On the problem asking if Kolmogorov-Arnold representation can be simplified (Q6591430)

Kolmogorov-Arnold representations express two-variate functions \(f\) by a sum of five terms of the form \N\[\Ng(\phi_i(x)+\psi_i(y)),\qquad i=1,2,3,4,5,\N\]\Nwhere \(g\) depends on \(f\) and the \(\psi\)s and \(\phi\)s are prescribed. All functions are assumed to be continuous, but the latter two sets of functions are required to be monotonically increasing too. They are a solution to Hilbert's famous thirteenth problem. In this paper, various choices are discussed in which the Kolmogorov-Arnold representations may be simplified for instance by reducing the number of summands in the expression.