Prediction of Mathematical Expression Declarations based on Spatial, Semantic, and Syntactic Analysis

Lin, Jason; Wang, Xing; Wang, Zelun; Beyette, Donald; Liu, Jyh-Charn

doi:10.1145/3342558.3345399

Cited by 6 publications

(6 citation statements)

References 13 publications

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“…Descriptions at the formula level do not however consider individual symbols and their meaning. Therefore, the next approaches looked into (ii) extracting descriptions of mathematical expressions within formulas (Kristianto, Topic, and Aizawa 2014;Lin et al 2019). But, to fully understand the formulas it is needed to (iii) extract the descriptions of the contained mathematical symbols, which is the SDR task.…”

Section: Related Sdr Tasksmentioning

confidence: 99%

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Symbol Description Reading

Lynch,

Eck,

Ploennigs

2024

AAAI

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Mathematical formulas give concise representations of a document's key ideas in many natural sciences and engineering domains. The symbols that make up formulas carry semantic meaning that may differ by document or equation. What does ? mean in a given paper? Interpreting the symbols that comprise formulas requires identifying descriptions from the surrounding text. We approach this task of symbol description reading as an application of current AI technologies targeting the tuning of large language models for particular domains and automation of machine learning. Our pipeline integrates AI question answering and natural language processing to read symbol descriptions. We consider extractive and generative AI model variations and apply our pipeline on two example tasks of symbol description reading. Promising results provide motivation for wider deployment for which we describe a microservice architecture and related challenges.

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Section: Related Sdr Tasksmentioning

confidence: 99%

“…But, knowledge in those domains is often formally modelled in mathematical formulas that the LLMs need to understand. Currently LLMs capture the text around the formulas, but, do not embed the knowledge within the formulas (Lin et al 2019). Two challenges currently limit the reach of LLMs to mathematical formulas.…”

Section: Problem Introduction and Significancementioning

confidence: 99%

Symbol Description Reading

Lynch,

Eck,

Ploennigs

2024

AAAI

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“…At first, the algorithm compares V E A and V E B to transform them into the same (ll. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Here, we define between-shared variables V bs as the variables shared between E A and E B , and within-shared variables V ws,E i as the variables shared between the equations within an equation group E i (ll.…”

Section: Equivalence Judgment Of Equation Groupsmentioning

confidence: 99%

“…Since a variable is sometimes expressed by different symbols among documents, we have to extract variable definitions [5][6][7] and unify the variable symbols' representations 8 before judging the equivalence of equation groups. Such a method can be developed independently of the equivalence judgment; thus, we assume that different symbols do not represent the same variable in this study.…”

Section: Introductionmentioning

confidence: 99%

Simple Algorithm for Judging Equivalence of Differential-Algebraic Equation Systems

Kato

Zhang

Kano

2022

Preprint

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Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing whether equation groups containing multiple equations are equivalent. However, existing tools cannot judge the equivalence of two equation groups; thus, we develop an algorithm to judge such an equivalence using a computer algebra system. The proposed algorithm first eliminates variables appearing only in either equation group. It then checks the equivalence of the equations one by one. If each equation in one equation group is equivalent to an equation in the other, the equation groups are judged equivalent; otherwise, non-equivalent. We generated 50 pairs of equation groups for evaluation. The proposed method accurately judged the equivalence of all pairs. This method is expected to facilitate comprehension of a large amount of mathematical information in STEM documents. Furthermore, this is a necessary step for machines to understand equations, including process models.

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“…NLP techniques often play a critical role in bridging the gap between presentation and semantic representations of math formulae. Recent studies on this topic include variable typing (Stathopoulos et al 2018), using the textual context for transformation from a presentation level to semantic level (Schubotz et al 2018), and identifying declarations of mathematical objects (Lin et al 2019).…”

Section: Math Information Retrievalmentioning

confidence: 99%

Mathematical Information Retrieval

Aizawa¹,

Kohlhase²

2020

The Information Retrieval Series

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We present an overview of the NTCIR Math Tasks organized during NTCIR-10, 11, and 12. These tasks are primarily dedicated to techniques for searching mathematical content with formula expressions. In this chapter, we first summarize the task design and introduce test collections generated in the tasks. We also describe the features and main challenges of mathematical information retrieval systems and discuss future perspectives in the field.

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Prediction of Mathematical Expression Declarations based on Spatial, Semantic, and Syntactic Analysis

Cited by 6 publications

References 13 publications

Symbol Description Reading

Symbol Description Reading

Simple Algorithm for Judging Equivalence of Differential-Algebraic Equation Systems

Mathematical Information Retrieval

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