Quantified advantage of discontinuous weight selection in approximations with deep neural networks

05/03/2017

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by   Dmitry Yarotsky, et al.

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We consider approximations of 1D Lipschitz functions by deep ReLU networks of a fixed width. We prove that without the assumption of continuous weight selection the uniform approximation error is lower than with this assumption at least by a factor logarithmic in the size of the network.