| Polynomial Bounds for VC Dimension of Sigmoidal 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, the VC Dimension of analog neural networks with the sigmoid activation function oe(y) = 1=1 + e \Gammay to be bounded by a quadratic polynomial in the number of programmable parameters. 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. Email: marek@cs.uni-bonn.de y Research supported in part by a Senior Research Fellowship of the SERC. Email: ajm@maths.ox.ac.uk 0 Introduction The most commonly used activation function in various neural networks applications is the sigmoid oe(y) = 1=1+e \Gammay (cf. [HKP91]). In Maass's 1993 lecture notes [M93], Open Problem 10 (see also [GJ93] and [MS93]) asks: Is the VC-dimension of analog neural nets with the sigmoid activation function oe(y) = 1=1+ e \Gammay ... | |||||||||||||||
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