Critical integration in neural and cognitive systems: Beyond power-law scaling as the hallmark of soft assembly

Inspired by models of self-organized criticality, a family of measures quantifies long-range correlations in neural and behavioral activity in the form of self-similar (e.g., power-law scaled) patterns across a range of scales. Long-range correlations are often taken as evidence that a system is near a critical transition, suggesting interaction-dominant, softly assembled relations between its parts. Psychologists and neuroscientists frequently use power-law scaling as evidence of critical regimes and soft assembly in neural and cognitive activity. Critics, however, argue that this methodology operates at most at the level of an analogy between cognitive and other natural phenomena. This is because power-laws do not provide information about a particular system's organization or what makes it specifically cognitive. We respond to this criticism using recent work in Integrated Information Theory. We propose a more principled understanding of criticality as a system's susceptibility to changes in its own integration, a property cognitive agents are expected to manifest. We contrast critical integration with power-law measures and find the former more informative about the underlying processes.