  Latent representations are the essence of deep generative models and
determine their usefulness and power. For latent representations to be useful
as generative concept representations, their latent space must support latent
space interpolation, attribute vectors and concept vectors, among other things.
We investigate and discuss latent variable modeling, including latent variable
models, latent representations and latent spaces, particularly hierarchical
latent representations and latent space vectors and geometry. Our focus is on
that used in variational autoencoders and generative adversarial networks.
