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We develop an intensive embedding for visualizing the space of allpredictions for probabalistic models, using replica theory. Our embedding isisometric (preserves the distinguishability between models) and faithful(yields low-dimensional visualizations of models with simple emergentbehavior). We apply our intensive embedding to the Ising model of statisticalmechanics and the $\Lambda$CDM model applied to cosmic microwave backgroundradiation. It provides an intuitive, quantitative visualization applicable torenormalization-group calculations and optimal experimental design.

Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background