  An appealing new principle for neural population codes is that correlations
among neurons organize neural activity patterns into a discrete set of
clusters, which can each be viewed as a noise-robust population "codeword".
Previous studies assumed that these codewords corresponded geometrically with
local peaks in the probability landscape of neural population responses. Here,
we analyze multiple datasets of the responses of ~150 retinal ganglion cells
and show that local probability peaks are absent under broad, non-repeated
stimulus ensembles, which are characteristic of natural behavior. However, we
find that neural activity still forms noise-robust clusters in this regime,
albeit clusters with a different geometry. We start by defining a soft local
maximum, which is a local probability maximum when constrained to a fixed spike
count. Next, we show that soft local maxima are robustly present, and can
moreover be linked across different spike count levels in the probability
landscape to form a "ridge". We found that these ridges are comprised of
combinations of spiking and silence in the neural population such that all of
the spiking neurons are members of the same neuronal community, a notion from
network theory. We argue that a neuronal community shares many of the
properties of Donald Hebb's classic cell assembly, and show that a simple,
biologically plausible decoding algorithm can recognize the presence of a
specific neuronal community.
