Linear Disentangled Representations and Unsupervised Action Estimation

Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models to optimise one of many disparate disentanglement metrics. It was only with Symmetry Based Disentangled Representation Learning that a robust mathematical framework was introduced to define precisely what is meant by a "linear disentangled representation". This framework determines 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. ForwardVAE 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 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.