The Capacity for Correlated Semantic Memories in the Cortex

We analyze an autoassociative network of Potts units, coupled via tensor connections, as an effective model of extended cortical networks with distinct short and long-range synaptic connections. To study semantic memory, organized in terms of the relations between the attributes of real-world knowledge, we formulate a generative model of item representation with correlations. The model ascribes such correlations to the influence of underlying "factors": items with more shared factors have more correlated representations. Moreover, if many factors are balanced, correlations are overall low; whereas if a few factors dominate (increasing a dominance parameter ζ), they become strong. Our model allows for correlations that are neither trivial (random) nor merely hierarchical (an ultrametric tree). The network can retrieve one from up to p ≃ CS^2/a weakly correlated items, of order 10,000,000 with human cortical parameters. When its storage capacity is exceeded, however, retrieval fails completely only for low ζ; above a critical dominance value, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: possibly a model of semantic memory resilience in remember/know paradigms.