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Existing MWP solvers employ sequence or binary tree to present the solutionexpression and decode it from given problem description. However, suchstructures fail to handle the variants that can be derived via mathematicalmanipulation, e.g., $(a_1+a_2) * a_3$ and $a_1 * a_3+a_2 * a_3$ can both bepossible valid solutions for a same problem but formulated as differentexpression sequences or trees. The multiple solution variants depictingdifferent possible solving procedures for the same input problem would raisetwo issues: 1) making it hard for the model to learn the mapping functionbetween the input and output spaces effectively, and 2) wrongly indicating\textit{wrong} when evaluating a valid expression variant. To address theseissues, we introduce a unified tree structure to present a solution expression,where the elements are permutable and identical for all the expressionvariants. We propose a novel non-autoregressive solver, named \textit{MWP-NAS},to parse the problem and deduce the solution expression based on the unifiedtree. For evaluating the possible expression variants, we design a path-basedmetric to evaluate the partial accuracy of expressions of a unified tree. Theresults from extensive experiments conducted on Math23K and MAWPS demonstratethe effectiveness of our proposed MWP-NAS. The codes and checkpoints areavailable at: \url{https://github.com/mengqunhan/MWP-NAS}.

Non-Autoregressive Math Word Problem Solver with Unified Tree Structure