LLM Agents Coordinate Symbolic Tools for Verified Sum-of-Squares Certificates
A new research paper on arXiv (2608.00326) introduces an agent that uses large language models (LLMs) to coordinate symbolic tools for verified sum-of-squares (SOS) certificates. The work addresses the challenge of proving polynomial nonnegativity via weighted SOS decomposition, a machine-checkable method. The agent combines algebraic task training, symbolic tools, and verifier-grounded optimization. The authors constructed 1.35 million synthetic examples covering eight supporting polynomial tasks, and applied supervised fine-tuning (SFT) on direct algebra problems and simulated symbolic traces, followed by Group Relative Policy Optimization (GRPO). The paper is categorized as an AI for mathematics study, highlighting the potential of LLM agents in formal verification.
Key facts
- Paper arXiv:2608.00326, announced as new.
- Focus on weighted sum-of-squares (SOS) decomposition for proving polynomial nonnegativity.
- Agent combines algebraic task training, symbolic tools, and verifier-grounded optimization.
- 1.35 million synthetic examples covering eight supporting polynomial tasks.
- Supervised fine-tuning (SFT) on direct algebra problems and simulated symbolic traces.
- Group Relative Policy Optimization (GRPO) used after SFT.
- Tool calling allows LLMs to invoke external computation during problem solving.
- Candidate decomposition can be checked exactly, but finding one requires coordination.
Entities
Institutions
- arXiv