High capacity, small world associative memory models

Models of associative memory usually have full connectivity or, if diluted, random symmetric connectivity. In contrast, biological neural systems have predominantly local, non-symmetric connectivity. Here we investigate sparse networks of threshold units, trained with the perceptron learning rule. The units are given position and are arranged in a ring. The connectivity graph varies between being local to random via a small world regime, with short path lengths between any two neurons. The connectivity may be symmetric or non-symmetric. The results show that it is the small world networks with non-symmetric weights and non-symmetric connectivity that perform best as associative memories. It is also shown that in highly dilute networks small world architectures will produce efficiently wired associative memories, which still exhibit good pattern completion abilities.