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

Dmitry Yarotsky

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arXiv · 1705.01365

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

Dmitry Yarotsky

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Abstract

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.

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Dmitry Yarotsky. 2017-05-03. Quantified advantage of discontinuous weight selection in approximations with deep neural networks. https://arxiv.org/abs/1705.01365

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