Learning to Coordinate Symbolic Tools: LLM Agents for Verified Sum-of-Squares Certificates

arXiv cs.AIAugust 4, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2608.00326v1 Announce Type: new Abstract: Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics. We study this setting through weighted sum-of-squares (SOS) decomposition, a machine-checkable route to proving polynomial nonnegativity and hence polynomial inequalities. A candidate decomposition can be checked exactly, but finding one requires choosing among non-unique regroupings and coordinating multiple symbolic transformations. We develop an agent that combines algebraic task training, symbolic tools, and verifier-grounded optimization for this task. Rather than traini

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