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Despite being intuitive, cognitive effort has proven difficult to define quantitatively. Here, we proposed to study cognitive effort by investigating the degree to which the brain deviates from its default state, where brain activity is scale-invariant. Specifically, we measured such deviations by examining changes in scale-invariance of brain activity as a function of task difficulty and posited suppression of scale-invariance as a proxy for exertion of cognitive effort. While there is some fMRI evidence supporting this proposition, EEG investigations on the matter are scant, despite the EEG signal being more suitable for analysis of scale invariance (i.e., having a much broader frequency range). In the current study we validated the correspondence between scale-invariance (H) of cortical activity recorded by EEG and task load during two working memory (WM) experiments with varying set sizes. Then, we used this neural signature to disentangle cognitive effort from the number of items stored in WM within participants. Our results showed monotonic decreases in H with increased set size, even after set size exceeded WM capacity. This behavior of H contrasted with behavioral performance and an oscillatory indicator of WM load (i.e., alpha-band desynchronization), both of which showed a plateau at difficulty levels surpassing WM capacity. This is the first reported evidence for the suppression of scale-invariance in EEG due to task difficulty, and our work suggests that H suppression may be used to quantify changes in cognitive effort even when working memory load is at maximum capacity., Competing Interests: Declaration of competing interest None., (Copyright © 2020 The Authors. Published by Elsevier Inc. All rights reserved.)