Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution 文章

arXiv:2506.21278v3 Announce Type: replace-cross Abstract: We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Kullback-Leibler divergence to a uniform spherical prior admits rapidly convergent series, stable quadrature, and high-concentration asymptotic forms.