Emergence of criticality in high-dimensional neural activity

In statistical physics, critical models sit near boundaries between regions of qualitatively different behavior. When inferring statistical models of neural activity, this proximity to criticality is often interpreted as evidence that the underlying system is fine-tuned. Here we challenge this interpretation. When mapping parameters to system behaviors (the forward problem), not all sets of parameters are created equal; some small regions in parameter space can map to large regions in behavior space. In fact, these special parameter values are precisely those near criticality. Thus, when inferring parameters from behaviors (the inverse problem), one should expect models to naturally cluster near critical points. We illustrate this flow toward criticality in the Curie-Weiss model of Ising spins, and we demonstrate that the flow becomes stronger as the size of the system increases. Across a wide range of neural recordings, we find that inferred models concentrate near criticality as the number of neurons increases despite substantial differences in the underlying systems. Together, these results provide an explanation for the emergence of criticality in high-dimensional systems without fine-tuning.