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We introduce a perceptron version of the Generalized Random Energy Model, andprove a quenched Sanov type large deviation principle for the empiricaldistribution of the random energies. The dual of the rate function has arepresentation through a variational formula which is closely related to theParisi variational formula for the SK-model.

A quenched large deviation principle and a Parisi formula for a Perceptron version of the GREM