A Survey on Universal Approximation Theorems
<|reference_start|>A Survey on Universal Approximation Theorems: 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.<|reference_end|>
@article{augustine2024a,
    title={A Survey on Universal Approximation Theorems},
    author={Midhun T Augustine},
    journal={arXiv preprint arXiv:2407.12895},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.12895},
    primaryClass={cs.LG cs.SY eess.SY}
}