Bayesian math word problem solvers with credibility level: know what they know and what they do not know
摘要
Training a model capable of solving math word problems (MWPs) is an interesting research topic in the field of natural language processing. The MWP solver takes a textual math problem as input and generates the solution expression as output. Existing research focuses on how to improve the accuracy of MWP solvers on various datasets. Given a MWP, the existing MWP solvers generate the solution expression, but do not know whether the generated solution expression is correct. Therefore, the existing MWP solvers do not know what they know and what they do not know. In this paper, we propose Bayesian MWP solvers and define a credibility level which is able to judge whether the generated solution expression is correct. We extend two existing MWP solvers with Monte Carlo dropout and Deep Ensembles to obtain Bayesian MWP solvers. With dropout turned on at test time, for each MWP, multiple stochastic forward passes are performed to generate multiple solution expressions. For each solution expression, we calculate the corresponding answer and multiple answers are obtained. We define the credibility level as the proportion of the most frequently occurring answer. We find that if the credibility level is high, the generated solution expression is most likely correct, and vice versa. With credibility level, the Bayesian MWP solvers know what they know and what they do not know. The effectiveness of the proposed Bayesian MWP solvers and credibility level is verified on various datasets.