English

On a nonhierarchical generalization of the Perceptron GREM

Probability 2021-06-15 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2106.07279,
  title  = {On a nonhierarchical generalization of the Perceptron GREM},
  author = {Nicola Kistler and Giulia Sebastiani},
  journal= {arXiv preprint arXiv:2106.07279},
  year   = {2021}
}