Noise-robust modes of the retinal population code have the geometry of "ridges" and correspond to neuronal communities

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 data sets of the responses of approximately 150 retinal ganglion cells and show that local probability peaks are absent under broad, nonrepeated 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 comprise 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.