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https://ah.lib.nccu.edu.tw/handle/140.119/129555
題名: | Complexity of neural networks on Fibonacci-Cayley tree | 作者: | 班榮超 Ban, Jung-Chao Chang, Chih-Hung |
貢獻者: | 應數系 | 關鍵詞: | Neural networks ; Learning problem ; Cayley tree ; Separation property, Entropy | 日期: | 五月-2019 | 上傳時間: | 28-四月-2020 | 摘要: | 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. | 關聯: | Journal of Algebra Combinatorics Discrete Structures and Applications, Vol.6, No.2, pp.105-122 | 資料類型: | article |
Appears in Collections: | 期刊論文 |
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