Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)
Peter Bartlett, Vitaly Maiorov, Ron Meir
We compute upper and lower bounds on the VC dimension of feedforward networks of units with piecewise polynomial activa(cid:173) tion functions. We show that if the number of layers is fixed, then the VC dimension grows as W log W, where W is the number of parameters in the network. This result stands in opposition to the case where the number of layers is unbounded, in which case the VC dimension grows as W 2 •