  The current methods for learning representations with auto-encoders almost
exclusively employ vectors as the latent representations. In this work, we
propose to employ a tensor product structure for this purpose. This way, the
obtained representations are naturally disentangled. In contrast to the
conventional variations methods, which are targeted toward normally distributed
features, the latent space in our representation is distributed uniformly over
a set of unit circles. We argue that the torus structure of the latent space
captures the generative factors effectively. We employ recent tools for
measuring unsupervised disentanglement, and in an extensive set of experiments
demonstrate the advantage of our method in terms of disentanglement,
completeness, and informativeness. The code for our proposed method is
available at https://github.com/rotmanmi/Unsupervised-Disentanglement-Torus.
