Equation Parsing : Mapping Sentences to Grounded Equations

Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pages 1088–1097, Austin, Texas, November 1-5, 2016. c⃝2016 Association for Computational Linguistics EQUATION PARSING : Mapping Sentences to Grounded Equations Subhro Roy Shyam Upadhyay Dan Roth University of Illinois, Urbana Champaign {sroy9, upadhya3, danr}@illinois.edu Abstract Identifying mathematical relations expressed in text is essential to understanding a broad range of natural language text from election reports, to financial news, to sport commen- taries to mathematical word problems. This paper focuses on identifying and understand- ing mathematical relations described within a single sentence. We introduce the problem of Equation Parsing – given a sentence, iden- tify noun phrases which represent variables, and generate the mathematical equation ex- pressing the relation described in the sentence. We introduce the notion of projective equation parsing and provide an efficient algorithm to parse text to projective equations. Our system makes use of a high precision lexicon of math- ematical expressions and a pipeline of struc- tured predictors, and generates correct equa- tions in 70% of the cases. In 60% of the time, it also identifies the correct noun phrase → variables mapping, significantly outperform- ing baselines. We also release a new annotated dataset for task evaluation. 1 Introduction Understanding text often involves reasoning with re- spect to quantities mentioned in it. Understanding the news article statement in Example 1 requires identifying relevant entities and the mathematical re- lations expressed among them in text, and determin- ing how to compose them. Similarly, solving a math word problem with a sentence like Example 2, re- quires realizing that it deals with a single number, knowing the meaning of “difference” and compos- Example 1 Emanuel’s campaign contribu- tions total three times those of his opponents put together. Example 2 Twice a number equals 25 less than triple the same number. Example 3 Flying with the wind , a bird was able to make 150 kilometers per hour. Example 4 The sum of two numbers is 80. Example 5 There are 54 5-dollar and 10- dollar notes. ing the right equation – “25” needs to be subtracted from a number only after it is multiplied by 3. As a first step towards understanding such rela- tions, we introduce the Equation Parsing task - given a sentence expressing a mathematical relation, the goal is to generate an equation representing the rela- tion, and to map the variables in the equation to their corresponding noun phrases. To keep the problem tractable, in this paper we restrict the final output equation form to have at most two (possibly coref- erent) variables, and assume that each quantity men- tioned in the sentence can be used at most once in the final equation.1 In example 1, the gold out- put of an equation parse should be V1 = 3 × V2, with V1 = “Emanuel’s campaign contributions” and V2 = “those of his opponents put together”. The task can be seen as a form of semantic parsing (Goldwasser and Roth, 2011; Kwiatkowski et …

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