TY - GEN
T1 - Tight bounds for the VC-dimension of piecewise polynomial networks
AU - Sakurai, Akito
PY - 1999/1/1
Y1 - 1999/1/1
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).
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M3 - Conference contribution
AN - SCOPUS:0344509373
SN - 0262112450
SN - 9780262112451
T3 - Advances in Neural Information Processing Systems
SP - 323
EP - 329
BT - Advances in Neural Information Processing Systems 11 - Proceedings of the 1998 Conference, NIPS 1998
PB - Neural information processing systems foundation
T2 - 12th Annual Conference on Neural Information Processing Systems, NIPS 1998
Y2 - 30 November 1998 through 5 December 1998
ER -