Title: Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions,
Abstract: The key idea of variational auto-encoders (VAEs) resembles that of
traditional auto-encoder models in which spatial information is supposed to be
explicitly encoded in the latent space. However, the latent variables in VAEs
are vectors, which can be interpreted as multiple feature maps of size 1x1.
Such representations can only convey spatial information implicitly when
coupled with powerful decoders. In this work, we propose spatial VAEs that use
feature maps of larger size as latent variables to explicitly capture spatial
information. This is achieved by allowing the latent variables to be sampled
from matrix-variate normal (MVN) distributions whose parameters are computed
from the encoder network. To increase dependencies among locations on latent
feature maps and reduce the number of parameters, we further propose spatial
VAEs via low-rank MVN distributions. Experimental results show that the
proposed spatial VAEs outperform original VAEs in capturing rich structural and
spatial information.