BERT is not The Count: Learning to Match Mathematical Statements with Proofs

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 LLMs 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.