### Abstract

0(ws(s log d+log(dqh/s))) and 0(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 ω{ωslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = Θ(h) and s is constant. For the special case q = 1, the VC-dimension is Θ(ws\ogd).

Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems |

Publisher | Neural information processing systems foundation |

Pages | 323-329 |

Number of pages | 7 |

ISBN (Print) | 0262112450, 9780262112451 |

Publication status | Published - 1999 |

Externally published | Yes |

Event | 12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United States Duration: 1998 Nov 30 → 1998 Dec 5 |

### Other

Other | 12th Annual Conference on Neural Information Processing Systems, NIPS 1998 |
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Country | United States |

City | Denver, CO |

Period | 98/11/30 → 98/12/5 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*Advances in Neural Information Processing Systems*(pp. 323-329). Neural information processing systems foundation.

**Tight bounds for the VC-dimension of piecewise polynomial networks.** / Sakurai, Akito.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Neural Information Processing Systems.*Neural information processing systems foundation, pp. 323-329, 12th Annual Conference on Neural Information Processing Systems, NIPS 1998, Denver, CO, United States, 98/11/30.

}

TY - GEN

T1 - Tight bounds for the VC-dimension of piecewise polynomial networks

AU - Sakurai, Akito

PY - 1999

Y1 - 1999

N2 - 0(ws(s log d+log(dqh/s))) and 0(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 ω{ωslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = Θ(h) and s is constant. For the special case q = 1, the VC-dimension is Θ(ws\ogd).

AB - 0(ws(s log d+log(dqh/s))) and 0(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 ω{ωslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = Θ(h) and s is constant. For the special case q = 1, the VC-dimension is Θ(ws\ogd).

UR - http://www.scopus.com/inward/record.url?scp=0344509373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344509373&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0344509373

SN - 0262112450

SN - 9780262112451

SP - 323

EP - 329

BT - Advances in Neural Information Processing Systems

PB - Neural information processing systems foundation

ER -