BERT Is Not The Count: Learning to Match Mathematical Statements with Proofs

Weixian Waylon Li, Yftah Ziser, Maximin Coavoux, Shay B. Cohen


Abstract
We introduce a task consisting in matching a proof to a given mathematical statement. The task fits well within current research on Mathematical Information Retrieval and, more generally, mathematical article analysis (Mathematical Sciences, 2014). We present a dataset for the task (the MATcH dataset) consisting of over 180k statement-proof pairs extracted from modern mathematical research articles. We find this dataset highly representative of our task, as it consists of relatively new findings useful to mathematicians. We propose a bilinear similarity model and two decoding methods to match statements to proofs effectively. While the first decoding method matches a proof to a statement without being aware of other statements or proofs, the second method treats the task as a global matching problem. Through a symbol replacement procedure, we analyze the “insights” that pre-trained language models have in such mathematical article analysis and show that while these models perform well on this task with the best performing mean reciprocal rank of 73.7, they follow a relatively shallow symbolic analysis and matching to achieve that performance.
Anthology ID:
2023.eacl-main.260
Volume:
Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics
Month:
May
Year:
2023
Address:
Dubrovnik, Croatia
Editors:
Andreas Vlachos, Isabelle Augenstein
Venue:
EACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
3581–3593
Language:
URL:
https://aclanthology.org/2023.eacl-main.260
DOI:
10.18653/v1/2023.eacl-main.260
Bibkey:
Cite (ACL):
Weixian Waylon Li, Yftah Ziser, Maximin Coavoux, and Shay B. Cohen. 2023. BERT Is Not The Count: Learning to Match Mathematical Statements with Proofs. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 3581–3593, Dubrovnik, Croatia. Association for Computational Linguistics.
Cite (Informal):
BERT Is Not The Count: Learning to Match Mathematical Statements with Proofs (Li et al., EACL 2023)
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PDF:
https://aclanthology.org/2023.eacl-main.260.pdf
Video:
 https://aclanthology.org/2023.eacl-main.260.mp4