Entropy bifurcation of neural networks on Cayley trees

Jung-Chao Ban; Chih-Hung Chang; Nai-Zhu Huang

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arXiv · 1706.09283

Entropy bifurcation of neural networks on Cayley trees

Jung-Chao Ban·Chih-Hung Chang·Nai-Zhu Huang

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Abstract

It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift of finite type is important when it comes to the discussion of the equilibrium solutions of neural networks on Cayley trees. Entropy is a frequently used invariant for measuring the complexity of a system, and constant entropy for an open set of coupling weights between neurons means that the specific network is stable. This paper gives a complete characterization for entropy spectrum of neural networks on Cayley trees and reveals whether the entropy bifurcates when the coupling weights change.

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Jung-Chao Ban, Chih-Hung Chang, Nai-Zhu Huang. 2018-02-27. Entropy bifurcation of neural networks on Cayley trees. https://arxiv.org/abs/1706.09283

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