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Erschienen in:
2019 | OriginalPaper | Buchkapitel
13. Approximation Properties of Perceptrons
verfasst von : Andrzej Bielecki
Erschienen in: Models of Neurons and Perceptrons: Selected Problems and Challenges
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Abstract
As it was mentioned in Sect. 8.1, an untrained perceptron can be treated as a family of functions \(\mathbb {R}^n\rightarrow \mathbb {R}^m\) indexed by a vector set of all its weights. A given training set, in turn, can be regarded as a set of the points to which a mapping should be approximated in the best way. The investigations of approximation abilities of neural networks are focused on the existence of an arbitrarily close approximation. They are also focused on the problem how accuracy depends on a complexity of a perceptron. In this chapter a few basic theorems that concern the approximation properties of perceptrons are discussed. The presented theorems are the classical results. In this monograph they are presented without the proofs which can be found in literature.