While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on the local geometry of the decoding model. This analysis uncovers the regularizer implicit in the $\beta$-VAE objective, and leads to an approximation consisting of a deterministic autoencoding objective plus analytic regularizers that depend on the Hessian or Jacobian of the decoding model, unifying VAEs with recent heuristics proposed for training regularized autoencoders. We empirically verify these findings, observing that the proposed deterministic objective indeed exhibits similar behavior to the $\beta$-VAE in terms of objective value and sample quality on CelebA and MNIST.

本文探讨了变分推断在学习生成模型和正则化变分自编码器中的作用，并提出了一种基于确定性自编码器目标函数的正则化方法，该方法与 $eta$-VAE 表现相似。

关于 $β$-VAEs 中的隐式正则化