On a nonhierarchical generalization of the Perceptron GREM

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We introduce a nonlinear, nonhierarchical generalization of Derrida’s GREM and establish through a Sanov-type large deviation analysis both a Boltzmann–Gibbs principle as well as a Parisi formula for the limiting free energy. In line with the predictions of the Parisi theory, the free energy is given by the minimal value over all Parisi functionals/hierarchical structures in which the original model can be coarse grained.