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- W4379251926 abstract "In 1989 George Cybenko proved in a landmark paper that wide shallow neural networks can approximate arbitrary continuous functions on a compact set. This universal approximation theorem sparked a lot of follow-up research. Shen, Yang and Zhang determined optimal approximation rates for ReLU-networks in $L^p$-norms with $p in [1,infty)$. Kidger and Lyons proved a universal approximation theorem for deep narrow ReLU-networks. Telgarsky gave an example of a deep narrow ReLU-network that cannot be approximated by a wide shallow ReLU-network unless it has exponentially many neurons. However, there are even more questions that still remain unresolved. Are there any wide shallow ReLU-networks that cannot be approximated well by deep narrow ReLU-networks? Is the universal approximation theorem still true for other norms like the Sobolev norm $W^{1,1}$? Do these results hold for activation functions other than ReLU? We will answer all of those questions and more with a framework of two expressive powers. The first one is well-known and counts the maximal number of linear regions of a function calculated by a ReLU-network. We will improve the best known bounds for this expressive power. The second one is entirely new." @default.
- W4379251926 created "2023-06-04" @default.
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- W4379251926 date "2023-05-31" @default.
- W4379251926 modified "2023-10-18" @default.
- W4379251926 title "On the Expressive Power of Neural Networks" @default.
- W4379251926 doi "https://doi.org/10.48550/arxiv.2306.00145" @default.
- W4379251926 hasPublicationYear "2023" @default.
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