Cayley树上神经网络的熵分支
Entropy bifurcation of neural networks on Cayley trees
摘要：
已经证明，具有树结构的可激发介质比其他网络拓扑结构表现得更好，考虑定义在Cayley树上的神经网络是很自然的。当讨论Cayley树上的神经网络的平衡解时，对一个称为有限型树移位的符号空间的研究是很重要的。熵是一个经常使用的不变量，用于衡量系统的复杂性，和恒定的熵为开集的神经元之间的耦合权重意味着特定的网络是稳定的。本文给出了Cayley树上神经网络熵谱的一个完整刻画，并揭示了当耦合权改变时熵谱是否分叉。
英文摘要：
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift of finite type is important when it comes to the discussion of the equilibrium solutions of neural networks on Cayley trees. Entropy is a frequently used invariant for measuring the complexity of a system, and constant entropy for an open set of coupling weights between neurons means that the specific network is stable. This paper gives a complete characterization for entropy spectrum of neural networks on Cayley trees and reveals whether the entropy bifurcates when the coupling weights change.
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。
