On-Line Learning with Restricted Training Sets: Exact Solution as Benchmark for General Theories
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
Rae et al. "On-Line Learning with Restricted Training Sets: Exact Solution as Benchmark for General Theories." Neural Information Processing Systems, 1998.Markdown
[Rae et al. "On-Line Learning with Restricted Training Sets: Exact Solution as Benchmark for General Theories." Neural Information Processing Systems, 1998.](https://mlanthology.org/neurips/1998/rae1998neurips-online/)BibTeX
@inproceedings{rae1998neurips-online,
title = {{On-Line Learning with Restricted Training Sets: Exact Solution as Benchmark for General Theories}},
author = {Rae, H. C. and Sollich, Peter and Coolen, Anthony C. C.},
booktitle = {Neural Information Processing Systems},
year = {1998},
pages = {316-322},
url = {https://mlanthology.org/neurips/1998/rae1998neurips-online/}
}