Automatic Description Construction for Math Expression via Topic Relation Graph

TL;DR

This paper introduces a hybrid model called MathDes that automatically constructs textual descriptions for math expressions by leveraging a Topic Relation Graph and ILP-based summarization, addressing document relevance and sparsity challenges.

Contribution

The paper proposes a novel approach combining a Topic Relation Graph and ILP-based summarization to generate descriptions for math expressions, improving over existing methods.

Findings

Outperforms baseline models in description quality.

Effectively retrieves relevant documents using TRG.

Demonstrates promising results in automatic math expression description.

Abstract

Math expressions are important parts of scientific and educational documents, but some of them may be challenging for junior scholars or students to understand. Nevertheless, constructing textual descriptions for math expressions is nontrivial. In this paper, we explore the feasibility to automatically construct descriptions for math expressions. But there are two challenges that need to be addressed: 1) finding relevant documents since a math equation understanding usually requires several topics, but these topics are often explained in different documents. 2) the sparsity of the collected relevant documents making it difficult to extract reasonable descriptions. Different documents mainly focus on different topics which makes model hard to extract salient information and organize them to form a description of math expressions. To address these issues, we propose a hybrid model (MathDes) which contains two important modules: Selector and Summarizer. In the Selector, a Topic Relation Graph (TRG) is proposed to obtain the relevant documents which contain the comprehensive information of math expressions. TRG is a graph built according to the citations between expressions. In the Summarizer, a summarization model under the Integer Linear Programming (ILP) framework is proposed. This module constructs the final description with the help of a timeline that is extracted from TRG. The experimental results demonstrate that our methods are promising for this task and outperform the baselines in all aspects.