| Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks (1995) | |||||||||||||||
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| . We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog neural networks with the sigmoidal activation function oe(y) = 1=1+e \Gammay is bounded by a quadratic polynomial O((lm) 2 ) in both the number l of programmable parameters, and the number m of nodes. The proof method of this paper generalizes to much wider class of Pfaffian activation functions and formulas, and gives also for the first time polynomial bounds on their VC Dimension. We present also some other applications of our method. 0 Introduction This paper studies the VC Dimension of general functional basis networks, and the resulting Boolean combinations of certain formulas. We develop a new method for proving explicit upper bounds for a wide class of analog neural networks with general Pfaffian activation functions. Research partially supported by the International Comput... | |||||||||||||||
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