Explicit integral representations for two-layer ReLU networks yield L2 approximation bounds for multivariate polynomials that depend on monomial coefficients and data distribution rather than dimension or degree.
The argument is a variation on a classical argument for identifying the optimal importance distribution in simple Monte Carlo integration
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Explicit integral representations and quantitative bounds for two-layer ReLU networks
Explicit integral representations for two-layer ReLU networks yield L2 approximation bounds for multivariate polynomials that depend on monomial coefficients and data distribution rather than dimension or degree.