Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Abstract

We study the necessary and sufficient complexity of ReLU neural networks—in terms of depth and number of weights—which is required for approximating classifier functions in an L-sense. As a model class, we consider the set E(R) of possibly discontinuous piecewise C functions f : [−1/2, 1/2] → R, where the different “smooth regions” of f are separated by C… (More)

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