Autoformalization with Large Language Models
This advances formal verification, program synthesis, and AI by providing a novel method for autoformalization, though it is incremental in improving existing theorem proving benchmarks.
The paper tackled the problem of autoformalization, translating natural language mathematics to formal specifications, by showing that large language models can correctly translate 25.3% of mathematical competition problems to Isabelle/HOL, and used this to improve a neural theorem prover, achieving a new state-of-the-art proof rate of 35.2% on the MiniF2F benchmark.
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 $35.2\%$.