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政大典藏 > College of Science > Department of Mathematical Sciences > Periodical Articles > Item 140.119/129555

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/129555

Title:	Complexity of neural networks on Fibonacci-Cayley tree
Authors:	班榮超 Ban, Jung-Chao Chang, Chih-Hung
Contributors:	應數系
Keywords:	Neural networks;Learning problem;Cayley tree;Separation property, Entropy
Date:	2019-05
Issue Date:	2020-04-28 13:54:34 (UTC+8)
Abstract:	This paper investigates the coloring problem on Fibonacci-Cayley tree, which is a Cayley graph whose vertex set is the Fibonacci sequence. More precisely, we elucidate the complexity of shifts of finite type defined on Fibonacci-Cayley tree via an invariant called entropy. We demonstrate that computing the entropy of a Fibonacci tree-shift of finite type is equivalent to studying a nonlinear recursive system and reveal an algorithm for the computation. What is more, the entropy of a Fibonacci tree-shift of finite type is the logarithm of the spectral radius of its corresponding matrix. We apply the result to neural networks defined on Fibonacci-Cayley tree, which reflect those neural systems with neuronal dysfunction. Aside from demonstrating a surprising phenomenon that there are only two possibilities of entropy for neural networks on Fibonacci-Cayley tree, we address the formula of the boundary in the parameter space.
Relation:	Journal of Algebra Combinatorics Discrete Structures and Applications, Vol.6, No.2, pp.105-122
Data Type:	article
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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