arXiv cs.AI· Sumedha, Abhishek Singh·· 11 小时前AI 评分18
稠密联想记忆的自由能景观：大偏差理论求解
Free energy landscape of Dense Associative Memory
AI 导读
研究者用大偏差理论求解并给出包括稠密联想记忆在内一大类联想记忆的自由能泛函通用表达式，并以 Hopfield 模型复现经典结果作为方法验证。针对有限模式数，推导出具有多项式交互和 Log-Sum-Exponential（LSE）激活的稠密联想记忆的温度相关自由能泛函，并在广延极限下得到无序平均基态能量景观。该框架揭示高阶稠密网络中记忆检索如何依赖初始状态，并给出 LSE 模型的精确无误阈值。
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