A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a dataset of nouns. We find that such correlations reduce the storage capacity of a Potts network to a limited extent, so that the number of concepts that can be stored and retrieved in a large, human-scale cortical network may still be of order 107, as originally estimated without correlations. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, 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: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving's remember/know paradigms.
Keywords: Potts network; attractor neural networks; autoassociative memory; cortex; semantic memory.