Free energy landscape of Dense Associative Memory
Abstract
Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also obtain the disorder-averaged ground-state energy landscape of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact error-free threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.
Related
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BibTeX
@misc{sumedha2026free,
title = {{Free energy landscape of Dense Associative Memory}},
author = {Sumedha and Abhishek Singh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.19195},
eprint = {2607.19195},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19195},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Free energy landscape of Dense Associative Memory
AU - Sumedha
AU - Abhishek Singh
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2607.19195
UR - https://arxiv.org/abs/2607.19195
AB - Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also obtain the disorder-averaged ground-state energy landscape of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact error-free threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.
ER -