A Bottom-Up DAG Structure Extraction Model for Math Word Problems

Research on automatically solving mathematical word problems (MWP) has a long history. Most recent works adopt the Seq2Seq approach to predict the result equations as a sequence of quantities and operators. Although result equations can be written as a sequence, it is essentially a structure. More precisely, it is a Direct Acyclic Graph (DAG) whose leaf nodes are the quantities, and internal and root nodes are arithmetic or comparison operators. In this paper, we propose a novel Seq2DAG approach to extract the equation set directly as a DAG structure. It extracts the structure in a bottom-up fashion by aggregating quantities and sub-expressions layer by layer iteratively. The advantages of our approach are threefold: it is intrinsically suitable to solve multivariate problems, it always outputs valid structure, and its computation satisfies commutative law for +, × and =. Experimental results on DRAW1K and Math23K datasets demonstrate that our model outperforms state-of-the-art deep learning methods. We also conduct detailed analysis on the results to show the strengths and limitations of our approach.