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Hausdorff Dimension of Multi-Layer Neural Networks

DOI: 10.4236/apm.2013.39A1002    2,441 Downloads   4,209 Views  

ABSTRACT

This elucidation investigates the Hausdorff dimension of the output space of multi-layer neural networks. When the factor map from the covering space of the output space to the output space has a synchronizing word, the Hausdorff dimension of the output space relates to its topological entropy. This clarifies the geometrical structure of the output space in more details.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Ban and C. Chang, "Hausdorff Dimension of Multi-Layer Neural Networks," Advances in Pure Mathematics, Vol. 3 No. 9A, 2013, pp. 9-14. doi: 10.4236/apm.2013.39A1002.

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