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The Universal Approximation Capabilities of Cylindrical Approximate Identity Neural Networks

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Abstract

Universal approximation capability of feedforward neural networks is one of the important theoretical concepts in artificial neural networks. In this study, a type of single-hidden-layer feedforward neural networks is presented. The networks is called feedforward cylindrical approximate identity neural networks. Then, universal approximation capabilities of the networks are investigated in two function spaces. Whereby the notions of cylindrical approximate identity and cylindrical convolution are introduced. The analyses are divided into two cases: In the first case, universal approximation capability of a single-hidden-layer feedforward cylindrical approximate identity neural networks to continuous bivariate functions on the infinite cylinder is investigated. In the latter case, universal approximation capability of the networks is extended to the pth-order Lebesgue integrable bivariate functions on the infinite cylinder.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    Zarita Zainuddin & Saeed Panahian Fard

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  1. Zarita Zainuddin
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  2. Saeed Panahian Fard
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Correspondence to Saeed Panahian Fard.

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Zainuddin, Z., Fard, S. The Universal Approximation Capabilities of Cylindrical Approximate Identity Neural Networks. Arab J Sci Eng 41, 3027–3034 (2016). https://doi.org/10.1007/s13369-016-2067-9

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  • DOI: https://doi.org/10.1007/s13369-016-2067-9

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