Emergence of criticality in models of real neurons.

Critical systems sit near boundaries between qualitatively distinct behaviors. When inferring models of neural activity, this proximity to criticality is thought to require the precise tuning of parameters. Here, we show that as the number of neurons increases, criticality can emerge naturally without fine-tuning. When computing observable statistics from parameters (the forward problem), some small regions in parameter space map to large regions in statistics space. These special parameters are precisely those near criticality. Thus, when inferring parameters from experimental measurements (the inverse problem), models concentrate near critical points, and this concentration becomes stronger as the system grows. We illustrate this flow toward criticality across many large-scale recordings in the mouse brain. In the Curie-Weiss model of Ising spins, we find that all of the recordings collapse to a first-order phase transition, despite substantial differences in the underlying systems. Together, these results suggest a resolution to the tension between criticality and fine-tuning in models of neural activity.