Cosnard, Michel; Koiran, Pascal; Paugam-Moisy, Hélène Bounds on the number of units for computing arbitrary dichotomies by multilayer perceptrons. (English) Zbl 0802.68107 J. Complexity 10, No. 1, 57-63 (1994). Summary: Multilayer perceptrons can compute arbitrary dichotomies of a set of \(N\) points of \([0,1]^ d\). The minimal size of such networks was studied by E. B. Baum [J. Complexity 4, No. 3, 193-215 (1988; Zbl 0648.68085)] using the parameter \(N\). In this paper, we show that this question can be addressed using another parameter, the minimum distance \(\delta\) between the two classes. We derive related upper and lower bounds on the size of nets capable of computing arbitrary dichotomies. MSC: 68T05 Learning and adaptive systems in artificial intelligence Keywords:multilayer perceptrons; dichotomies Citations:Zbl 0648.68085 PDFBibTeX XMLCite \textit{M. Cosnard} et al., J. Complexity 10, No. 1, 57--63 (1994; Zbl 0802.68107) Full Text: DOI