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A theorem is proved to the effect that three-layered perceptrons with an infinite number of computing units can represent arbitrary mapping if the desired mapping and the input-output characteristics of the computing units satisfy some constraints. The proof is constructive, and each coefficient is explicitly presented. The theorem theoretically guarantees a kind of universality for three-layered perceptrons. Although two-layered perceptrons (simple perceptrons) cannot represent arbitrary functions, three-layers prove necessary and sufficient. The relationship between the model used in the proof and the distributed storage and processing of information is also discussed.>
Irie et al. (Fri,) studied this question.