UNIVERSAL APPROXIMATION UNDER CONSTRAINTS IS POSSIBLE WITH TRANSFORMERS

Many practical problems need the output of a machine learning model to satisfy a set of constraints, K. There are, however, no known guarantees that classical neural networks can exactly encode constraints while simultaneously achieving universality. We provide a quantitative constrained universal approximation theorem which guarantees that for any convex or non-convex compact set K and any continuous function f : Rⁿ ! K, there is a …