Existing MWP solvers employ sequence or binary tree to present the solution
expression and decode it from given problem description. However, such
structures fail to handle the identical variants derived via mathematical
manipulation, e.g., $(a_1+a_2)*a_3$ and $a_1*a_3+a_2*a_3$ are for the same
problem but formulating different expression sequences and trees, which would
raise two issues in MWP solving: 1) different output solutions for the same
input problem, making the model hard to learn the mapping function between
input and output spaces, and 2) difficulty of evaluating solution expression
that indicates wrong between the above examples. To address these issues, we
first introduce a unified tree structure to present expression, where the
elements are permutable and identical for all the expression variants. We then
propose a novel non-autoregressive solver, dubbed MWP-NAS, to parse the problem
and reason the solution expression based on the unified tree. For the second
issue, to handle the variants in evaluation, we propose to match the unified
tree and design a path-based metric to evaluate the partial accuracy of
expression. Extensive experiments have been conducted on Math23K and MAWPS, and
the results demonstrate the effectiveness of the proposed MWP-NAS. The codes
and checkpoints are available at: this https URL

研究提出了一种基于统一树结构和新型非自回归求解器 MWP-NAS 的数学语言问题求解方法，并设计了路径度量来评估表达式的部分准确性，实验结果显示该方法在 Math23K 数据集上取得了良好的效果。