Attractor neural networks with patchy connectivity

We investigate the effects of patchy (clustered) connectivity in sparsely connected attractor neural networks (NNs). This study is motivated by the fact that the connectivity of pyramidal neurons in layer II/III of the mammalian visual cortex is patchy and sparse. The storage capacity of hypercolumnar attractor NNs that use the Hopfield and Willshaw learning rules with this kind of connectivity is investigated analytically as well as by simulation experiments. We find that patchy connectivity gives a higher storage capacity, given an overall sparse connectivity and regardless of learning rule.