The Kolmogorov–Arnold representation is a proven adequate replacement of a continuous multivariate function by a 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.

Kolmogorov-Arnold表示已被一个变量的多个函数的层次结构证明是连续多变量函数的适当替代。这种表示的经证实的存在激发了许多研究者寻找其构造的实用方法，因为这种模型满足了机器学习的需求。本文表明，Kolmogorov-Arnold表示不仅是功能的组合，而且是离散Urysohn算子的树的特殊情况。本文介绍了用于构造此类Urysohn树的新型，快速且计算稳定的算法。除了连续的多元函数，建议的算法还涵盖了带有量化输入以及量化和连续输入相结合的情况。