On the Training of a Kolmogorov Network

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.