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

TL;DR

This paper introduces a perceptron variant of the GREM, establishing a quenched large deviation principle for the empirical energy distribution and connecting it to the Parisi formula, advancing understanding of complex energy landscapes.

Contribution

It develops a perceptron-based GREM model and proves a quenched large deviation principle, linking it to the Parisi variational formula for the SK-model.

Findings

Established a quenched Sanov type large deviation principle for the model

Derived a variational formula related to the Parisi formula

Connected the perceptron GREM to classical spin glass theory

Abstract

We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation through a variational formula which is closely related to the Parisi variational formula for the SK-model.