Free energy landscape of Dense Associative Memory

Sumedha; Abhishek Singh

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arXiv · 2607.19195

Free energy landscape of Dense Associative Memory

Sumedha·Abhishek Singh

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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.

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cond-mat.dis-nn cond-mat.stat-mech cs.AI

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Sumedha, Abhishek Singh. 2026-07-21. Free energy landscape of Dense Associative Memory. https://arxiv.org/abs/2607.19195

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