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. * Equal contribution. the latent circle, while a normal VAE becomes highly unstable. This is to be expected as a Gaussian prior is concentrated around the origin, while the KL-divergence tries to reconcile the differences between S 1 and R 2 . A more detailed discussion of this 'manifold mismatch' problem will follow in subsection 2.3.We demonstrate the utility of replacing the normal distribution with the von Mises-Fisher distribution for generating latent representations by conducting a range of experiments in three distinct settings. First, we show that 1 https://github.com/nicola-decao/s-vae

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