Tight bounds for the VC-dimension of piecewise polynomial networks

Akito Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

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 languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
Pages323-329
Number of pages7
ISBN (Print)0262112450, 9780262112451
Publication statusPublished - 1999
Externally publishedYes
Event12th Annual Conference on Neural Information Processing Systems, NIPS 1998 - Denver, CO, United States
Duration: 1998 Nov 301998 Dec 5

Other

Other12th Annual Conference on Neural Information Processing Systems, NIPS 1998
CountryUnited States
CityDenver, CO
Period98/11/3098/12/5

Fingerprint

Polynomials
Chemical activation
Neural networks

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Sakurai, A. (1999). Tight bounds for the VC-dimension of piecewise polynomial networks. In 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.

Advances in Neural Information Processing Systems. Neural information processing systems foundation, 1999. p. 323-329.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sakurai, A 1999, Tight bounds for the VC-dimension of piecewise polynomial networks. in 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.
Sakurai A. Tight bounds for the VC-dimension of piecewise polynomial networks. In Advances in Neural Information Processing Systems. Neural information processing systems foundation. 1999. p. 323-329
Sakurai, Akito. / Tight bounds for the VC-dimension of piecewise polynomial networks. Advances in Neural Information Processing Systems. Neural information processing systems foundation, 1999. pp. 323-329
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