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Technical Report NC-TR-02-134
2002-134
Computing Time Lower Bounds for Recurrent Sigmoidal Neural Networks
Michael Schmitt
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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