| 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
|
