| Bounding VC-Dimension for Neural Networks: Progress and Prospects (1995) | |||||||||||||||
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| . Techniques from differential topology are used to give polynomial bounds for the VC-dimension of sigmoidal neural networks. The bounds are quadratic in w, the dimension of the space of weights. Similar results are obtained for a wide class of Pfaffian activation functions. The obstruction (in differential topology) to improving the bound to an optimal bound O (w log w) is discussed, and attention is paid to the role of other parameters involved in the network architecture. ? Dept. of Computer Science, University of Bonn, 53117 Bonn. Research partially supported by the DFG Grant KA 673/4-1, and by ESPRIT BR Grants 7097 and ECUS 030. ?? Mathematical Institute, University of Oxford, Oxford OX1 3LB. Research supported in part by a Senior Research Fellowship of the SERC. 1 Introduction We refer to Macintyre-Sontag [MS93](cf, e.g., also [AB92] and [GJ93]) for all notions required from the theory of neural architectures, and to Hirsch for necessary notions from differential topology [... | |||||||||||||||
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