How to practically use the Kolmogorov-Arnold theorem?

Question

Mathematics

Hello! The theorem states that a function of many variables can be represented as a superposition of functions of two variables. How to practically decompose a function of many variables into a sum of functions of two variables? It's good for optimization

Answer 1

A superposition is not a sum. This is when another function is substituted into one function as an argument.
For example, x*y*zyou will never decompose into a sum. But, if you take f(a,b) = a*b, then you can do f(x,f(y,z)).

It's good for optimization

This superposition will not be better for optimization from any point of view.
In practice, this can be done like this - put all the brackets next to all the operations in the expression. Each operation is its own function. Here is your superposition.