A Survey on Deep Learning for Theorem Proving

TL;DR

This survey reviews recent advances in applying deep learning, especially large language models, to various aspects of theorem proving, highlighting datasets, evaluation metrics, challenges, and future directions.

Contribution

It provides a comprehensive overview of deep learning techniques in theorem proving, including approaches, datasets, evaluation, and critical analysis of challenges and future prospects.

Findings

Deep learning has significantly impacted theorem proving research.

Large language models are increasingly used for proof generation and formalization.

The survey identifies key challenges and promising future research directions.

Abstract

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large language models, has sparked a notable surge of research exploring these techniques to enhance the process of theorem proving. This paper presents a comprehensive survey of deep learning for theorem proving by offering (i) a thorough review of existing approaches across various tasks such as autoformalization, premise selection, proofstep generation, and proof search; (ii) an extensive summary of curated datasets and strategies for synthetic data generation; (iii) a detailed analysis of evaluation metrics and the performance of state-of-the-art methods; and (iv) a critical discussion on the persistent challenges and the promising avenues for future exploration. Our survey aims to serve as a foundational reference for deep learning approaches in theorem proving, inspiring and catalyzing further research endeavors in this rapidly growing field. A curated list of papers is available at https://github.com/zhaoyu-li/DL4TP.