The first attempts to consider the behavior of so-called "random neural nets" in a systematic way have led to a series of problems concerned with relations between the "structure" and the "function" of such nets. The "structure" of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of "this" neuron synapsing on "that" one, but rather in terms of tendencies and probabilities associated with points or regions in the net.
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