Automated Discovery of Mathematical Definitions in Text

Automatic definition extraction from texts is an important task that has numerous applications in several natural language processing fields such as summarization, analysis of scientific texts, automatic taxonomy generation, ontology generation, concept identification, and question answering. For definitions that are contained within a single sentence, this problem can be viewed as a binary classification of sentences into definitions and non-definitions. Definitions in scientific literature can be generic (Wikipedia) or more formal (mathematical articles). In this paper, we focus on automatic detection of one-sentence definitions in mathematical texts, which are difficult to separate from surrounding text. We experiment with several data representations, which include sentence syntactic structure and word embeddings, and apply deep learning methods such as convolutional neural network (CNN) and recurrent neural network (RNN), in order to identify mathematical definitions. Our experiments demonstrate the superiority of CNN and its combination with RNN, applied on the syntactically-enriched input representation. We also present a new dataset for definition extraction from mathematical texts. We demonstrate that the use of this dataset for training learning models improves the quality of definition extraction when these models are then used for other definition datasets. Our experiments with different domains approve that mathematical definitions require special treatment, and that using cross-domain learning is inefficient.