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Free energy and fluctuations of generalized bipartite Sherrington-Kirkpatrick models and generalized Hopfield models
Abstract
We consider the free energy of generalized bipartite Sherrington-Kirkpatrick models in the high temperature regime, with one spin normalized and the other either normalized or i.i.d. We derive a unified formula for the limiting free energy in both settings. We also prove that the fluctuations of the free energy converge to a Gaussian distribution under mild assumptions. The proof is based on a bipartite multigraph expansion, which also gives free energy results for generalized Hopfield models and log likelihood ratio of spiked rectangular models.
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BibTeX
@misc{choo2026free,
title = {{Free energy and fluctuations of generalized bipartite Sherrington-Kirkpatrick models and generalized Hopfield models}},
author = {Hyunsuk Choo and Ji Oon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29055},
eprint = {2610.29055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29055},
}
RIS
TY - UNPB
TI - Free energy and fluctuations of generalized bipartite Sherrington-Kirkpatrick models and generalized Hopfield models
AU - Hyunsuk Choo
AU - Ji Oon Lee
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29055
UR - https://arxiv.org/abs/2610.29055
AB - We consider the free energy of generalized bipartite Sherrington-Kirkpatrick models in the high temperature regime, with one spin normalized and the other either normalized or i.i.d. We derive a unified formula for the limiting free energy in both settings. We also prove that the fluctuations of the free energy converge to a Gaussian distribution under mild assumptions. The proof is based on a bipartite multigraph expansion, which also gives free energy results for generalized Hopfield models and log likelihood ratio of spiked rectangular models.
ER -