Correlations and signatures of criticality in neural population models

Large-scale recording methods make it possible to measure the statistics of neural population activity and to gain insights into the principles that govern the collective activity of neural ensembles.  One hypothesis that has emerged from this approach is that neural populations are poised at a thermodynamic critical point. Support for this notion has come from a recent series of studies  which identified signatures of criticality (such as a divergence of the specific heat with population size) in the statistics of neural activity recorded from populations of retinal ganglion cells, and hypothesized that the retina might be optimised to be operating at this critical point.

What mechanisms can explain these observations?  Do they require the neural system to be fine-tuned to be poised at the critical point, or do they robustly emerge in generic circuits? How are signatures of criticality related to the structure of correlations within the neural population? We here show that these effects arise in a simple simulation of retinal population activity. They robustly appear across a range of parameters including biologically implausible ones, and can be understood analytically in a simple model. The specific heat diverges linearly  with population size n whenever the (average) correlation is independent of n— in particular, this is generally true when subsampling a large, correlated population.  These observations pose the question of whether signatures of criticality are indicative of an optimised coding strategy, or whether they arise as byproduct of sub-sampling a neural population with correlations.