  A fundamental problem in neuroscience is understanding how working memory --
the ability to store information at intermediate timescales, like 10s of
seconds -- is implemented in realistic neuronal networks. The most likely
candidate mechanism is the attractor network, and a great deal of effort has
gone toward investigating it theoretically. Yet, despite almost a quarter
century of intense work, attractor networks are not fully understood. In
particular, there are still two unanswered questions. First, how is it that
attractor networks exhibit irregular firing, as is observed experimentally
during working memory tasks? And second, how many memories can be stored under
biologically realistic conditions? Here we answer both questions by studying an
attractor neural network in which inhibition and excitation balance each other.
Using mean field analysis, we derive a three-variable description of attractor
networks. From this description it follows that irregular firing can exist only
if the number of neurons involved in a memory is large. The same mean field
analysis also shows that the number of memories that can be stored in a network
scales with the number of excitatory connections, a result that has been
suggested for simple models but never shown for realistic ones. Both of these
predictions are verified using simulations with large networks of spiking
neurons.
