Non-Autoregressive Math Word Problem Solver with Unified Tree Structure

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: https://github.com/mengqunhan/MWP-NAS