High Performance Associative Memory Models with Low Wiring Costs

The performance of sparsely-connected associative memories built from sets of perceptrons configured in a ring structure is investigated using different patterns of connectivity. Architectures based on uniform and linear distributions of restricted maximum connection length are compared to those based on Gaussian distributions and to networks created by progressively rewiring a locally-connected network. It is found that while all four architectures are capable of good pattern-completion performance in sparse networks, the Gaussian, restricted-linear and restricted-uniform architectures require lower mean wiring lengths to achieve the same results. It is shown that in order to achieve good pattern-completion at low wiring costs, connectivity should be localized, though not completely local, and that distal connections are not necessary.