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

TL;DR

This paper introduces a new dataset and methods for matching mathematical statements with their proofs, revealing that pre-trained language models perform well but rely on shallow symbolic cues.

Contribution

The paper presents the MATcH dataset, a bilinear similarity model, and analysis of language models' capabilities in mathematical statement-proof matching.

Findings

Mean reciprocal rank of 73.7 achieved by models

Models rely on shallow symbolic analysis

Proposed methods improve matching accuracy

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.