  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 variants that can be derived via mathematical
manipulation, e.g., $(a_1+a_2) * a_3$ and $a_1 * a_3+a_2 * a_3$ can both be
possible valid solutions for a same problem but formulated as different
expression sequences or trees. The multiple solution variants depicting
different possible solving procedures for the same input problem would raise
two issues: 1) making it hard for the model to learn the mapping function
between the input and output spaces effectively, and 2) wrongly indicating
\textit{wrong} when evaluating a valid expression variant. To address these
issues, we introduce a unified tree structure to present a solution expression,
where the elements are permutable and identical for all the expression
variants. We propose a novel non-autoregressive solver, named \textit{MWP-NAS},
to parse the problem and deduce the solution expression based on the unified
tree. For evaluating the possible expression variants, we design a path-based
metric to evaluate the partial accuracy of expressions of a unified tree. The
results from extensive experiments conducted on Math23K and MAWPS demonstrate
the effectiveness of our proposed MWP-NAS. The codes and checkpoints are
available at: \url{https://github.com/mengqunhan/MWP-NAS}.
