|
NeuroCOLT
Technical Report NC-TR-00-063
A
Precise Characterization of the Class of Languages Recognized by Neural
Nets under Gaussian and other Common Noise Distributions
Wolfgang
Maass
Abstract
We consider recurrent analog neural nets where each gate is subject
to Gaussian noise, or any other common noise distribution whose probability
density function is nonzero on a large set. We show that many regular
languages cannot be recognized by networks of this type, for example
the language $\{w \in \{0,1\}^* |\; w \mbox{ begins with } 0\}$, and
we give a precise characterization of those languages which can be
recognized. 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 {\it feedforward} analog neural nets that are robust
with regard to analog noise of this type.
Download
Compressed Postscript
|