Dense Associative Memory (DAM) models generalize the classical Hopfield model by incorporating n-body or exponential interactions that greatly enhance storage capacity. While the criticality of DAM models has been largely investigated, mainly within a statistical equilibrium picture, little attention has been devoted to the temporal self-organizing behavior induced by learning. In this work, we investigate the behavior of a stochastic exponential DAM (SEDAM) model through the lens of Temporal Complexity (TC), a framework that characterizes complex systems by intermittent transition events between order and disorder and by scale-free temporal statistics. Transition events associated with birth-death of neural avalanche structures are exploited for the TC analyses and compared with analogous transition events based on coincidence structures. We systematically explore how TC indicators depend on control parameters, i.e., noise intensity and memory load. Our results reveal that the SEDAM model exhibits regimes of complex intermittency characterized by nontrivial temporal correlations and scale-free behavior, indicating the spontaneous emergence of self-organizing dynamics. Notably, such regimes arise over finite intervals of noise intensity rather than at a single critical point, consistent with the concept of extended criticality. Further, the noise intensity range needed to reach the critical region, where self-organizing behavior emerges, slightly decreases as the memory load increases. This study highlights the relevance of TC as a complementary framework for understanding learning and information processing in artificial and biological neural systems, revealing the link between the memory load and the self-organizing capacity of the network.

翻译：稠密联想记忆（DAM）模型通过引入多体或指数相互作用来推广经典Hopfield模型，从而大幅增强存储容量。尽管DAM模型的临界性已在统计平衡图景下得到广泛研究，但学习所诱导的时间自组织行为却鲜受关注。本文通过时间复杂性（TC）框架研究随机指数稠密联想记忆（SEDAM）模型的行为，该框架通过有序与无序之间的间歇转换事件以及无标度时间统计特征来刻画复杂系统。我们利用与神经雪崩结构生灭相关的转换事件进行TC分析，并将其与基于符合结构的类似转换事件进行比较。我们系统探究了TC指标如何依赖于控制参数（即噪声强度与记忆负载）。结果表明，SEDAM模型表现出具有非平凡时间相关性和无标度行为的复杂间歇性状态，表明自组织动力学的自发涌现。值得注意的是，此类状态出现在有限的噪声强度区间内而非单一临界点，这与扩展临界性概念一致。此外，达到临界区域（自组织行为涌现的区域）所需的噪声强度范围随记忆负载增加而略有减小。本研究凸显了TC作为理解人工与生物神经网络学习与信息处理的补充性框架的重要性，揭示了记忆负载与网络自组织能力之间的内在联系。