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Mapping Boolean Functions with Neural Networks having Binary Weights and Zero Thresholds

Deolalikar, Vinay

HPL-2001-64R1

Keyword(s): Binary Neural Networks; Boolean Function Mapping; 1- layer Networks; 2-layer Networks

Abstract: In this paper, the ability of a Binary Neural Network comprising only neurons with zero thresholds and binary weights to map given samples of a Boolean function is studied. A mathematical model describing a network with such restrictions is developed. It is shown that this model is quite amenable to algebraic manipulation. A key feature of the model is that it replaces the two input and output variables with a single "normalized" variable. The model is then used to provide apriori criteria, stated in terms of the new variable, that a given Boolean function must satisfy in order to be mapped by a network having one or two layers. These criteria provide necessary, and in the case of a 1-layer network, sufficient conditions for samples of a Boolean function to be mapped by a Binary Neural Network with zero thresholds. It is shown that the necessary conditions imposed by the 2-layer network are, in some sense, minimal. Notes: Copyright 2001 IEEE. Reprinted, with permission, from IEEE Transactions on Neural Networks

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