Spherical Cauchy Variational Autoencoders: Heavy Angular Tails and Exact KL Evaluation
Read the original on arXiv AI →The paper introduces the spherical Cauchy distribution as a new hyperspherical posterior for variational autoencoders, avoiding the complications of the von Mises–Fisher and Power Spherical alternatives. By using stereographic projection and a Möbius transformation, the authors obtain exact posterior samples and a closed‑form KL divergence that terminates in a finite polynomial for even dimensions and admits certified truncation for odd dimensions. Empirical results show that the spherical Cauchy yields faster inference and lower reconstruction loss on MNIST and improved negative log‑likelihood on smallNORB compared to existing methods.
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