ML Anthology

Almost Linear VC Dimension Bounds for Piecewise Polynomial Networks

Peter L. Bartlett, Vitaly Maiorov, Ron Meir
NeurIPS 1998 pp. 190-196
/neurips/1998/bartlett1998neurips-almost/

Abstract

We compute upper and lower bounds on the VC dimension of feedforward networks of units with piecewise polynomial activa(cid:173) tion functions. We show that if the number of layers is fixed, then the VC dimension grows as W log W, where W is the number of parameters in the network. This result stands in opposition to the case where the number of layers is unbounded, in which case the VC dimension grows as W 2 •

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Text

Bartlett et al. "Almost Linear VC Dimension Bounds for Piecewise Polynomial Networks." Neural Information Processing Systems, 1998.

Markdown

[Bartlett et al. "Almost Linear VC Dimension Bounds for Piecewise Polynomial Networks." Neural Information Processing Systems, 1998.](https://mlanthology.org/neurips/1998/bartlett1998neurips-almost/)

BibTeX

@inproceedings{bartlett1998neurips-almost,
  title     = {{Almost Linear VC Dimension Bounds for Piecewise Polynomial Networks}},
  author    = {Bartlett, Peter L. and Maiorov, Vitaly and Meir, Ron},
  booktitle = {Neural Information Processing Systems},
  year      = {1998},
  pages     = {190-196},
  url       = {https://mlanthology.org/neurips/1998/bartlett1998neurips-almost/}
}