  Weakly supervised question answering usually has only the final answers as
supervision signals while the correct solutions to derive the answers are not
provided. This setting gives rise to the spurious solution problem: there may
exist many spurious solutions that coincidentally derive the correct answer,
but training on such solutions can hurt model performance (e.g., producing
wrong solutions or answers). For example, for discrete reasoning tasks as on
DROP, there may exist many equations to derive a numeric answer, and typically
only one of them is correct. Previous learning methods mostly filter out
spurious solutions with heuristics or using model confidence, but do not
explicitly exploit the semantic correlations between a question and its
solution. In this paper, to alleviate the spurious solution problem, we propose
to explicitly exploit such semantic correlations by maximizing the mutual
information between question-answer pairs and predicted solutions. Extensive
experiments on four question answering datasets show that our method
significantly outperforms previous learning methods in terms of task
performance and is more effective in training models to produce correct
solutions.
