文章基本信息

标题：VC Dimension of Sigmoidal and General Pfaffian Networks
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作者：Marek Karpinski ; Angus Macintyre
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1995
卷号：1995
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：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 (y)=11+e−y 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.
关键词：Boolean Computation, Neural Networks, Pfaffian Activation Functions and Formulas, Sparse Networks, VC Dimension