The Structured `Low Temperature' Phase of the Retinal Population Code

Recent advances in experimental techniques have allowed the simultaneous
recordings of populations of hundreds of neurons, fostering a debate about
the nature of the collective structure of population neural activity. Much
of this debate has focused on the empirical findings of a phase transition
in the parameter space of maximum entropy models describing the measured
neural probability distributions, interpreting this phase transition to
indicate a critical tuning of the neural code. Here, we instead focus on
the possibility that this is a first-order phase transition which provides
evidence that the real neural population is in a `structured',
collective state. We show that this collective state is robust to changes
in stimulus ensemble and adaptive state. We find that the pattern of
pairwise correlations between neurons has a strength that is well within
the strongly correlated regime and does not require fine tuning,
suggesting that this state is generic for populations of 100+ neurons. We
find a clear correspondence between the emergence of a phase transition,
and the emergence of attractor-like structure in the inferred energy
landscape. A collective state in the neural population, in which neural
activity patterns naturally form clusters, provides a consistent
interpretation for our results.