Autoformalization with Large Language Models

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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 Ranked #1 on Automated Theorem Proving on miniF2F-test (using extra training data)

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Task Dataset Model Metric Name Metric Value Global Rank Uses Extra
Training Data
Automated Theorem Proving miniF2F-test Thor + expert iteration on autoformalised theorems Pass@1 35.2 # 1


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