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.

中文翻译：

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用于构建 Kolmogorov-Arnold 表示的深度机器学习算法

Kolmogorov-Arnold 表示被证明可以用一个变量的多个函数的层次结构代替连续的多元函数。这种表示的证明存在激发了许多研究人员寻找其构建的实用方法，因为这种模型满足了机器学习的需求。本文表明 Kolmogorov-Arnold 表示不仅是函数的组合，而且还是离散 Urysohn 算子树的特例。本文介绍了用于构建此类 Ury​​sohn 树的新的、快速且计算稳定的算法。除了连续多元函数之外，建议的算法还涵盖了量化输入以及量化和连续输入组合的情况。