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.

翻译：本文提出了一种名为“相关密集关联记忆”（Correlated Dense Associative Memory, CDAM）的新型关联记忆模型，该模型在连续值记忆模式的统一框架中整合了自联想与异联想机制。通过采用任意图结构对记忆模式进行语义关联，本文对CDAM进行了理论与数值分析，揭示了四种不同的动力学模式：自联想、窄异联想、宽异联想及中性静息。受抑制性调控研究的启发，本文采用反赫布学习规则来控制异联想的范围、提取图中社区结构的多尺度表示，并稳定时序序列的回忆。实验展示证明了CDAM在处理真实世界数据、复现经典神经科学实验、执行图像检索以及模拟任意有限自动机方面的有效性。