Non-Autoregressive Math Word Problem Solver with Unified Tree Structure

TL;DR

This paper introduces a non-autoregressive method using a unified tree structure to solve math word problems, effectively handling multiple valid solution variants and improving parsing accuracy.

Contribution

The paper proposes a novel unified tree structure and a non-autoregressive solver, MWP-NAS, to better handle solution variants in math word problems.

Findings

Achieves higher accuracy on Math23K and MAWPS datasets.

Effectively models multiple solution variants with a unified tree.

Outperforms existing autoregressive methods.

Abstract

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}.