  An implicit goal in works on deep generative models is that such models
should be able to generate novel examples that were not previously seen in the
training data. In this paper, we investigate to what extent this property holds
for widely employed variational autoencoder (VAE) architectures. VAEs maximize
a lower bound on the log marginal likelihood, which implies that they will in
principle overfit the training data when provided with a sufficiently
expressive decoder. In the limit of an infinite capacity decoder, the optimal
generative model is a uniform mixture over the training data. More generally,
an optimal decoder should output a weighted average over the examples in the
training data, where the magnitude of the weights is determined by the
proximity in the latent space. This leads to the hypothesis that, for a
sufficiently high capacity encoder and decoder, the VAE decoder will perform
nearest-neighbor matching according to the coordinates in the latent space. To
test this hypothesis, we investigate generalization on the MNIST dataset. We
consider both generalization to new examples of previously seen classes, and
generalization to the classes that were withheld from the training set. In both
cases, we find that reconstructions are closely approximated by nearest
neighbors for higher-dimensional parameterizations. When generalizing to unseen
classes however, lower-dimensional parameterizations offer a clear advantage.
