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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The paper is motivated by a recent Plos CB paper by Makin et al 2013, which used numerical simulations of a particular latent variable model that (in this model), performing density estimation of sensory population activity yielded latent variables which retained all the information about the underlying stimulus-variable. In the present paper, the authors ask the question of whether these results hold more gernally. They prove mathematically (assuming some sufficient conditions) that this results holds for a range of models, but also provide counter-examples that it does not always hold. Quality: Results seem sound, but I did not check the proof very rigorously.