Combinatorics and connectionism

Abstract In recent years there has been a great deal of interest in ‘connectionism’. This name covers a variety of activities, some of them wholly non-mathematical, concerned with processes which resemble the cognitive functions of the human brain. In this paper I shall use standard graph-theoretic terminology to describe some mathematical aspects of this work. A fundamental problem is to formalize the notion of learning in such a way that significant mathematical results can be obtained. The notion of ‘probably approximately correct’ learning turns out to be appropriate and important results have been obtained by using the notion of dimension due to Vapnik and Chervonenkis.

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