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Representations of Boolean Functions by Perceptron Networks
Kůrková, Věra
Limitations of capabilities of shallow perceptron networks are investigated. Lower bounds are derived for growth of numbers of units and sizes of output weights in networks representing Boolean functions of d variables. It is shown that for large d, almost any randomly chosen Boolean function cannot be tractably represented by shallow perceptron networks, i.e., each its representation requires a network with number of units or sizes of output weights depending on d exponentially

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