  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.
