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Disentangled representation learning has seen a surge in interest over recenttimes, generally focusing on new models which optimise one of many disparatedisentanglement metrics. Symmetry Based Disentangled Representation learningintroduced a robust mathematical framework that defined precisely what is meantby a "linear disentangled representation". This framework determined that suchrepresentations would depend on a particular decomposition of the symmetrygroup acting on the data, showing that actions would manifest throughirreducible group representations acting on independent representationalsubspaces. Caselles-Dupre et al [2019] subsequently proposed the first model toinduce and demonstrate a linear disentangled representation in a VAE model. Inthis work we empirically show that linear disentangled representations are notgenerally present in standard VAE models and that they instead require alteringthe loss landscape to induce them. We proceed to show that such representationsare a desirable property with regard to classical disentanglement metrics.Finally we propose a method to induce irreducible representations which forgoesthe need for labelled action sequences, as was required by prior work. Weexplore a number of properties of this method, including the ability to learnfrom action sequences without knowledge of intermediate states and robustnessunder visual noise. We also demonstrate that it can successfully learn 4independent symmetries directly from pixels.

Linear Disentangled Representations and Unsupervised Action Estimation