EquGener: A Reasoning Network for Word Problem Solving by Generating Arithmetic Equations

EquGener: A Reasoning Network for Word Problem Solving by Generating Arithmetic Equations Pruthwik Mishra MT & NLP Lab, KCIS LTRC, IIIT-Hyderabad Litton J Kurisinkel IREL Lab, KCIS LTRC, IIIT-Hyderabad Dipti Misra Sharma MT & NLP Lab, KCIS LTRC, IIIT-Hyderabad Vasudeva Varma IREL Lab, KCIS LTRC, IIIT-Hyderabad Abstract Word problem solving has always been a challenging task as it involves reasoning across sentences, identification of operations and their order of application on relevant operands. Most of the earlier systems at- tempted to solve word problems with tailored features for handling each category of prob- lems. In this paper, we present a new approach to solve simple arithmetic problems. Through this work we introduce a novel method where we first learn a dense representation of the problem description conditioned on the ques- tion in hand. We leverage this representa- tion to generate the operands and operators in the appropriate order. Our approach improves upon the state-of-the-art system by 3% in one benchmark dataset while ensuring comparable accuracies in other datasets. 1 Introduction According to (Koncel-Kedziorski et al., 2015; Hos- seini et al., 2014), a word problem narrates a par- tial world state consisting of entities, entity holders, quantities and other participants. It either changes the state of entities or expounds the relationships be- tween them. At the end, the problem queries about a quantity which can be obtained by arithmetically combining several quantities mentioned in the ques- tion as shown in Table 1. Natural language under- standing plays a key role in solving any Mathemati- cal Word Problem (MWP). Automating such prob- lem solving requires better reasoning across sen- tences, also involves complex inference using world knowledge, co-reference resolution and a large vo- cabulary. Simple keyword or pattern matching is less equipped to take up such a challenge (Bakman, 2007). There are 112 short trees and 119 tall trees currently in the park . Park workers will plant 105 short trees today . How many short trees will the park have when the workers are fin- ished ? Answer : 112 + 105 Table 1: Mathematical Word Problem Example Previous systems either rely heavily on specific set of problem abstractions based on verb categories (Hosseini et al., 2014) or learning equations from pre-defined set of templates (Kushman et al., 2014). Deep neural solvers (Wang et al., 2017) proposed a combination of sequence-to-sequence model and information retrieval system. However, an ideal equation generation system for a word problem should be able to identify components of the equation and form the equation in an orderly fashion independent of syntax or vocabulary of the sentences. In this work, we introduce EquGener - an equation generator using a memory network with an equation decoder. Intuitively, a human math solver collects relevant details from the problem description which equip her to solve the problem (Dellarosa, 1986). Driven by this intuition, we learn a dense semantic representation of the problem description consisting of multiple sentences, conditioned on the question in hand. An equation necessary to solve the question …

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