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- Title
Complexity of neural networks on Fibonacci-Cayley tree.
- Authors
Jung-Chao Ban; Chih-Hung Chang
- 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.
- Subjects
ARTIFICIAL neural networks; FIBONACCI sequence; CAYLEY graphs; TREES; NONLINEAR systems
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2019, Vol 6, Issue 2, p105
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.560410