Magnushammer: A Transformer-Based Approach to Premise Selection

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Hauptverfasser: Mikuła, Maciej, Tworkowski, Szymon, Antoniak, Szymon, Piotrowski, Bartosz, Jiang, Albert Qiaochu, Zhou, Jin Peng, Szegedy, Christian, Kuciński, Łukasz, Miłoś, Piotr, Wu, Yuhuai
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Veröffentlicht: 2023
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author Mikuła, Maciej
Tworkowski, Szymon
Antoniak, Szymon
Piotrowski, Bartosz
Jiang, Albert Qiaochu
Zhou, Jin Peng
Szegedy, Christian
Kuciński, Łukasz
Miłoś, Piotr
Wu, Yuhuai
author_facet Mikuła, Maciej
Tworkowski, Szymon
Antoniak, Szymon
Piotrowski, Bartosz
Jiang, Albert Qiaochu
Zhou, Jin Peng
Szegedy, Christian
Kuciński, Łukasz
Miłoś, Piotr
Wu, Yuhuai
contents This paper presents a novel approach to premise selection, a crucial reasoning task in automated theorem proving. Traditionally, symbolic methods that rely on extensive 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 engineering overhead. Our method, Magnushammer, outperforms the most advanced and widely used automation tool in interactive theorem proving called 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 \method with a language-model-based automated theorem prover, we further improve the state-of-the-art proof success rate from $57.0\%$ to $71.0\%$ on the PISA benchmark using $4$x fewer parameters. Moreover, we develop and open source a novel dataset for premise selection, containing textual representations of (proof state, relevant premise) pairs. To the best of our knowledge, this is the largest available premise selection dataset, and the first one for the Isabelle proof assistant.
format Preprint
id arxiv_https___arxiv_org_abs_2303_04488
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Magnushammer: A Transformer-Based Approach to Premise Selection
Mikuła, Maciej
Tworkowski, Szymon
Antoniak, Szymon
Piotrowski, Bartosz
Jiang, Albert Qiaochu
Zhou, Jin Peng
Szegedy, Christian
Kuciński, Łukasz
Miłoś, Piotr
Wu, Yuhuai
Machine Learning
Artificial Intelligence
Logic in Computer Science
This paper presents a novel approach to premise selection, a crucial reasoning task in automated theorem proving. Traditionally, symbolic methods that rely on extensive 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 engineering overhead. Our method, Magnushammer, outperforms the most advanced and widely used automation tool in interactive theorem proving called 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 \method with a language-model-based automated theorem prover, we further improve the state-of-the-art proof success rate from $57.0\%$ to $71.0\%$ on the PISA benchmark using $4$x fewer parameters. Moreover, we develop and open source a novel dataset for premise selection, containing textual representations of (proof state, relevant premise) pairs. To the best of our knowledge, this is the largest available premise selection dataset, and the first one for the Isabelle proof assistant.
title Magnushammer: A Transformer-Based Approach to Premise Selection
topic Machine Learning
Artificial Intelligence
Logic in Computer Science
url https://arxiv.org/abs/2303.04488