  Incorporating symmetries can lead to highly data-efficient and generalizable
models by defining equivalence classes of data samples related by
transformations. However, characterizing how transformations act on input data
is often difficult, limiting the applicability of equivariant models. We
propose learning symmetric embedding networks (SENs) that encode an input space
(e.g. images), where we do not know the effect of transformations (e.g.
rotations), to a feature space that transforms in a known manner under these
operations. This network can be trained end-to-end with an equivariant task
network to learn an explicitly symmetric representation. We validate this
approach in the context of equivariant transition models with 3 distinct forms
of symmetry. Our experiments demonstrate that SENs facilitate the application
of equivariant networks to data with complex symmetry representations.
Moreover, doing so can yield improvements in accuracy and generalization
relative to both fully-equivariant and non-equivariant baselines.
