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Abstract

Large-scale recording methods make it possible to measure the statistics of neural population activity, and thereby 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 [1], and that this may have important functional consequences. Support for this hypothesis has come from studies [2,3] that 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. 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 [4,5,6]? We show that indicators for thermodynamic criticality arise in a simple simulation of retinal population activity, and without the need for fine-tuning or adaptation. Using simple statistical models [7], we demonstrate that peak specific heat grows with population size whenever the (average) correlation is independent of the number of neurons. The latter is always true when uniformly subsampling a large, correlated population. For weakly correlated populations, the rate of divergence of the specific heat is proportional to the correlation strength. This predicts that neural populations would be strongly correlated if they were optimized to maximize specific heat, which is in contrast with theories of efficient coding that make the opposite prediction. Our findings suggest that indicators for thermodynamic criticality might not require an optimized coding strategy, but rather arise as consequence of subsampling a stimulusdriven neural population.