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：本文提出一种名为相关密集联想记忆（CDAM）的新型联想记忆模型，该模型在连续值记忆模式的统一框架下整合了自联想与异联想功能。通过采用任意图结构对记忆模式进行语义关联，CDAM的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、宽异联想及中性静默。受抑制性调节研究的启发，本文采用反赫布学习规则控制异联想范围，提取图中社群结构的多尺度表征，并稳定时序序列的回忆。实验结果表明，CDAM在处理真实数据、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具有显著效能。