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arXiv · 1810.10032

Negative results for approximation using single layer and multilayer feedforward neural networks

J. M. Almira·P. E. Lopez-de-Teruel·D. J. Romero-Lopez·F. Voigtlaender
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Abstract

We prove a negative result for the approximation of functions defined on compact subsets of $\mathbb{R}^d$ (where $d \geq 2$) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to approximate using these neural networks as one may want. We also demonstrate an analogous result (for general $d \in \mathbb{N}$) for neural networks with an \emph{arbitrary} number of hidden layers, for activation functions that are either rational functions or continuous splines with finitely many pieces.

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J. M. Almira, P. E. Lopez-de-Teruel, D. J. Romero-Lopez, F. Voigtlaender. 2018-10-23. Negative results for approximation using single layer and multilayer feedforward neural networks. https://arxiv.org/abs/1810.10032

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