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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes projecting the parameters of an MRF onto the set of fast-mixing parameters: parameters for which MCMC quickly converges to the true distribution. The authors introduce a Euclidean projection operator that implements this property, but note that it can be difficult to apply. They then smooth it by requiring the projection to be close to an additional matrix input. This is sufficient for many cases, but can be applied repeatedly when the true Euclidean projection is required.