Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions
This work addresses a limitation in VAEs for researchers and practitioners in computer vision or generative modeling, but it is incremental as it builds on existing VAE frameworks.
The authors tackled the problem of variational auto-encoders (VAEs) implicitly encoding spatial information by proposing spatial VAEs that use matrix-variate normal distributions to explicitly capture spatial features in latent variables, resulting in improved performance over original VAEs in capturing structural and spatial information.
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.