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Abstract:
O(ws(s
log + log
(dqh / s)))
and
O(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
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
(ws
log
(dqh / s))
is a lower bound for the VC-dimension of such a network set, which
are tight for the cases
s =
(h)
and
s
is constant. For the special case
q=1,
the VC-dimension is
(ws
log
d).
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