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 evaluate the disorder-averaged ground-state energy 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 full-retrieval threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.

Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI)

arXiv:2607.19195 [cond-mat.dis-nn]

(or arXiv:2607.19195v1 [cond-mat.dis-nn] for this version)

https://doi.org/10.48550/arXiv.2607.19195 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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