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Year 2019, Volume 6 , Issue 2, Pages 105 - 122 2019-05-07

Complexity of neural networks on Fibonacci-Cayley tree

Jung-chao BAN [1] , Chih-hung CHANG [2]

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.

Keywords

Neural networks, Learning problem, Cayley tree, Separation property, Entropy

References

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Details

Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-4920-6945
Author: Jung-chao BAN

Orcid: 0000-0001-7352-5148
Author: Chih-hung CHANG (Primary Author)
Thanks This work is partially supported by the Ministry of Science and Technology, ROC (Contract No MOST 107- 2115-M-259-004-MY2 and 107-2115-M-390-002-MY2).
Dates

Publication Date : May 7, 2019

Cite

Bibtex @research article { jacodesmath560410, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, pages = {105 - 122}, doi = {10.13069/jacodesmath.560410}, title = {Complexity of neural networks on Fibonacci-Cayley tree}, key = {cite}, author = {Ban, Jung-chao and Chang, Chih-hung} }
APA Ban, J , Chang, C . (2019). Complexity of neural networks on Fibonacci-Cayley tree . Journal of Algebra Combinatorics Discrete Structures and Applications , 6 (2) , 105-122 . DOI: 10.13069/jacodesmath.560410
MLA Ban, J , Chang, C . "Complexity of neural networks on Fibonacci-Cayley tree" . Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 105-122 <https://dergipark.org.tr/en/pub/jacodesmath/article/560410>
Chicago Ban, J , Chang, C . "Complexity of neural networks on Fibonacci-Cayley tree". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 105-122
RIS TY - JOUR T1 - Complexity of neural networks on Fibonacci-Cayley tree AU - Jung-chao Ban , Chih-hung Chang Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.560410 DO - 10.13069/jacodesmath.560410 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 105 EP - 122 VL - 6 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.560410 UR - https://doi.org/10.13069/jacodesmath.560410 Y2 - 2019 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Complexity of neural networks on Fibonacci-Cayley tree %A Jung-chao Ban , Chih-hung Chang %T Complexity of neural networks on Fibonacci-Cayley tree %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 2 %R doi: 10.13069/jacodesmath.560410 %U 10.13069/jacodesmath.560410
ISNAD Ban, Jung-chao , Chang, Chih-hung . "Complexity of neural networks on Fibonacci-Cayley tree". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 2 (May 2019): 105-122 . https://doi.org/10.13069/jacodesmath.560410
AMA Ban J , Chang C . Complexity of neural networks on Fibonacci-Cayley tree. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 105-122.
Vancouver Ban J , Chang C . Complexity of neural networks on Fibonacci-Cayley tree. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 105-122.
IEEE J. Ban and C. Chang , "Complexity of neural networks on Fibonacci-Cayley tree", Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 2, pp. 105-122, May. 2019, doi:10.13069/jacodesmath.560410
Authors of the Article
Jung-chao BAN [1]
Chih-hung CHANG [2]
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