# Universal Approximation Under Constraints is Possible with Transformers

@article{Kratsios2021UniversalAU, title={Universal Approximation Under Constraints is Possible with Transformers}, author={Anastasis Kratsios and Behnoosh Zamanlooy and Tianlin Liu and Ivan Dokmani'c}, journal={ArXiv}, year={2021}, volume={abs/2110.03303} }

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 : R → K, there is a probabilistic transformer F̂ whose randomized outputs all lie…

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