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arXiv · 2407.12895

A Survey on Universal Approximation Theorems

Midhun T Augustine
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Abstract

This paper discusses various theorems on the approximation capabilities of neural networks (NNs), which are known as universal approximation theorems (UATs). The paper gives a systematic overview of UATs starting from the preliminary results on function approximation, such as Taylor's theorem, Fourier's theorem, Weierstrass approximation theorem, Kolmogorov - Arnold representation theorem, etc. Theoretical and numerical aspects of UATs are covered from both arbitrary width and depth.

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Midhun T Augustine. 2024-07-17. A Survey on Universal Approximation Theorems. https://arxiv.org/abs/2407.12895

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