Layout and Semantics: Combining Representations for Mathematical Formula Search

Math-aware search engines need to support formulae in queries. Mathematical expressions are typically represented as trees defining their operational semantics or visual layout. We propose searching both formula representations using a three-layer model. The first layer selects candidates using spectral matching over tree node pairs. The second layer aligns a query with candidates and computes similarity scores based on structural matching. In the third layer, similarity scores are combined using linear regression. The two representations are combined using retrieval in parallel indices and regression over similarity scores. For NTCIR-12 Wikipedia Formula Browsing task relevance rankings, we see each layer increasing ranking quality and improved results when combining representations as measured by Bpref and nDCG scores.