Mathematics is a highly specialized domain with its own unique set of challenges. Despite this, there has been relatively little research on natural language processing for mathematical texts, and there are few mathematical language resources aimed at NLP. In this paper, we aim to provide annotated corpora that can be used to study the language of mathematics in different contexts, ranging from fundamental concepts found in textbooks to advanced research mathematics. We preprocess the corpora with a neural parsing model and some manual intervention to provide part-of-speech tags, lemmas, and dependency trees. In total, we provide 182397 sentences across three corpora. We then aim to test and evaluate several noteworthy natural language processing models using these corpora, to show how well they can adapt to the domain of mathematics and provide useful tools for exploring mathematical language. We evaluate several neural and symbolic models against benchmarks that we extract from the corpus metadata to show that terminology extraction and definition extraction do not easily generalize to mathematics, and that additional work is needed to achieve good performance on these metrics. Finally, we provide a learning assistant that grants access to the content of these corpora in a context-sensitive manner, utilizing text search and entity linking. Though our corpora and benchmarks provide useful metrics for evaluating mathematical language processing, further work is necessary to adapt models to mathematics in order to provide more effective learning assistants and apply NLP methods to different mathematical domains.
Mathematical symbol definition extraction is important for improving scholarly reading interfaces and scholarly information extraction (IE). However, the task poses several challenges: math symbols are difficult to process as they are not composed of natural language morphemes; and scholarly papers often contain sentences that require resolving complex coordinate structures. We present SymDef, an English language dataset of 5,927 sentences from full-text scientific papers where each sentence is annotated with all mathematical symbols linked with their corresponding definitions. This dataset focuses specifically on complex coordination structures such as "respectively" constructions, which often contain overlapping definition spans. We also introduce a new definition extraction method that masks mathematical symbols, creates a copy of each sentence for each symbol, specifies a target symbol, and predicts its corresponding definition spans using slot filling. Our experiments show that our definition extraction model significantly outperforms RoBERTa and other strong IE baseline systems by 10.9 points with a macro F1 score of 84.82. With our dataset and model, we can detect complex definitions in scholarly documents to make scientific writing more readable.
Definition Extraction systems are a valuable knowledge source for both humans and algorithms. In this paper we describe our submissions to the DeftEval shared task (SemEval-2020 Task 6), which is evaluated on an English textbook corpus. We provide a detailed explanation of our system for the joint extraction of definition concepts and the relations among them. Furthermore we provide an ablation study of our model variations and describe the results of an error analysis.
We explore the performance of Bidirectional Encoder Representations from Transformers (BERT) at definition extraction. We further propose a joint model of BERT and Text Level Graph Convolutional Network so as to incorporate dependencies into the model. Our proposed model produces better results than BERT and achieves comparable results to BERT with fine tuned language model in DeftEval (Task 6 of SemEval 2020), a shared task of classifying whether a sentence contains a definition or not (Subtask 1).
This work presents our contribution in the context of the 6th task of SemEval-2020: Extracting Definitions from Free Text in Textbooks (DeftEval). This competition consists of three subtasks with different levels of granularity: (1) classification of sentences as definitional or non-definitional,(2) labeling of definitional sentences, and (3) relation classification. We use various pretrained language models (i.e., BERT, XLNet, RoBERTa, SciBERT, and ALBERT) to solve each of the three subtasks of the competition. Specifically, for each language model variant, we experiment by both freezing its weights and fine-tuning them. We also explore a multi-task architecture that was trained to jointly predict the outputs for the second and the third subtasks. Our best performing model evaluated on the DeftEval dataset obtains the 32nd place for the first subtask and the 37th place for the second subtask. The code is available for further research at: https://github.com/avramandrei/DeftEval.
Definition Extraction (DE) is one of the well-known topics in Information Extraction that aims to identify terms and their corresponding definitions in unstructured texts. This task can be formalized either as a sentence classification task (i.e., containing term-definition pairs or not) or a sequential labeling task (i.e., identifying the boundaries of the terms and definitions). The previous works for DE have only focused on one of the two approaches, failing to model the inter-dependencies between the two tasks. In this work, we propose a novel model for DE that simultaneously performs the two tasks in a single framework to benefit from their inter-dependencies. Our model features deep learning architectures to exploit the global structures of the input sentences as well as the semantic consistencies between the terms and the definitions, thereby improving the quality of the representation vectors for DE. Besides the joint inference between sentence classification and sequential labeling, the proposed model is fundamentally different from the prior work for DE in that the prior work has only employed the local structures of the input sentences (i.e., word-to-word relations), and not yet considered the semantic consistencies between terms and definitions. In order to implement these novel ideas, our model presents a multi-task learning framework that employs graph convolutional neural networks and predicts the dependency paths between the terms and the definitions. We also seek to enforce the consistency between the representations of the terms and definitions both globally (i.e., increasing semantic consistency between the representations of the entire sentences and the terms/definitions) and locally (i.e., promoting the similarity between the representations of the terms and the definitions).
We present DefExt, an easy to use semi supervised Definition Extraction Tool. DefExt is designed to extract from a target corpus those textual fragments where a term is explicitly mentioned together with its core features, i.e. its definition. It works on the back of a Conditional Random Fields based sequential labeling algorithm and a bootstrapping approach. Bootstrapping enables the model to gradually become more aware of the idiosyncrasies of the target corpus. In this paper we describe the main components of the toolkit as well as experimental results stemming from both automatic and manual evaluation. We release DefExt as open source along with the necessary files to run it in any Unix machine. We also provide access to training and test data for immediate use.