  Several regularization methods have recently been introduced which force the
latent activations of an autoencoder or deep neural network to conform to
either a Gaussian or hyperspherical distribution, or to minimize the implicit
rank of the distribution in latent space. In the present work, we introduce a
novel regularizing loss function which simulates a pairwise repulsive force
between items and an attractive force of each item toward the origin. We show
that minimizing this loss function in isolation achieves a hyperspherical
distribution. Moreover, when used as a regularizing term, the scaling factor
can be adjusted to allow greater flexibility and tolerance of eccentricity,
thus allowing the latent variables to be stratified according to their relative
importance, while still promoting diversity. We apply this method of Eccentric
Regularization to an autoencoder, and demonstrate its effectiveness in image
generation, representation learning and downstream classification tasks.
