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from Part Five - Neural Networks
Published online by Cambridge University Press: 21 April 2022
In this chapter, it is proved that the set of multivariate functions generated by shallow networks is dense in the space of continuous functions on a compact set if and only if the activation function is not a polynomial. For the specific choice of the ReLU activation function, a two-sided estimate of the approximation rate of Lipschitz functions by shallow networks is also provided. The argument for the lower estimate makes use of an upper estimate on the VC-dimension of shallow ReLU networks.
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