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Language Model Search for Verifiable Controllers: The PCE Method

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The research team proposes the "Proof-Carrying Evolution" (PCE) method: when searching for controllers, the language model simultaneously provides a formal certificate, and only candidates that pass certificate verification are returned; what is ultimately deployed is the control law together with the certificate, and the language model is used only in the design phase. The authors compared four language models with classical search and synthesis methods on rate-limited docking, maneuvering target tracking, and SO(3) attitude control. Verification differs by problem: for linear problems, certificates are verified using exact rational arithmetic during the search; on SO(3), floating-point verification is used first, followed by exact re-verification of each reported champion. The best run of each method also obtained a Lean 4 proof. The authors report that the median across all search runs remains below that of hand-tuned control laws.

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  1. Proof-Carrying Evolution: Language Models Design Formally Verifiable Controllers

    The study proposes Proof-Carrying Evolution (PCE), in which a language model provides both a controller and its certificate during search; only candidates that pass certificate verification can be returned, and the deployed artifact is the control law together with its certificate. The authors compare four language models with classical search and synthesis methods on speed-limited docking, maneuvering-target pursuit, and SO(3) attitude control. Certificates for linear problems are verified using exact rational arithmetic; on SO(3), floating-point verification is followed by exact re-verification of each reported champion. The best run of each method also receives a Lean 4 proof.

    arXiv cs.RO ·

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Planning and decision makingMotion controlRobot models and learningResearch papers

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