The Onset of Parisi's Complexity in a Mismatched Inference Problem

Francesco Camilli; Pierluigi Contucci; Emanuele Mingione

doi:10.3390/e26010042

The Onset of Parisi's Complexity in a Mismatched Inference Problem

Entropy (Basel). 2023 Dec 30;26(1):42. doi: 10.3390/e26010042.

Authors

Francesco Camilli¹, Pierluigi Contucci², Emanuele Mingione²

Affiliations

¹ The Abdus Salam International Center for Theoretical Physics, 34151 Trieste, Italy.
² Dipartimento di Matematica, Alma Mater Studiorum-Universita di Bologna, 40127 Bologna, Italy.

Abstract

We show that a statistical mechanics model where both the Sherringhton-Kirkpatrick and Hopfield Hamiltonians appear, which is equivalent to a high-dimensional mismatched inference problem, is described by a replica symmetry-breaking Parisi solution.

Keywords: high-dimensional inference; replica symmetry breaking; spin glasses; statistical mechanics.

Grants and funding

PIerluigi Contucci and Emanuele Mingione were partially supported by the EU H2020 ICT48 project Humane AI Net contract number 952026; by the Italian Extended Partnership PE01—FAIR Future Artificial Intelligence Research—Proposal code PE00000013 under the MUR National Recovery and Resilience Plan; by the project PRIN 2022—Proposal code: J53D23003690006.