Analyses for L (p) [a, b]-norm approximation capability of flexible approximate identity neural networks

作者：Fard Saeed Panahian; Zainuddin Zarita^*

来源：Neural Computing & Applications, 2014, 24(1): 45-50.

DOI：10.1007/s00521-013-1493-9

• Flexible approximate identity functions
• Flexible approximate identity neural networks
• Generalized Gaussian neural networks
• Generalized Gaussian distribution
• Universal approximation
• Lebesgue approximation

This study investigates the universal approximation capability of a three-layered feedforward flexible approximate identity neural networks under the L (p) [a, b]-norm. We are motivated to study such a problem by the fact that the L (p) [a, b]-norm has the capability of improving approximation performance significantly. Using flexible approximate identity functions as introduced in our previous study, we prove that any Lebesgue integrable function on the closed and bounded real interval [a, b] will converge to itself under the L (p) [a, b]-norm if it convolves with flexible approximate identity functions. Using this result, we also establish a main theorem. The proof of the main theorem is in the framework of the theory of epsilon-net.

• 出版日期2014-1