  Learning disentangled representations is a key step towards effectively
discovering and modelling the underlying structure of environments. In the
natural sciences, physics has found great success by describing the universe in
terms of symmetry preserving transformations. Inspired by this formalism, we
propose a framework, built upon the theory of group representation, for
learning representations of a dynamical environment structured around the
transformations that generate its evolution. Experimentally, we learn the
structure of explicitly symmetric environments without supervision from
observational data generated by sequential interactions. We further introduce
an intuitive disentanglement regularisation to ensure the interpretability of
the learnt representations. We show that our method enables accurate
long-horizon predictions, and demonstrate a correlation between the quality of
predictions and disentanglement in the latent space.
