| VC Dimension of Sigmoidal and General Pfaffian Networks (1995) | |||||||||||||||
Abstract | |||||||||||||||
| 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. Research partially supported by the International Computer Science Institute, Berkeley, by the DFG Grant KA 673/4-1, and by the ESPRIT BR Grants 7097 and ECUS 030. Research partially done while visiting Dept. of Computer Science at Princeton University. Email: marek@cs.uni-bonn.de y Research supported in part by a Senior Research Fellowship of the EP... | |||||||||||||||
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