Dowsing for Math Answers: Exploring MathCQA with a Math-aware Search Engine

Abstract

Solving math problems can be challenging. It is so challenging that one might wish to seek insights from the internet, looking for related references to understand more about the problems. Even more, one might wish to actually search for the answer, believing that some wise people have already solved the problem and shared their intelligence selflessly. However, searching for relevant answers for a math problem effectively from those sites is itself not trivial.

This thesis details how a math-aware search engine Tangent-L---which adopts a traditional text retrieval model (Bag-of-Words scored by BM25+ using formulas' symbol pairs and other features as "words''---tackles the challenge of finding answers to math questions. Various adaptations for Tangent-L to this challenge are explored, including query conversion, weighting scheme of math features, and result re-ranking.

In a recent workshop series named Answer Retrieval for Questions on Math (ARQMath), and with math problems from Math StackExchange, the submissions based on these adaptations of Tangent-L achieved the best participant run for two consecutive years, performing better than many participating models designed with machine learning and deep learning models. The major contributions of this thesis are the design and implementation of the three-stage approach to adapting Tangent-L to the challenge, and the detailed analyses of many variants to understand which aspects are most beneficial. The code repository is available, as is a data exploration too built for interested participants to view the math questions in this ARQMath challenge and check the performance of their answer rankings.