论文标题
用于构建Kolmogorov-Arnold代表的深度机器学习算法
A deep machine learning algorithm for construction of the Kolmogorov-Arnold representation
论文作者
论文摘要
kolmogorov-arnold表示是通过一个变量的多个函数的层次结构进行了证实的连续多元函数的足够替代。事实证明的这种代表的存在激发了许多研究人员的构建方式，因为这种模型可以满足机器学习的需求。本文表明，Kolmogorov-Arnold表示不仅是函数的组成，而且是离散Urysohn操作员树的特定情况。本文介绍了用于构建此类Urysohn树的新的，快速和计算稳定的算法。除了连续的多元函数外，建议的算法还涵盖了定量输入以及定量和连续输入的组合的情况。本文还包含在公开可用数据集上测试建议算法的多个结果，该算法也被其他研究人员用于基准测试。
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.
