I had never heard of the Kolmogorov-Arnold Representation Theorem before. It states roughly that any multivariable function can be represented by repeatedly adding a single variable function whose input is a sum of single variable functions for each of the variables (of course, that isn't a precise statement).
Here is the formula for a function of $x$ and $y$ (i.e. that $n=2$) using Theorem $2$ from this paper: $$f(x,y)=\sum_{k=1}^5 g(\phi_k(x)+\lambda \phi_k(y))$$
Note that this representation is a bit differently written. We have $k=q+1$ and $\phi(x+k\epsilon)=\phi_k(x).$
Are there any simple (and non-trivial) examples? I have searched around online and can only find what seems to be very complicated proofs of the theorem but no actual concrete examples.
How about $f(x,y)=x^2+y$ or $f(x,y)=xy^3$, etc.? I really don't see a simple way to construct such $g$ and $\phi_k$.
Also, I couldn't figure out which tags would be appropriate here.