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I trained the variational autoencoder . Suppose if we take the mnist dataset and visualize it, the distribution of classes are clustered but are very close to each other. When i take a point/encoding vector(ex: label 1) from a class and do the nearest neighbor, i get other labels(ex : 7,0,3,6,9) as nearest neighbors.

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This is difficult unless you use the labels somehow, e.g., via semi-supervised learning. Even if you just simply jointly trained a classifier $y = C(z)$ to output digit labels on the latent space, this would be likely to provide much better nearest neighbours.

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