论文信息 - A structured proof of the Kolmogorov superposition theorem

A structured proof of the Kolmogorov superposition theorem

We present a well-structured detailed exposition of a well-known proof of the following celebrated result solving Hilbert’s 13th problem on superpositions. For functions of 2 variables the statement is as follows. Kolmogorov Theorem. There are continuous functions φ1, . . . , φ5 : [ 0, 1 ] → [ 0, 1 ] such that for any continuous function f : [ 0, 1 ] → R there is a continuous function h : [ 0, 3 ]→ R such that for any x, y ∈ [ 0, 1 ] we have

A. Skopenkov | S. Dzhenzher

[1] Vasco Brattka,et al. From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem , 2007 .

[2] Y. Sternfeld. Hilbert's 13th problem and dimension , 1989 .

[3] G. Lorentz,et al. Constructive approximation : advanced problems , 1996 .