A Precise Characterization of the Class of Languages Recognized by Neural Nets under Gaussian and Other Common Noise Distributions

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Wolfgang Maass, Eduardo Sontag


We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probabil(cid:173) ity 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 E {O, I} * I w begins with O}, and we give a precise characterization of those languages which can be recognized. This result implies severe constraints on possibilities for constructing recurrent ana(cid:173) log neural nets that are robust against realistic types of analog noise. On the other hand we present a method for constructing feed forward analog neural nets that are robust with regard to analog noise of this type.