Abstract
An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with L^{2}(\mathcal{D}) errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution \mathcal{D}.
