Dowsing for Math Answers with Tangent-L

We present our application of the math-aware search engine Tangent-L to the ARQMath Community Question Answering (CQA) task. Our approach performs well, placing in the top three positions out of all 23 submissions, including the baseline runs. Tangent-L, built on the text search platform Lucene, handles math formulae by first converting a formula’s Presentation MathML representation into a Symbol Layout Tree, followed by extraction of math tuples from the tree that serve as search terms. It applies BM25 ranking to all math tuples and natural language terms in a document during searching. For the CQA task, we index all question-answer pairs in the Math Stack Exchange corpus. At query time, we first convert a topic question into a bag of formulae and keywords that serves as a formal query. We then execute the queries using Tangent-L to find the best matches. Finally, we re-rank the matches by a regression model that was trained on metadata attributes from the corpus. Our primary run produces an nDCG′ value of 0.278 and MAP′ value of 0.063, where these are two common measures of quality for ranked retrieval. However, our best performance, an nDCG′ value of 0.345 and MAP′ value of 0.139, is achieved by an alternate run without re-ranking. Follow-up experiments help to explain which aspects of our approach lead to our success.