有向稀疏Hopfield网络的层次结构和模式恢复
Network Hierarchy and Pattern Recovery in Directed Sparse Hopfield Networks
摘要：
许多现实世界的网络是有向的、稀疏的和分层的，在层次结构中混合了前馈和反馈连接。此外，少量的“主”节点通常能够驱动整个系统。我们研究了稀疏的，有向的，Hopfield类神经网络的模式呈现和恢复的动力学，使用营养分析来验证它们的层次结构。这是一个最近的方法，它量化了每个节点在层次结构中的局部位置（营养级）以及网络的全局方向性（营养相干性）。我们表明，即使在一个经常性的网络，系统的状态可以控制的一个小的子集的神经元，可以确定其低营养水平。我们还发现，在模式恢复任务的性能可以显着提高通过调整营养的连贯性和其他拓扑性质的网络。这可以解释在动物大脑中观察到的相对稀疏和连贯的结构，并为改进人工神经网络的架构提供见解。此外，我们希望我们通过数值分析证明的原则，在这里将是相关的一个广泛的一类系统，其基础网络结构是有向的和稀疏的，如生物，社会或金融网络。
英文摘要：
Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using Trophic Analysis to characterise their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain, and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate, through numerical analysis, here will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social or financial networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
