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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:[應用數學系] 期刊論文

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