  The Kolmogorov-Arnold representation is a proven adequate replacement of a
continuous multivariate function by an hierarchical structure of multiple
functions of one variable. The proven existence of such representation inspired
many researchers to search for a practical way of its construction, since such
model answers the needs of machine learning. This article shows that the
Kolmogorov-Arnold representation is not only a composition of functions but
also a particular case of a tree of the discrete Urysohn operators. The article
introduces new, quick and computationally stable algorithm for constructing of
such Urysohn trees. Besides continuous multivariate functions, the suggested
algorithm covers the cases with quantised inputs and combination of quantised
and continuous inputs. The article also contains multiple results of testing of
the suggested algorithm on publicly available datasets, used also by other
researchers for benchmarking.
