Magnushammer: A Transformer-based Approach to Premise Selection

Maciej Mikula, Szymon Antoniak, Szymon Tworkowski, Albert Qiaochu Jiang, Jin Peng Zhou, Christian Szegedy, Lukasz Kucinski, Piotr Milos, Yuhuai Wu

Abstract: Premise selection is a fundamental problem of automated theorem proving. Previous works often use intricate symbolic methods, rely on domain knowledge, and require significant engineering effort to solve this task. In this work, we show that Magnushammer, a neural transformer-based approach, can outperform traditional symbolic systems by a large margin. Tested on the PISA benchmark, Magnushammer achieves $59.5\%$ proof rate compared to a $38.3\%$ proof rate of Sledgehammer, the most mature and popular symbolic-based solver. Furthermore, by combining Magnushammer with a neural formal prover based on a language model, we significantly improve the previous state-of-the-art proof rate from $57.0\%$ to $71.0\%$.