发表机构
The University of Tokyo; RIKEN center for AIP; Ochanomizu University; Hiroshima City University（东京大学; 理化学研究所AIP中心; 御茶水女子大学; 广岛市立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非对称稠密联想记忆模型的顺序检索动力学，利用生成泛函分析推导出极限环吸引子的动力学方程，并发现存储容量随相互作用阶数增加而单调下降。
AI 中文摘要
我们研究了一个$n$体非对称稠密联想记忆模型的检索动力学，其中通过在高阶Hebbian相互作用中移动一个模式索引来实现顺序检索。该模型表现出对存储模式的顺序检索，且检索状态对应于稳定的极限环吸引子。存储容量定义为该极限环保持稳定时的最大加载率。利用生成泛函分析，我们推导了描述顺序检索状态的动力学方程。生成泛函分析揭示，在非对称模型中，延迟自相互作用项消失，由此产生的重叠动力学可由Amari-Maginu型信噪比分析重现。此外，我们发现对于相互作用阶数$n\ge 3$，归一化存储容量随相互作用阶数增加而单调下降，这与对称的现代Hopfield模型形成对比。
英文摘要
We study the retrieval dynamics of an $n$-body asymmetric dense associative memory model, in which sequential retrieval is implemented by shifting one pattern index in the higher-order Hebbian interaction. The model exhibits sequential retrieval of the stored patterns, and the retrieval state corresponds to a stable limit-cycle attractor. The storage capacity is defined as the maximum loading rate for which this limit cycle remains stable. Using generating functional analysis, we derive the dynamical equations describing the sequential retrieval state. The generating functional analysis reveals that the retarded self-interaction term vanishes in the asymmetric model, and the resulting overlap dynamics is reproduced by an Amari-Maginu-type signal-to-noise analysis. Also, we find that for the interaction order $n\ge 3$, the normalized storage capacity decreases monotonically with increasing interaction order, in contrast to symmetric Modern Hopfield models.
Comments15 pages, 6 figures
