Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution

• URL: http://arxiv.org/abs/2506.21278v2
• Date: Mon, 14 Jul 2025 10:06:29 GMT
• Title: Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution
• Authors: Lukas Sablica, Kurt Hornik,
• Abstract summary: We propose a novel variational autoencoder (VAE) architecture that employs a spherical Cauchy (spCauchy) latent distribution.<n>Unlike traditional Gaussian latent spaces or the widely used von Mises-Fisher (vMF) distribution, spCauchy provides a more natural hyperspherical representation of latent variables.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel variational autoencoder (VAE) architecture that employs a spherical Cauchy (spCauchy) latent distribution. Unlike traditional Gaussian latent spaces or the widely used von Mises-Fisher (vMF) distribution, spCauchy provides a more natural hyperspherical representation of latent variables, better capturing directional data while maintaining flexibility. Its heavy-tailed nature prevents over-regularization, ensuring efficient latent space utilization while offering a more expressive representation. Additionally, spCauchy circumvents the numerical instabilities inherent to vMF, which arise from computing normalization constants involving Bessel functions. Instead, it enables a fully differentiable and efficient reparameterization trick via M\"obius transformations, allowing for stable and scalable training. The KL divergence can be computed through a rapidly converging power series, eliminating concerns of underflow or overflow associated with evaluation of ratios of hypergeometric functions. These properties make spCauchy a compelling alternative for VAEs, offering both theoretical advantages and practical efficiency in high-dimensional generative modeling.

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