Full solution for the storage of correlated memories in an autoassociative memory

Abstract

We complement our previous work [arxiv: 0707.0565] with the full (non diluted) solution describing the stable states of an attractor network that stores correlated patterns of activity. The new solution provides a good fit of simulations of a network storing the feature norms of McRae and colleagues [McRae et al, 2005], experimentally obtained combinations of features representing concepts in semantic memory. We discuss three ways to improve the storage capacity of the network: adding uninformative neurons, removing informative neurons and introducing popularity-modulated hebbian learning. We show that if the strength of synapses is modulated by an exponential decay of the popularity of the pre-synaptic neuron, any distribution of patterns can be stored and retrieved with approximately an optimal storage capacity - i.e, C ~ I.p, the minimum number of connections per neuron needed to sustain the retrieval of a pattern is proportional to the information content of the pattern multiplied by the number of patterns stored in the network.