# Representational Power of ReLU Networks and Polynomial Kernels: Beyond Worst-Case Analysis

@article{Koehler2018RepresentationalPO, title={Representational Power of ReLU Networks and Polynomial Kernels: Beyond Worst-Case Analysis}, author={Frederic Koehler and Andrej Risteski}, journal={ArXiv}, year={2018}, volume={abs/1805.11405} }

There has been a large amount of interest, both in the past and particularly recently, into the power of different families of universal approximators, e.g. ReLU networks, polynomials, rational functions. However, current research has focused almost exclusively on understanding this problem in a worst-case setting, e.g. bounding the error of the best infinity-norm approximation in a box. In this setting a high-degree polynomial is required to even approximate a single ReLU.
However, in real…

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