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On the use of the Kullback–Leibler divergence in Variational Autoencoders

The loss function used for the training of Variational Autoencoders (VAEs) is divided in two terms. The first one measures the quality of the autoencoding, i.e. the error between the original sample and its reconstruction. The second term is the Kullback-Leibler divergence (abbreviated KL divergence) with respect to a standard multivariate normal distribution. We will illustrate with a few plots the influence of the KL divergence on the encoder and decoder outputs.