稠密联想记忆的自由能景观研究
Free energy landscape of Dense Associative Memory
AI 导读
一篇 arXiv 论文用大偏差理论求解了包括稠密联想记忆在内的一类联想记忆模型的自由能泛函一般表达式，并复现了 Hopfield 模型的经典结果。针对有限模式数，论文推导了具有多项式相互作用和 Log-Sum-Exponential（LSE）激活函数的稠密联想记忆随温度变化的自由能泛函，并给出 LSE 模型的精确无错阈值。该框架还揭示了高阶稠密网络中记忆检索对初始状态的依赖。
正文 · 原文
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.
| Comments: | 6 pages, 1 figure |
| Subjects: | Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2607.19195 [cond-mat.dis-nn] |
| (or arXiv:2607.19195v3 [cond-mat.dis-nn] for this version) | |
| https://doi.org/10.48550/arXiv.2607.19195 arXiv-issued DOI via DataCite |
Submission history
From: Sumedha [view email]
[v1]
Tue, 21 Jul 2026 15:30:53 UTC (295 KB)
[v2]
Wed, 22 Jul 2026 20:42:50 UTC (285 KB)
[v3]
Fri, 30 Oct 2026 04:49:58 UTC (288 KB)
来源：arXiv cs.AI · arxiv.org