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

利用重尾模型改进变分自编码器（VAE）框架，提出$t^3$VAE，通过信息几何的洞察力和$t$分布，在先验、编码器和解码器中引入$t$分布，形成更适合真实数据集的力度形式的联合模型。在重尾合成数据的训练中，$t^3$VAE展现出优秀的低密度区域生成性能，并在CelebA和非平衡CIFAR-100数据集上比其他模型显著优越。

$t^3$变分自编码器：使用学生$t$分布和功率散度学习重尾数据