  Compositional, structured models are appealing because they explicitly
decompose problems and provide interpretable intermediate outputs that give
confidence that the model is not simply latching onto data artifacts. Learning
these models is challenging, however, because end-task supervision only
provides a weak indirect signal on what values the latent decisions should
take. This often results in the model failing to learn to perform the
intermediate tasks correctly. In this work, we introduce a way to leverage
paired examples that provide stronger cues for learning latent decisions. When
two related training examples share internal substructure, we add an additional
training objective to encourage consistency between their latent decisions.
Such an objective does not require external supervision for the values of the
latent output, or even the end task, yet provides an additional training signal
to that provided by individual training examples themselves. We apply our
method to improve compositional question answering using neural module networks
on the DROP dataset. We explore three ways to acquire paired questions in DROP:
(a) discovering naturally occurring paired examples within the dataset, (b)
constructing paired examples using templates, and (c) generating paired
examples using a question generation model. We empirically demonstrate that our
proposed approach improves both in- and out-of-distribution generalization and
leads to correct latent decision predictions.
