  Enforcing distributions of latent variables in neural networks is an active
subject. It is vital in all kinds of generative models, where we want to be
able to interpolate between points in the latent space, or sample from it.
Modern generative AutoEncoders (AE) like WAE, SWAE, CWAE add a regularizer to
the standard (deterministic) AE, which allows to enforce Gaussian distribution
in the latent space. Enforcing different distributions, especially
topologically nontrivial, might bring some new interesting possibilities, but
this subject seems unexplored so far.
  This article proposes a new approach to enforce uniform distribution on
d-dimensional torus. We introduce a circular spring loss, which enforces
minibatch points to be equally spaced and satisfy cyclic boundary conditions.
  As example of application we propose multiple-path morphing. Minimal distance
geodesic between two points in uniform distribution on latent space of angles
becomes a line, however, torus topology allows us to choose such lines in
alternative ways, going through different edges of $[-\pi,\pi]^d$.
  Further applications to explore can be for example trying to learn real-life
topologically nontrivial spaces of features, like rotations to automatically
recognize 2D rotation of an object in picture by training on relative angles,
or even 3D rotations by additionally using spherical features - this way
morphing should be close to object rotation.
