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Abstract:
Existing proofs demonstrating the computational limitations
of Recurrent Cascade Correlation (RCC) and similar networks
(Fahlman, 1991; Bachrach, 1988; Mozer, 1988) explicitly limit their
results to units having sigmoidal or hard-threshold transfer
functions (Giles et al., 1995; Kremer, 1996). The proof given here
shows that for any finite, discrete transfer function used by the
units of an RCC network, there are finite-state automata (FSA) that
the network cannot model, no matter how many units are used. The
proof also applies to continuous transfer functions with a finite
number of fixed points, such as sigmoid and radial basis
functions.
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