On the Universal Approximation Capability of Flexible Approximate Identity Neural Networks

Fard, Saeed Panahian; Zainuddin, Zarita

doi:10.1007/978-1-4614-7010-6_23

Cited by 11 publications

(1 citation statement)

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“…In 2012, we presented the universal approximation capability of double approximate identity neural networks in real Lebesgue spaces [14]. In 2013, we proved that a three layer feedforward flexible approximate identity neural networks are universal approximators in the space of continuous functions and in the space of real Lebesgue functions [15], [16]. Moreover, we also proved the universal approximation capabilities of Mellin approximate identity neural networks [17].…”

Section: Introductionmentioning

confidence: 93%

The Universal Approximation Capabilities of 2pi-Periodic Approximate Identity Neural Networks

Fard

Zainuddin

2013

2013 International Conference on Information Science and Cloud Computing Companion

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A fundamental theoretical aspect of artificial neural networks is related to the investigation of the universal approximation capability of a new type of a three-layer feedforward neural networks. In this study, we present four theorems concerning the universal approximation capabilities of a three-layer feedforward 2pi-periodic approximate identity neural networks. Using 2pi-periodic approximate identity, we prove two theorems which show the universal approximation capability of a threelayer feedforward 2pi-periodic approximate identity neural networks in the space of continuous 2pi-periodic functions. The proofs of these theorems are based on the convolution linear operators and the theory of -net. Using 2pi-periodic approximate identity again, we also prove another two theorems which show the universal approximation capability of these networks in the space of pth-order Lebesgue integrable 2pi-periodic functions.Index Terms-Universal approximation, 2pi-periodic approximate identity, 2pi-periodic approximate identity neural networks, continuous 2pi-periodic functions, pth-order Lebesgue integrable 2pi-periodic functions, Generalized Minkowski inequality.

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Section: Introductionmentioning

confidence: 93%