Eccentric regularization: minimizing hyperspherical energy without explicit projection

Xuefeng Li, Alan Blair

Abstract: 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 simple and 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, and demonstrate its effectiveness as a regularizer for an image auto-encoder. Moreover, a reduction in the regularization parameter leads to a modest increase in the eccentricity of the distribution in latent space. This enhances image generation, and allows the eigenvectors of the covariance matrix to be extracted as deep principal components, which can be used for data analysis, image generation, visualization and downstream classification.