Autoformalization with Large Language Models

Yuhuai Wu, Albert Qiaochu Jiang, Wenda Li, Markus Norman Rabe, Charles E Staats, Mateja Jamnik, Christian Szegedy

Keywords: Large language models, Autoformalization, Formal Math, miniF2F.

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~$35.2\%$.

TL;DR: Large language models can be used to do autoformalization, allowing us to achieve in a new SOTA on miniF2F benchmark.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2205.12615/code)