I introduce a novel associative memory model named Correlated Dense
Associative Memory (CDAM), which integrates both auto- and hetero-association
in a unified framework for continuous-valued memory patterns. Employing an
arbitrary graph structure to semantically link memory patterns, CDAM is
theoretically and numerically analysed, revealing four distinct dynamical
modes: auto-association, narrow hetero-association, wide hetero-association,
and neutral quiescence. Drawing inspiration from inhibitory modulation studies,
I employ anti-Hebbian learning rules to control the range of
hetero-association, extract multi-scale representations of community structures
in graphs, and stabilise the recall of temporal sequences. Experimental
demonstrations showcase CDAM's efficacy in handling real-world data,
replicating a classical neuroscience experiment, performing image retrieval,
and simulating arbitrary finite automata.

提出了一种名为相关密集关联记忆（CDAM）的新型关联记忆模型，通过整合自关联和异关联在一个统一的框架中来处理连续值记忆模式。采用任意图结构来语义链接记忆模式，CDAM 在理论和数值上得到分析，揭示了四种不同的动力学模式：自关联、窄异关联、宽异关联和中性静息。借鉴抑制性调制研究，采用反赫布学习规则控制异关联的范围，提取图中社区结构的多尺度表示，并稳定时序序列的回想。实验演示展示了 CDAM 在处理现实世界数据、复制经典神经科学实验、执行图像检索和模拟任意有限自动机方面的效果。