lemma construction, goal reformulation, and symbolic backend selection, while complementary backends such as sum-of-squares, Bernstein, and successive difference-substitution produce exact certificates for Lean4 proof generation. Experimental results show that IneqAgent solv
Technical Mechanism Analysis
The core mechanism of IneqAgent lies in the deep integration of its agentic framework with symbolic computation. Its main components include:
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Lemma-level Monte Carlo Tree Search (MCTS): This is used to coordinate lemma construction, goal reformulation, and symbolic backend selection. This method enhances proof efficiency by intelligently exploring possible proof paths.
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Symbolic Computation Backends: These include sum-of-squares, Bernstein, and successive difference-substitution methods, which generate exact proof certificates. These backends, combined with steps generated by the LLM, ensure the completeness and accuracy of the proofs.
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Lean4 Integration: IneqAgent integrates LLM-generated steps with Lean4's feedback mechanism, using Lean4's verification capabilities to build complete proofs and check their consistency with the original theorems.
Engineering Trade-offs and Performance
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Performance Advantages: IneqAgent achieves a 94.09% success rate on four benchmarks, significantly outperforming traditional direct agent methods. Its performance is particularly strong at low inference cost thresholds, demonstrating its potential in resource-constrained environments.
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Inference Cost: IneqAgent has lower inference costs for successful runs compared to direct agents, indicating its efficiency and cost-effectiveness.
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Limitations: While IneqAgent performs well on multiple benchmarks, its reliance on symbolic computation backends may limit its application in more complex or non-standard problems. Additionally, the reasoning capabilities of LLMs in handling highly abstract or complex mathematical concepts still present challenges.
Developer Deployment and Recommendations
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Applicable Scenarios: IneqAgent is suitable for fields requiring high-precision formal proofs, such as mathematical research, program verification, and theorem proving.
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Deployment Recommendations: It is recommended to deploy IneqAgent in a computing environment equipped with strong symbolic computation capabilities and to use Lean4 for verification. Developers can also integrate IneqAgent into existing proof assistant tools using its open interface.
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Future Directions: Future research could explore the application of IneqAgent in a wider range of fields, such as physics, engineering, and economics. Additionally, further optimization of the collaborative work between LLMs and symbolic computation could enhance proof efficiency and robustness.
— END —Source: ArXiv AI (cs.AI) (2026-10-16)
Tags: #IneqAgent #Lean4 #Formal Proof #Agentic Framework #LLMs & Foundation Models
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