  In the loss function of Variational Autoencoders there is a well known
tension between two components: the reconstruction loss, improving the quality
of the resulting images, and the Kullback-Leibler divergence, acting as a
regularizer of the latent space. Correctly balancing these two components is a
delicate issue, easily resulting in poor generative behaviours. In a recent
work, Dai and Wipf obtained a sensible improvement by allowing the network to
learn the balancing factor during training, according to a suitable loss
function. In this article, we show that learning can be replaced by a simple
deterministic computation, helping to understand the underlying mechanism, and
resulting in a faster and more accurate behaviour. On typical datasets such as
Cifar and Celeba, our technique sensibly outperforms all previous VAE
architectures.
