Magnushammer: A Transformer-Based Approach to Premise Selection

Maciej Mikuła, Szymon Antoniak, Szymon Tworkowski, Bartosz Piotrowski, Albert Jiang, Jin Peng Zhou, Christian Szegedy, Łukasz Kuciński, Piotr Miłoś, Yuhuai Wu

Keywords: transformers, interactive theorem proving, automated reasoning, contrastive learning, premise selection

TL;DR: Contrastively trained transformers outperform state-of-the-art symbolic methods for premise selection, a challenging reasoning task of selecting relevant facts for proving new theorems in formal mathematics.

Abstract: We present Magnushammer: a novel approach to premise selection -- a crucial task in automated theorem proving. Traditionally, symbolic methods that rely on domain knowledge and engineering effort are applied to this task. In contrast, this work demonstrates that contrastive training with the transformer architecture can achieve higher-quality retrieval of relevant premises, without the domain knowledge or feature engineering overhead. Magnushammer outperforms the most advanced and widely used automation tool in interactive theorem proving: Sledgehammer. On the PISA and miniF2F benchmarks Magnushammer achieves $59.5\%$ (against $38.3\%$) and $34.0\%$ (against $20.9\%$) success rates, respectively. By combining Magnushammer with a language-model-based theorem prover, we further improve the state-of-the-art proof success rate from $57.0\%$ to $71.0\%$ on the PISA benchmark. Moreover, we develop and open source a novel, large dataset for premise selection.

Submission Number: 23