From criticality to cognitive effort: scale-invariant EEG dynamics supporting cognitive flexibility are suppressed by effort

The critical brain hypothesis contends that brains operate near a phase transition where excitation and inhibition are balanced, enabling neural dynamics to rapidly adapt and reorganize for cognitive demands. Allocating control resources to maintain stable task representations likely shifts brains away from criticality. Here, we test whether proximity to criticality indexes the balance between flexible adaptation and effortful task engagement. To do so, we adapt a time-resolved measure of scale invariance in EEG amplitude fluctuations (d2), capable of quantifying distance-to-criticality under non-stationary conditions - as during cognitive tasks. We benchmark our measure using ground-truth simulations of a neural mass model and show that d2 is lowest when excitation and inhibition are balanced. Next, we apply d2 to data collected during a task-switching paradigm and find that more demanding trials increased deviation from criticality, whereas greater flexibility, faster responses, and higher accuracy occurred closer to criticality. These effects were region-specific: deviation at posterior electrodes predicted worse performance, while deviations at frontal midline electrodes predicted better performance. Together, these results suggest that deviations from criticality reflect both cognitive load and effort exertion, highlighting EEG amplitude scale-invariance as a sensitive marker of adaptive neural dynamics under cognitive demand.