Asymptotic Eigenvectors, Topological Patterns and Recurrent Networks
نویسنده
چکیده
The notions of asymptotic eigenvectors and asymptotic eigenvalues are defined. Based on these notions a special probability rule for pattern selection in a Hopfield type dynamics is introduced. The underlying network is considered to be a d -regular graph, where d is an integer denoting the number of nodes connected to each neuron. It is shown that as far as the degree d is less than a critical value c d , the number of stored patterns with (1) m O μ = can be much larger than that in a standard recurrent network with Bernouill random patterns. As observed in [4] the probability rule we study here turns out to be related to the spontaneous activity of the network. So our result might be an evidence for the idea that some spontaneous activities intend to reorganize information for improving the capacity .
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