"MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB." . . "Theoretical mathematics." . . . . . "Networks and the best approximation property"@en . "Networks and the best approximation property" . . . . . . . . . . . . . "Networks and the Best Approximation Property"@en . . . "Networks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We prove that networks derived from regularization theory and including Radial Basis functions (Poggio and Girosi, 1989), have a similar property. From the point of view of approximation theory, however, the property of approximation continuous functions arbitrarily well is not sufficient for characterizing good approximation schemes. More critical is the property of best approximation. The main result of this paper is that multilayer networks, of the type used in backpropagation, are not best approximation. For regularization networks (in particular Radial Basis Function networks) we prove existence and uniqueness of best approximation."@en . . . . . . . . "Layers." . . "Approximation(mathematics)" . . "Whitaker College. Center for Biological Information Processing." . . "Whitaker College of Health Sciences, Technology, and Management. Center for Biological Information Processing." . . "Massachusetts Institute of Technology. Artificial Intelligence Laboratory." . . "Networks." . . "Functions." . . "Functions(mathematics)" . . . . "Continuity." . . "Theory." . .