Learning to Rank for Mathematical Formula Retrieval

In Mathematical Information Retrieval (MIR), formulae can be used in a query to match other similar formulae in documents. However, due to the structural complexity of formulae, specialized processing is needed for formula matching. Formulae may be represented by their appearance in Symbol Layout Trees (SLTs) or by their syntax in Operator Trees (OPTs). Previous approaches for formula retrieval used one or both of these representations and used unification to improve search results for inexact matches (e.g., allowing different variable names to match). On these representations, models for matching full expressions (trees), subexpressions, and paths have been used. Recently embedding models were used to represent formulae as vectors. In this paper, the effectiveness of retrieval models and formula representations are studied to identify their relative strengths and weaknesses. Then, a learning to rank model is proposed, using SVM-rank over similarity scores from different formula retrieval models as features. Experiments on the ARQMath formula retrieval task results show that the proposed learning to rank model is effective, producing new state-of-the-art results.