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Text2Math model for semantically parsing text into math expressions

-By Yanyan Zou and Wei Lu 
StatNLP 
Research Group Singapore University of Technology and Design



Abstract
We propose Text2Math, a model for semantically parsing text into math expressions. The model can be used to solve different math related problems including arithmetic word problems and equation parsing problems. Unlike previous approaches, we tackle the problem from an endto-end structured prediction perspective where our algorithm aims to predict the complete math expression at once as a tree structure, where minimal manual efforts are involved in the process. Empirical results on benchmark datasets demonstrate the efficacy of our approach.
Designing computer algorithms that can automatically solve math word problems is a challenge for the AI research community. Two representative tasks have been proposed and studied recently – solving arithmetic word problems and equation parsing as illustrated in image The former task focuses on mapping the input paragraph (which may involve multiple sentences) into a target math expression, from which an answer can be calculated. The latter task focuses on mapping a description (usually a single sentence) into a math equation that typically involves one or more unknowns.

Expression Tree

We first define tree representations for math expressions, which will then be regarded as the semantic representations used in the standard semantic parsing setup. 
The nodes involved in the math expression trees can be classified into two categories, namely, operator and quantity nodes. Specifically, operator nodes are the tree nodes that define the types of operations involved in expressions. In this work we consider ADD (addition, +), SUB (subtraction, −), MUL (multiplication, ×) and DIV (division, ÷). We also regard the equation sign (=) as an operation involved in math expressions and use EQU to denote it. We consider two types of quantity nodes: CON denoting constants, and VAR for unknown variables. Table 1 lists the above nodes. 
Each tree node comes with an arity which specifies the number of direct child nodes that should appear below the given node. For example, the operator node SUB with arity 2 is expecting two child nodes below it in the expression tree, while CON with arity 0 is supposed to be a leaf node. The two math expressions in Figure 1 can be equivalently represented by expression trees consisting of such nodes.



Conclusion

In this work, we propose a unified structured prediction approach, Text2Math, to solving both arithmetic word problems and equation parsing tasks. We leverage a novel joint representation to automatically learn the correspondence between words and math expressions which reflects semantic closeness. Different from many existing models, Text2Math is agnostic of the semantics of operands and learns to map from text to math expressions in an end-to-end manner based on a data-driven approach. Experiments demonstrate the efficacy of our model. In the future, we would like to investigate how such an approach can be applied to more complicated math word problems, like algebra word problems where a problem usually maps to an equation set. Another interesting direction is to investigate how to incorporate world knowledge into the graph-based approach to boost the performance

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