  We present a Hopfield-like autoassociative network for memories representing
examples of concepts. Each memory is encoded by two activity patterns with
complementary properties. The first is dense and correlated across examples
within concepts, and the second is sparse and exhibits no correlation among
examples. The network stores each memory as a linear combination of its
encodings. During retrieval, the network recovers sparse or dense patterns with
a high or low activity threshold, respectively. As more memories are stored,
the dense representation at low threshold shifts from examples to concepts,
which are learned from accumulating common example features. Meanwhile, the
sparse representation at high threshold maintains distinctions between examples
due to the high capacity of sparse, decorrelated patterns. Thus, a single
network can retrieve memories at both example and concept scales and perform
heteroassociation between them. We obtain our results by deriving macroscopic
mean-field equations that yield capacity formulas for sparse examples, dense
examples, and dense concepts. We also perform network simulations that verify
our theoretical results and explicitly demonstrate the capabilities of the
network.
