Generalization and PAC learning: some new results for the class ofgeneralized single-layer networks
Holden, S.B.; Rayner, P.J.W.
Neural Networks, IEEE Transactions on
Volume 6, Issue 2, Mar 1995 Page(s):368 - 380
Digital Object Identifier 10.1109/72.363472
Summary:The ability of connectionist networks to generalize is often cited
as one of their most important properties. We analyze the generalization
ability of the class of generalized single-layer networks (GSLNs), which
includes Volterra networks, radial basis function networks,
regularization networks, and the modified Kanerva model, using
techniques based on the theory of probably approximately correct (PAC)
learning which have previously been used to analyze the generalization
ability of feedforward networks of linear threshold elements (LTEs). An
introduction to the relevant computational learning theory is included.
We derive necessary and sufficient conditions on the number of training
examples required by a GSLN to guarantee a particular generalization
performance. We compare our results to those given previously for
feedforward networks of LTEs and show that, on the basis of the
currently available bounds, the sufficient number of training examples
for GSLNs is typically considerably less than for feedforward networks
of LTEs with the same number of weights. We show that the use of
self-structuring techniques for GSLNs may reduce the number of training
examples sufficient to guarantee good generalization performance, and we
provide an explanation for the fact that GSLNs can require a relatively
large number of weights
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