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29 March 2024
 
  » arxiv » 1510.0779

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On the structure of multi-layer cellular neural networks: Complexity between two layers
Jung-Chao Ban ; Chih-Hung Chang ;
Date 3 Oct 2015
AbstractLet $mathbf{Y}$ be the solution space of an $n$-layer cellular neural network, and let $mathbf{Y}^{(i)}$ and $mathbf{Y}^{(j)}$ be the hidden spaces, where $1 leq i, j leq n$. ($mathbf{Y}^{(n)}$ is called the output space.) The classification and the existence of factor maps between two hidden spaces, that reaches the same topological entropies, are investigated in [Ban et al., J.~Differential Equations extbf{252}, 4563-4597, 2012]. This paper elucidates the existence of factor maps between those hidden spaces carrying distinct topological entropies. For either case, the Hausdorff dimension $dim mathbf{Y}^{(i)}$ and $dim mathbf{Y}^{(j)}$ can be calculated. Furthermore, the dimension of $mathbf{Y}^{(i)}$ and $mathbf{Y}^{(j)}$ are related upon the factor map between them.
Source arXiv, 1510.0779
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