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NeuroCOLT
Technical Report NC-TR-97-043
Analog Neural
Nets with Gaussian or other Common Noise Distributions cannot
Recognise Arbitrary Regular Languages
Wolfgang
Maass
Technische Universitaet Graz, Austria
Eduardo
D. Sontag
Rutgers University, USA
Abstract
We consider recurrent analog neural nets where the output of each
gate is subject to Gaussian noise, or any other common noise distribution
that is nonzero on a large set. We show that many regular languages
cannot be recognised by networks of this type, and we give a precise
characterization of those languages which can be recognised. This
result implies severe constraints on possibilities for constructing
recurrent analog neural nets that are robust against realistic types
of analog noise. On the other hand we present a method for constructing
feedforward analog neural nets that are robust with regard to analog
noise of this type.
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