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Autoformalization with Large Language Models

Yuhuai Wu · Albert Qiaochu Jiang · Wenda Li · Markus Rabe · Charles Staats · Mateja Jamnik · Christian Szegedy

Hall J (level 1) #512

Keywords: [ Autoformalization ] [ Large language models ] [ miniF2F. ] [ Formal Math ]

Abstract: Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence.While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion ($25.3\%$) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from~$29.6\%$ to~$35.2\%$.

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