A semantic-based deep learning approach for mathematical expression retrieval
Pavan Kumar Perepu
TL;DR
The paper tackles the challenge of retrieving mathematical expressions by focusing on semantic similarity rather than purely syntactic matching. It introduces a DRNN trained on an auxiliary complexity classification task using integer-encoded LaTeX MEs to produce fixed-length semantic features extracted before the final layer; queries are retrieved by Euclidean distance against a database of precomputed features, enabling linear-time retrieval. The approach is demonstrated on a PACME database of $829$ expressions, and the results show that semantic retrieval yields semantically meaningful matches and is flexible to target different notions (e.g., complexity), with potential applications in plagiarism detection. The method avoids padding by using global pooling, and the authors discuss extending the framework to distributed ME databases for scalability.
Abstract
Mathematical expressions (MEs) have complex two-dimensional structures in which symbols can be present at any nested depth like superscripts, subscripts, above, below etc. As MEs are represented using LaTeX format, several text retrieval methods based on string matching, vector space models etc., have also been applied for ME retrieval problem in the literature. As these methods are based on syntactic similarity, recently deep learning approaches based on embedding have been used for semantic similarity. In our present work, we have focused on the retrieval of mathematical expressions using deep learning approaches. In our approach, semantic features are extracted from the MEs using a deep recurrent neural network (DRNN) and these features have been used for matching and retrieval. We have trained the network for a classification task which determines the complexity of an ME. ME complexity has been quantified in terms of its nested depth. Based on the nested depth, we have considered three complexity classes of MEs: Simple, Medium and Complex. After training the network, outputs just before the the final fully connected layer are extracted for all the MEs. These outputs form the semantic features of MEs and are stored in a database. For a given ME query, its semantic features are computed using the trained DRNN and matched against the semantic feature database. Matching is performed based on the standard euclidean distance and top 'k' nearest matches are retrieved, where 'k' is a user-defined parameter. Our approach has been illustrated on a database of 829 MEs.