  Disentangled representation learning has seen a surge in interest over recent
times, generally focusing on new models which optimise one of many disparate
disentanglement metrics. Symmetry Based Disentangled Representation learning
introduced a robust mathematical framework that defined precisely what is meant
by a "linear disentangled representation". This framework determined that such
representations would depend on a particular decomposition of the symmetry
group acting on the data, showing that actions would manifest through
irreducible group representations acting on independent representational
subspaces. Caselles-Dupre et al [2019] subsequently proposed the first model to
induce and demonstrate a linear disentangled representation in a VAE model. In
this work we empirically show that linear disentangled representations are not
generally present in standard VAE models and that they instead require altering
the loss landscape to induce them. We proceed to show that such representations
are a desirable property with regard to classical disentanglement metrics.
Finally we propose a method to induce irreducible representations which forgoes
the need for labelled action sequences, as was required by prior work. We
explore a number of properties of this method, including the ability to learn
from action sequences without knowledge of intermediate states and robustness
under visual noise. We also demonstrate that it can successfully learn 4
independent symmetries directly from pixels.
