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Error bounds for approximations with deep ReLU networks
Abstract
We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz functions we describe adaptive depth-6 network architectures more efficient than the standard shallow architecture.
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LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
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Zhou, D.-X. (2020) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2019.06.004 · Cited by 530
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Zhou, D.-X. (2020) · Neural Networks · doi:10.1016/j.neunet.2020.01.018 · Cited by 263
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
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Metadata
- Authors
- Yarotsky, D.
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 2017-10
- Volume
- 94
- Pages
- 103-114
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2528305538
- Cited by
- 1,085
- References
- 1
- FWCI
- 33.29
- Type
- journal article
- Language
- en
- Open access
- closed
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