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Summary: Learning of the Non-Threshold Functions of
Multiple-Valued Logic by a Single Multi-Valued
Neuron With a Periodic Activation Function
Igor Aizenberg
Department of Computer Science
Texas A&M University-Texarkana
Texarkana, USA
igor.aizenberg@tamut.edu
Abstract-- In this paper, a theory of multiple-valued threshold
functions over the field of complex numbers is further developed.
k-valued threshold functions over the field of complex numbers
can be learned using a single multi-valued neuron (MVN). We
propose a new approach for the projection of a k-valued function,
which is not a threshold one, to m-valued logic (m>k), where this
function becomes a partially defined m-valued threshold function
and can be learned by a single MVN. To build this projection, a
periodic activation function for the MVN is used. This new
activation function and a modified learning algorithm make it
possible to learn nonlinearly separable multiple-valued functions
using a single MVN.
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