  We present a simple non-generative approach to deep representation learning
that seeks equivariant deep embedding through simple objectives. In contrast to
existing equivariant networks, our transformation coding approach does not
constrain the choice of the feed-forward layer or the architecture and allows
for an unknown group action on the input space. We introduce several such
transformation coding objectives for different Lie groups such as the
Euclidean, Orthogonal and the Unitary groups. When using product groups, the
representation is decomposed and disentangled. We show that the presence of
additional information on different transformations improves disentanglement in
transformation coding. We evaluate the representations learnt by transformation
coding both qualitatively and quantitatively on downstream tasks, including
reinforcement learning.
