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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper introduces a series of bounds on some approximations of the partition function for graphical models. They first bound from below the lower bound provided by'ExactOnTree' approximations, and then show that, for a binary pariwise models, clamping (i.e. The paper is clear and interesting. Insight about the quality of lower bounds that are used in many applications is obiously usefull.