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

A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

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

Discovering Mathematical Objects of Interest -- A Study of Mathematical Notations

Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems. The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking $P_{n}^{(\alpha, \beta)}\!\left(x\right)$ with `Jacobi polynomial'); (3) we extend zbMATH's search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.Comment: Proceedings of The Web Conference 2020 (WWW'20), April 20--24, 2020, Taipei, Taiwa

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

Approach and Preliminary Results for Early Growth Technology Analysis

Even experts cannot be fully aware of all the promising developments in broad and complex fields of technology, such as renewable energy. Fortunately, there exist many diverse sources of information that report new technological developments, such as journal publications, news stories, and blogs. However, the volume of data contained in these sources is enormous; it would be difficult for a human to read and digest all of this information - especially in a timely manner. This paper describes a novel application of technology mining techniques to these diverse information sources to study, visualize, and identify the evolution of promising new technologies - a challenge we call 'early growth technology analysis.' For the work reported herein, we use as inputs information about millions of published documents contained in sources such as SCIRCUS, Inspec, and Compendex. We accomplish this analysis through the use of bibliometric analysis, consisting of three key steps: 1. Extract related keywords (from keywords in articles) 2. Determine the annual occurrence frequencies of these keywords 3. Identify those exhibiting rapid growth, particularly if starting from a low base. To provide a focus for the experiments and subsequent discussions, a pilot study was conducted in the area of 'renewable energy,' though the techniques and methods developed are neutral to the domain of study. Preliminary results and conclusions from the case study are presented and are discussed in the context of the effectiveness of the proposed methodology

Bridging the Gap Between Indexing and Retrieval for Differentiable Search Index with Query Generation

The Differentiable Search Index (DSI) is an emerging paradigm for information retrieval. Unlike traditional retrieval architectures where index and retrieval are two different and separate components, DSI uses a single transformer model to perform both indexing and retrieval. In this paper, we identify and tackle an important issue of current DSI models: the data distribution mismatch that occurs between the DSI indexing and retrieval processes. Specifically, we argue that, at indexing, current DSI methods learn to build connections between the text of long documents and the identifier of the documents, but then retrieval of document identifiers is based on queries that are commonly much shorter than the indexed documents. This problem is further exacerbated when using DSI for cross-lingual retrieval, where document text and query text are in different languages. To address this fundamental problem of current DSI models, we propose a simple yet effective indexing framework for DSI, called DSI-QG. When indexing, DSI-QG represents documents with a number of potentially relevant queries generated by a query generation model and re-ranked and filtered by a cross-encoder ranker. The presence of these queries at indexing allows the DSI models to connect a document identifier to a set of queries, hence mitigating data distribution mismatches present between the indexing and the retrieval phases. Empirical results on popular mono-lingual and cross-lingual passage retrieval datasets show that DSI-QG significantly outperforms the original DSI model.Comment: 11 page