The impact of connectivity on the memory capacity and the retrieval dynamics of Hopfield-type networks

Most models of neural associative memory have used networks with broad connectivity. However, this seems unrealistic from a neuroanatomical perspective. A simple model of associative memory with emergent properties was introduced by Hopfield [5]. We choose this widely known model to investigate the impact of connectivity on the storage capacity and the retrieval dynamics in artificial associative networks. In this paper, we use sparse topologies where only a small fraction of possible connections were actually active. For these diluted topologies, we test different kinds of architecture; namely, randomly connected networks, regularly connected networks, small-world networks, and modular networks. Computer experiments reveal that, among these diluted topologies, the modular architectures, that exhibit a relatively high clustering coefficient and whose characteristic path lengths and total physical wiring lengths are short, produce the far better results in terms of memory storage and generalization abilities. Theoretical implications and extensions to this work are discussed.