Associative memory in realistic neuronal networks

Almost two decades ago, Hopfield [1] showed that networks of highly reduced model neurons can exhibit multiple attracting fixed points, thus providing a substrate for associative memory. It is still not clear, however, whether realistic neuronal networks can support multiple attractors. The main difficulty is that neuronal networks in vivo exhibit a stable background state at low firing rate, typically a few Hz. Embedding attractor is easy; doing so without destabilizing the background is not. Previous work [2,3] focused on the sparse coding limit, in which a vanishingly small number of neurons are involved in any memory. Here we investigate the case in which the number of neurons involved in a memory scales with the number of neurons in the network. In contrast to the sparse coding limit, we find that multiple attractors can co-exist robustly with a stable background state. Mean field theory is used to understand how the behavior of the network scales with its parameters, and simulations with analog neurons are presented.

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