Abstract
Capabilities of radial convolution kernel networks to approximate multivariate functions are investigated. A necessary condition for universal approximation property of convolution kernel networks is given. Kernels that satisfy the condition in arbitrary dimension are investigated in terms of their Hankel and Fourier transforms. A computational example is presented to assess approximation capabilities of different convolution kernel networks.
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Notes
- 1.
Note that the convolution kernel networks represent a different concept from the nowadays very popular concept of the convolutional neural networks [7]. The first has a shallow architecture in contrast to the deep one of the latter case.
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Acknowledgments
This work was supported by the COST Grant LD13002 provided by the Ministry of Education, Youth and Sports of the Czech Republic and institutional support of the Institute of Computer Science RVO 67985807.
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Coufal, D. (2016). Kernel Networks for Function Approximation. In: Jayne, C., Iliadis, L. (eds) Engineering Applications of Neural Networks. EANN 2016. Communications in Computer and Information Science, vol 629. Springer, Cham. https://doi.org/10.1007/978-3-319-44188-7_22
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DOI: https://doi.org/10.1007/978-3-319-44188-7_22
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