Mapping Boolean Functions with Neural Networks having Binary Weights and

[摘要] 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 9 Pages

[发布机构] HP Development Company

[学科分类] 计算机科学（综合）

[关键词] Binary Neural Networks;Boolean Function Mapping;1- layer Networks;2-layer Networks