Universal Approximation Theorem

Definition

Any Continuous Function $F$ on a compact subset of ${\mathbb{R}}^n$ domain can be approximated to any degree of accuracy. $\forall ϵ>0,\exists N,\text{s.t.}|F(\mathbf{x})-\sum _{k=1}^N{c}_k\sigma (W\mathbf{x}+\mathbf{b})|<ϵ$ where $\sigma$ is Sigmoid Function.