  Machine learning systems, especially with overparameterized deep neural
networks, can generalize to novel test instances drawn from the same
distribution as the training data. However, they fare poorly when evaluated on
out-of-support test points. In this work, we tackle the problem of developing
machine learning systems that retain the power of overparameterized function
approximators while enabling extrapolation to out-of-support test points when
possible. This is accomplished by noting that under certain conditions, a
"transductive" reparameterization can convert an out-of-support extrapolation
problem into a problem of within-support combinatorial generalization. We
propose a simple strategy based on bilinear embeddings to enable this type of
combinatorial generalization, thereby addressing the out-of-support
extrapolation problem under certain conditions. We instantiate a simple,
practical algorithm applicable to various supervised learning and imitation
learning tasks.
