Which one is better: presentation-based or content-based math search?

Mathematical content is a valuable information source and retrieving this content has become an important issue. This paper compares two searching strategies for math expressions: presentation-based and content-based approaches. Presentation-based search uses state-of-the-art math search system while content-based search uses semantic enrichment of math expressions to convert math expressions into their content forms and searching is done using these content-based expressions. By considering the meaning of math expressions, the quality of search system is improved over presentation-based systems

Mathematical Information Retrieval based on type embeddings and query expansion

We present an approach to mathematical information retrieval (MIR) that exploits a special kind of technical terminology, referred to as a mathematical type. In this paper, we present and evaluate a type detection mechanism and show its positive effect on the retrieval of research-level mathematics. Our best model, which performs query expansion with a type-aware embedding space, strongly outperforms standard IR models with state-of-the-art query expansion (vector space-based and language modelling-based), on a relatively new corpus of research-level queries

Math Information Retrieval using a Text Search Engine

Combining text and mathematics when searching in a corpus with extensive mathematical notation remains an open problem. Recent results for math information retrieval systems on the math and text retrieval task at NTCIR-12, for example, show room for improvement, even though formula retrieval appears to be fairly successful. This thesis explores how to adapt the state-of-the-art BM25 text ranking method to work well when searching for math and text together. Symbol layout trees are used to represent math formulas, and features are extracted from the trees, which are then used as search terms for BM25. This thesis explores various features of symbol layout trees and explores their effects on retrieval performance. Based on the results, a set of features are recommended that can be used effectively in a conventional text-based retrieval engine. The feature set is validated using various NTCIR math only benchmarks. Various proximity measures show math and text are closer in documents deemed rel- evant than documents deemed non-relevant for NTCIR queries. Therefore it would seem that proximity could improve ranking for math information retrieval systems when search- ing for both math and text. Nevertheless, two attempts to include proximity when scoring matches were unsuccessful in improving retrieval effectiveness. Finally, the BM25 ranking of both math and text using the feature set designed for formula retrieval is validated by various NTCIR math and text benchmarks

Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment

Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other

Leveraging Formulae and Text for Improved Math Retrieval

Large collections containing millions of math formulas are available online. Retrieving math expressions from these collections is challenging. Users can use formula, formula+text, or math questions to express their math information needs. The structural complexity of formulas requires specialized processing. Despite the existence of math search systems and online community question-answering websites for math, little is known about mathematical information needs. This research first explores the characteristics of math searches using a general search engine. The findings show how math searches are different from general searches. Then, test collections for math-aware search are introduced. The ARQMath test collections have two main tasks: 1) finding answers for math questions and 2) contextual formula search. In each test collection (ARQMath-1 to -3) the same collection is used, Math Stack Exchange posts from 2010 to 2018, introducing different topics for each task. Compared to the previous test collections, ARQMath has a much larger number of diverse topics, and improved evaluation protocol. Another key role of this research is to leverage text and math information for improved math information retrieval. Three formula search models that only use the formula, with no context are introduced. The first model is an n-gram embedding model using both symbol layout tree and operator tree representations. The second model uses tree-edit distance to re-rank the results from the first model. Finally, a learning-to-rank model that leverages full-tree, sub-tree, and vector similarity scores is introduced. To use context, Math Abstract Meaning Representation (MathAMR) is introduced, which generalizes AMR trees to include math formula operations and arguments. This MathAMR is then used for contextualized formula search using a fine-tuned Sentence-BERT model. The experiments show tree-edit distance ranking achieves the current state-of-the-art results on contextual formula search task, and the MathAMR model can be beneficial for re-ranking. This research also addresses the answer retrieval task, introducing a two-step retrieval model in which similar questions are first found and then answers previously given to those similar questions are ranked. The proposed model, fine-tunes two Sentence-BERT models, one for finding similar questions and another one for ranking the answers. For Sentence-BERT model, raw text as well as MathAMR are used

数学情報アクセスのための数式表現の検索と曖昧性解消

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 渋谷 哲朗, 東京大学教授 萩谷 昌己, 東京大学准教授 蓮尾 一郎, 東京大学准教授 鶴岡 慶雅, 東京工業大学准教授 藤井 敦University of Tokyo(東京大学