Hyperspherical Variational Auto-Encoders

The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments we show how such a hyperspherical VAE, or S-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, N-VAE, in low dimensions on other data types. Code at http: //github. com/nicola-decao/s-vae-tf and https: //github. com/nicola-decao/s-vae-pytorch