Analysis of the Collective Properties of "Neural Networks" and Their Relation to the Structure and Concepts of Memory

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The mathematical structure of the collective excitations of model neural networks will be examined for the relevance which they may have to the essential aspects of "higher nervous function." An examination of this subject requires that much be known about the pattern of connections between nerve cells. Since this cannot be provided directly from neurobiological experiments, we will work with the case of associative memory, where the nature of the connections is believed to be due to the structure in the information provided by the external world. The nature of the collective properties is expected to depend on the topology of the underlying neural circuits. The fundamental question is whether the interactions between any collective excitations have useful computational properties.