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Résumé : In the previous chapters, we discussed latent variable models that map a latent variable z to an observed variable x using (a series of) stochastic transformations p Z | X ( z | x ). By considering the map to be stochastic, methods such as the discussed variational autoencoder (Kingma and Welling, 2014, 2019) can easily change the dimensionality of the latent space: adding dimensions is done by mixing in noise random variables, while reducing dimensions is achieved through contractive maps like pooling. The probabilistic framework makes this easy to handle.