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The variational autoencoder (VAE) typically employs a standard normal prioras a regularizer for the probabilistic latent encoder. However, the Gaussiantail often decays too quickly to effectively accommodate the encoded points,failing to preserve crucial structures hidden in the data. In this paper, weexplore the use of heavy-tailed models to combat over-regularization. Drawingupon insights from information geometry, we propose $t^3$VAE, a modified VAEframework that incorporates Student's t-distributions for the prior, encoder,and decoder. This results in a joint model distribution of a power form whichwe argue can better fit real-world datasets. We derive a new objective byreformulating the evidence lower bound as joint optimization of KL divergencebetween two statistical manifolds and replacing with $\gamma$-power divergence,a natural alternative for power families. $t^3$VAE demonstrates superiorgeneration of low-density regions when trained on heavy-tailed synthetic data.Furthermore, we show that $t^3$VAE significantly outperforms other models onCelebA and imbalanced CIFAR-100 datasets.

$t^3$-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence