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Abstract:
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.
References
[1] J. J. Hopfield. Neural networks and physical systems with
emergent collective computational abilities.
Proc. Natl. Acad. Sci.
, 79:2554-2558, 1982.
[2] N. Brunel. Persistent activity and the single-cell
frequency-current curve in a cortical network model.
Network: Computation in Neural Systems
, 11:261-280, 2000.
[3] P. E. Latham and S. N. Nirenberg. Intrinsic dynamics in
cultured neuronal networks.
Soc. Neuroscience Abstract
, 25:2259, 1999.
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