EBERT: A lightweight expression-enhanced large-scale pre-trained language model for mathematics education

Abstract

Within the realm of mathematics education, there exist several challenging supervised tasks that educators and researchers encounter, such as question difficulty prediction and mathematical expression understanding. To address these challenges, researchers have introduced unsupervised pre-trained models specifically tailored for mathematics education, yielding promising outcomes. However, the existing literature fails to consider the domain-specific characteristics of mathematics, particularly the structural features in pre-trained corpora and extensive expressions, which makes them costly expensive and time-consuming. To tackle this problem, we propose a lightweight expression-enhanced large-scale pre-trained language model, called EBERT, for mathematics education. Specifically, we select a large number of expression-enriched exercises to further pre-train the original BERT. To depict the inherent structural features existed in expressions, the initial step involves the creation of an Operator Tree for each expression. Subsequently, each exercise is transformed into a corresponding Question&Answer tree (QAT) to serve as the model input. Notably, to ensure the preservation of semantic integrity within the QAT, a specialized Expression Enhanced Matrix is devised to confine the visibility of individual tokens. Additionally, a new pre-training task, referred to as Question&Answer Matching, is introduced to capture exercise-related structural information at the semantic level. Through three downstream tasks in mathematical education, we prove that EBERT outperforms several state-of-the-art baselines (such as MathBERT and GPT-3) in terms of ACC and F1-score.