Tight Bounds for the VC-Dimension of Piecewise Polynomial Networks
Abstract
O(ws(s log d+log(dqh/ s))) and O(ws((h/ s) log q) +log(dqh/ s)) are upper bounds for the VC-dimension of a set of neural networks of units with piecewise polynomial activation functions, where s is the depth of the network, h is the number of hidden units, w is the number of adjustable parameters, q is the maximum of the number of polynomial segments of the activation function, and d is the maximum degree of the polynomials; also n(wslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = 8(h) and s is constant. For the special case q = 1, the VC-dimension is 8(ws log d).
Cite
Text
Sakurai. "Tight Bounds for the VC-Dimension of Piecewise Polynomial Networks." Neural Information Processing Systems, 1998.Markdown
[Sakurai. "Tight Bounds for the VC-Dimension of Piecewise Polynomial Networks." Neural Information Processing Systems, 1998.](https://mlanthology.org/neurips/1998/sakurai1998neurips-tight/)BibTeX
@inproceedings{sakurai1998neurips-tight,
title = {{Tight Bounds for the VC-Dimension of Piecewise Polynomial Networks}},
author = {Sakurai, Akito},
booktitle = {Neural Information Processing Systems},
year = {1998},
pages = {323-329},
url = {https://mlanthology.org/neurips/1998/sakurai1998neurips-tight/}
}