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We prove a theorem concerning the approximation of multivariate functions bydeep ReLU networks, for which the curse of the dimensionality is lessened. Ourtheorem is based on a constructive proof of the Kolmogorov--Arnoldsuperposition theorem, and on a subset of multivariate continuous functionswhose outer superposition functions can be efficiently approximated by deepReLU networks.

Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem