# mk:icann02

### Summary

*On the Training of a Kolmogorov Network*. Mario Köppen. In Artificial Neural Networks - ICANN 2002, pages 474-479, Madrid, Spain, August 2002, 2002. (URL)

### Abstract

The Kolmogorov theorem gives that the representation of continuous and bounded real-valued functions of n variables by the superposition of functions of one variable and addition is always possible. Based on the fact that each proof of the Kolmogorov theorem or its variants was a constructive one so far, there is the principal possibility to attain such a representation. This paper reviews a procedure for obtaining the Kolmogorov representation of a function, based on an approach given by David Sprecher. The construction, adapted to our purposes, is considered in more detail for an image function. It comes out that such a representation is featureless (with regard to analytical properties of the represented function), and basically resembles a look-up procedure, employing fuzzy singletons around functions values that were looked up for generalization.

### Bibtex entry

`@INPROCEEDINGS { mk:icann02,`

ABSTRACT = { The Kolmogorov theorem gives that the representation of continuous and bounded real-valued functions of n variables by the superposition of functions of one variable and addition is always possible. Based on the fact that each proof of the Kolmogorov theorem or its variants was a constructive one so far, there is the principal possibility to attain such a representation. This paper reviews a procedure for obtaining the Kolmogorov representation of a function, based on an approach given by David Sprecher. The construction, adapted to our purposes, is considered in more detail for an image function. It comes out that such a representation is featureless (with regard to analytical properties of the represented function), and basically resembles a look-up procedure, employing fuzzy singletons around functions values that were looked up for generalization. },

ADDRESS = { Madrid, Spain, August 2002 },

AUTHOR = { Mario Köppen },

BOOKTITLE = { Artificial Neural Networks - ICANN 2002 },

MODIFIED = { 2008-02-28 14:58:44 +0900 },

DOI = { 10.1007/3-540-46084-5_77 },

EDITOR = { Jos\'e R.~Dorronsoro },

HASABSTRACT = { Yes },

PAGES = { 474--479 },

PDF = { icann02.pdf },

PUBLISHER = { Springer-Verlag Heidelberg },

SERIES = { LNCS 2415 },

TITLE = { On the Training of a Kolmogorov Network },

URL = { http://www.springerlink.com/content/rgu9n2fy0e1f3n51 },

YEAR = { 2002 },

1 = { http://www.springerlink.com/content/rgu9n2fy0e1f3n51 },

2 = { http://dx.doi.org/10.1007/3-540-46084-5_77 },

}