Autoformalization in the Era of Large Language Models: A Survey

TL;DR

This survey reviews recent advances in autoformalization driven by large language models, highlighting its role in transforming informal math into formal proofs, improving verifiability, and outlining future research directions.

Contribution

It provides a comprehensive overview of autoformalization techniques, applications, challenges, and open-source resources in the context of large language models.

Findings

Autoformalization enhances the verifiability of LLM outputs.

Large language models have significantly advanced autoformalization capabilities.

Open challenges include data quality and model interpretability.

Abstract

Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both theoretical and applied domains. Driven by the rapid progress in artificial intelligence, particularly large language models (LLMs), this field has witnessed substantial growth, bringing both new opportunities and unique challenges. In this survey, we provide a comprehensive overview of recent advances in autoformalization from both mathematical and LLM-centric perspectives. We examine how autoformalization is applied across various mathematical domains and levels of difficulty, and analyze the end-to-end workflow from data preprocessing to model design and evaluation. We further explore the emerging role of autoformalization in enhancing the verifiability of LLM-generated outputs, highlighting its potential to improve both the trustworthiness and reasoning capabilities of LLMs. Finally, we summarize key open-source models and datasets supporting current research, and discuss open challenges and promising future directions for the field.