Approximation of functions by neural networks

Andreas Thom

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arXiv · 1901.10267

Approximation of functions by neural networks

Andreas Thom

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Abstract

We study the approximation of measurable functions on the hypercube by functions arising from affine neural networks. Our main achievement is an approximation of any measurable function $f \colon W_n \to [-1,1]$ up to a prescribed precision $\varepsilon>0$ by a bounded number of neurons, depending only on $\varepsilon$ and not on the function $f$ or $n \in \mathbb N$.

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Andreas Thom. 2019-01-29. Approximation of functions by neural networks. https://arxiv.org/abs/1901.10267

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