bioRxiv2025
The hypothesis that the brain operates near criticality has far-reaching implications for brain function and is supported by growing experimental evidence. Observations of scale-invariant brain activity agree with this hypothesis, but what about when brain activity is not scale-invariant? Should we reject the criticality hypothesis When power-laws poorly fit the data or when strong oscillations occur (dominated by a specific time scale)? Here we show several ways that criticality can be hidden from traditional data analytic approaches, leading to false negative conclusions. We use a parsimonious high-dimensional model to demonstrate how neural systems may separate different dynamical modes into different subspaces, simultaneously generating non-critical dynamics, critical oscillations, and scale-invariant avalanches. Our results point to a need for new methods capable of revealing hidden criticality and suggest that criticality could be more prevalent than previously thought, hidden in subspaces not readily revealed by standard data analyses. Does the brain operate in a dynamical regime close to a critical phase transition? This question is fundamental; the nature of neural computation is strongly impacted by whether a system is close to or far from criticality [1-5]. Evidence suggesting that the brain operates close to criticality has accumulated at an accelerating pace over the past two decades (a recent meta analysis found 31 reports in 2024 alone [2]). The two most common types of experimental evidence have been based on neuronal avalanche analysis [1, 6, 7] and long-range temporal correlation analysis [8-12]. Both these approaches examine a one-dimensional time series of collective neural activity, averaged over large populations of neurons, seeking temporally-correlated, scale-invariant fluctuations that obey specific scaling laws predicted by theory. In many cases, measurements agree with these predictions; the success and persistence of the criticality hypothesis rests on these cases. However, it is not difficult to find measurements that do not agree, with fluctuations poorly described by power-laws and scaling laws. Another common observation that, naively, seems to contradict criticality is oscillatory brain activity with a particular dominant frequency. At first glance, either the lack of power-laws or the prominence of a dominant oscillatory time scale appear to contradict the criticality hypothesis. What should we conclude from these apparently contradictory observations? Assuming that all the experimental observations are sound and valid, there are two possible explanations, not necessarily mutually exclusive. First, it could be that there are biophysical control parameters constantly in flux in the brain, causing shifts in proximity to criticality. In this scenario, non-scale-invariant data reflect true deviations from criticality and we should conclude that the brain is, at times, closer to and, at other times, further from criticality. This view has been proposed in multiple previous studies and is consistent with substantial experimental evidence [6, 13-19]. However, here we argue that there is an important, but rarely considered, second plausible explanation. It could be that traditional methods for assessing criticality can be fooled. In this case, the system dynamics could be truly critical and scale-invariant, but not visible to traditional methods. We first show why such hidden criticality is plausible considering general mathematical arguments and relevant experimental evidence. Then, we use a parsimonious computational model to demonstrate concrete examples of ground truth scale-invariant critical dynamics that are missed by traditional analyses of population average activity. Moreover, our model shows how critical oscillations, avalanches, and other non-critical modes of dynamics can coexist, by separating each different mode into a distinct low-dimensional subspace. All together, our results suggest that the combination of these various subspaces make up the high-dimensional dynamical system commonly observed in the brain. Our results reconcile multiple, seemingly discrepant, experimental observations and describe prospects for new methods that can reveal hidden criticality.