BERT Is Not The Count: Learning to Match Mathematical Statements with Proofs
Weixian Waylon Li, Yftah Ziser, Maximin Coavoux, Shay B. Cohen · 2023
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.1 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.2 * Work mostly done at the University of Edinburgh. 1 Our dataset and code are available at https:// github.com/waylonli/MATcH.2 Like Bert, The Count (or Count von Count; ) is a character from the television show Sesame Street.The Count likes counting, and his main role in the show is to teach this skill to children.