  Variational auto-encoders (VAEs) are a powerful approach to unsupervised
learning. They enable scalable approximate posterior inference in
latent-variable models using variational inference (VI). A VAE posits a
variational family parameterized by a deep neural network called an encoder
that takes data as input. This encoder is shared across all the observations,
which amortizes the cost of inference. However the encoder of a VAE has the
undesirable property that it maps a given observation and a
semantics-preserving transformation of it to different latent representations.
This "inconsistency" of the encoder lowers the quality of the learned
representations, especially for downstream tasks, and also negatively affects
generalization. In this paper, we propose a regularization method to enforce
consistency in VAEs. The idea is to minimize the Kullback-Leibler (KL)
divergence between the variational distribution when conditioning on the
observation and the variational distribution when conditioning on a random
semantic-preserving transformation of this observation. This regularization is
applicable to any VAE. In our experiments we apply it to four different VAE
variants on several benchmark datasets and found it always improves the quality
of the learned representations but also leads to better generalization. In
particular, when applied to the Nouveau Variational Auto-Encoder (NVAE), our
regularization method yields state-of-the-art performance on MNIST and
CIFAR-10. We also applied our method to 3D data and found it learns
representations of superior quality as measured by accuracy on a downstream
classification task.
