On a constructive proof of Kolmogorov's superposition theorem
In 1957 Kolmogorov showed that any continuous function \(f:[0,1]^n\to \mathbb{R}\) can be represented as a composition of addition and some functions of one variable. His proof was not constructive. Recently Kolmogorov's superposition theorem was applied in the study of neural networks. Motivated by these applications, Sprecher [Neural Netw. 9, No. 5, 765--772 (1996); Neural. Netw. 10, No. 3, 447--457 (1997)] proposed a numerical algorithm which gives a constructive proof of the theorem. \textit{M. Köppen} [Lect. Notes Comput. Sci. 2415, 474--479 (2002; Zbl 1013.68811)] observed that the Sprecher argumentation contains some gaps and suggested modifications, but without any proof. In this paper the authors, using the idea of Köppen, show that Sprecher's algorithm converges. It seems, it is the first correct constructive proof of Kolmogorov's superposition theorem.
scientific article; zbMATH DE number 5659502
scientific article