Magnushammer: A Transformer-Based Approach to Premise Selection
This work addresses the problem of reducing engineering effort and improving accuracy in automated theorem proving for researchers and practitioners, representing a strong specific gain rather than an incremental improvement.
The paper tackles premise selection in automated theorem proving by introducing Magnushammer, a transformer-based method that outperforms the Sledgehammer tool with success rates of 59.5% vs. 38.3% on PISA and 34.0% vs. 20.9% on miniF2F, and improves proof success from 57.0% to 71.0% on PISA with fewer parameters.
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.