  Working in high-dimensional latent spaces, the internal encoding of data in
Variational Autoencoders becomes naturally sparse. We discuss this known but
controversial phenomenon sometimes refereed to as overpruning, to emphasize the
under-use of the model capacity. In fact, it is an important form of
self-regularization, with all the typical benefits associated with sparsity: it
forces the model to focus on the really important features, highly reducing the
risk of overfitting. Especially, it is a major methodological guide for the
correct tuning of the model capacity, progressively augmenting it to attain
sparsity, or conversely reducing the dimension of the network removing links to
zeroed out neurons. The degree of sparsity crucially depends on the network
architecture: for instance, convolutional networks typically show less
sparsity, likely due to the tighter relation of features to different spatial
regions of the input.
