Kolmogorov–Arnold representation theorem

every multivariate continuous function $f: [0,1]^n \to \mathbb{R}$ can be represented as superposition of continuous single-variable functions

definition

if $f$ is a multivariate continuous function, then $f$ can be written as a finite composition of continuous single-variable functions with binary operation of addition. Formally:

$$\displaystyle f(\mathbf {x} )=f(x_{1},\ldots ,x_{n})=\sum _{q=0}^{2n}\Phi _{q}\!\left(\sum _{p=1}^{n}\phi_{q,p}(x_{p})\right)$$

where $\phi_{q,p} : [0,1] \to \mathbb{R}$ and $\Phi_q: \mathbb{R} \to \mathbb{R}$