ML Anthology

Correction to 'Lower Bounds on the VC-Dimension of Smoothly Parametrized Function Classes'

Wee Sun Lee, Peter L. Bartlett, Robert C. Williamson
NeCo 1997 pp. 765-769
doi:10.1162/NECO.1997.9.4.765 /neco/1997/lee1997neco-correction/

Abstract

The earlier article gives lower bounds on the VC-dimension of various smoothly parameterized function classes. The results were proved by showing a relationship between the uniqueness of decision boundaries and the VC-dimension of smoothly parameterized function classes. The proof is incorrect; there is no such relationship under the conditions stated in the article. For the case of neural networks with tanh activation functions, we give an alternative proof of a lower bound for the VC-dimension proportional to the number of parameters, which holds even when the magnitude of the parameters is restricted to be arbitrarily small.

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Cite

Text

Lee et al. "Correction to 'Lower Bounds on the VC-Dimension of Smoothly Parametrized Function Classes'." Neural Computation, 1997. doi:10.1162/NECO.1997.9.4.765

Markdown

[Lee et al. "Correction to 'Lower Bounds on the VC-Dimension of Smoothly Parametrized Function Classes'." Neural Computation, 1997.](https://mlanthology.org/neco/1997/lee1997neco-correction/) doi:10.1162/NECO.1997.9.4.765

BibTeX

@article{lee1997neco-correction,
  title     = {{Correction to 'Lower Bounds on the VC-Dimension of Smoothly Parametrized Function Classes'}},
  author    = {Lee, Wee Sun and Bartlett, Peter L. and Williamson, Robert C.},
  journal   = {Neural Computation},
  year      = {1997},
  pages     = {765-769},
  doi       = {10.1162/NECO.1997.9.4.765},
  volume    = {9},
  url       = {https://mlanthology.org/neco/1997/lee1997neco-correction/}
}