  Learning representations that can disentangle explanatory attributes
underlying the data improves interpretabilty as well as provides control on
data generation. Various learning frameworks such as VAEs, GANs and
auto-encoders have been used in the literature to learn such representations.
Most often, the latent space is constrained to a partitioned representation or
structured by a prior to impose disentangling. In this work, we advance the use
of a latent representation based on a product space of Orthogonal Spheres
PrOSe. The PrOSe model is motivated by the reasoning that latent-variables
related to the physics of image-formation can under certain relaxed assumptions
lead to spherical-spaces. Orthogonality between the spheres is motivated via
physical independence models. Imposing the orthogonal-sphere constraint is much
simpler than other complicated physical models, is fairly general and flexible,
and extensible beyond the factors used to motivate its development. Under
further relaxed assumptions of equal-sized latent blocks per factor, the
constraint can be written down in closed form as an ortho-normality term in the
loss function. We show that our approach improves the quality of
disentanglement significantly. We find consistent improvement in
disentanglement compared to several state-of-the-art approaches, across several
benchmarks and metrics.
