Generalizing Math Word Problem Solvers via Solution Diversification

TL;DR

This paper introduces a new training framework for math word problem solvers that leverages solution diversification through a buffer and discriminator, enhancing their ability to generate multiple correct solutions and improving overall performance.

Contribution

The paper proposes a novel solution diversification framework with a buffer and discriminator, applicable across various supervision settings, to improve MWP solver generalization.

Findings

Framework improves solver performance on Math23k and Weak12k datasets.

Encourages generation of diverse and correct solutions.

Enhances generalizability of MWP solvers.

Abstract

Current math word problem (MWP) solvers are usually Seq2Seq models trained by the (one-problem; one-solution) pairs, each of which is made of a problem description and a solution showing reasoning flow to get the correct answer. However, one MWP problem naturally has multiple solution equations. The training of an MWP solver with (one-problem; one-solution) pairs excludes other correct solutions, and thus limits the generalizability of the MWP solver. One feasible solution to this limitation is to augment multiple solutions to a given problem. However, it is difficult to collect diverse and accurate augment solutions through human efforts. In this paper, we design a new training framework for an MWP solver by introducing a solution buffer and a solution discriminator. The buffer includes solutions generated by an MWP solver to encourage the training data diversity. The discriminator controls the quality of buffered solutions to participate in training. Our framework is flexibly applicable to a wide setting of fully, semi-weakly and weakly supervised training for all Seq2Seq MWP solvers. We conduct extensive experiments on a benchmark dataset Math23k and a new dataset named Weak12k, and show that our framework improves the performance of various MWP solvers under different settings by generating correct and diverse solutions.