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Abstract:
Recurrent neural networks of analog units are computers for
real-valued functions. We study the time complexity of real
computation in general recurrent neural networks. These have
sigmoidal, linear, and product units of unlimited order as nodes
and no restrictions on the weights. For networks operating in
discrete time, we exhibit a family of functions with arbitrarily
high complexity, and we derive almost tight bounds on the time
required to compute these functions. Thus, evidence is given of
the computational limitations that time-bounded analog recurrent
neural networks are subject to.
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