Generic properties of a computational task predict human effort and performance
It has been shown that computational hardness of cognitive tasks affects people’s effort and ability to solve problems reliably. However, prior empirical studies lack generality. They quantify computational hardness of tasks based on particular algorithms or for specific problems. Here, we propose a set of measures of computational hardness of individual instances of a task in a way that is independent of any algorithm or computational model and can be generalized to other problems. Specifically, we introduce two measures, typical-case complexity (TCC), a measure of average hardness of a random ensemble of instances, and instance complexity (IC), an instance-specific metric. Both measures are related to structural properties of instances. We then test the effect of those measures on human behavior by asking participants to solve instances of two variants of the 0-1 knapsack problem, a canonical and ubiquitous NP-hard problem. We find that participants spent more time on instances with higher TCC and IC, but that decision quality was lower in those instances. We propose that the study of mathematical properties of tasks related to computational hardness can contribute to the development of computationally plausible accounts of human decision-making, just like stochastic properties have proven to be critical to our understanding of human decisions in probabilistic tasks.
The neural dynamics associated with computational complexity
Many everyday tasks require people to solve computationally complex problems. However, little is known about the effects of computational hardness on the neural processes associated with solving such problems. Here, we draw on computational complexity theory to address this issue. We performed an experiment in which participants solved several instances of the 0-1 knapsack problem, a combinatorial optimization problem, while undergoing ultra-high field (7T) functional magnetic resonance imaging (fMRI). Instances varied in two task-independent measures of intrinsic computational hardness: complexity and proof hardness. We characterise a network of brain regions whose activation was correlated with both measures but in distinct ways, including the anterior insula, dorsal anterior cingulate cortex and the intra-parietal sulcus/angular gyrus. Activation and connectivity changed dynamically as a function of complexity and proof hardness, in line with theoretical computational requirements. Overall, our results suggest that computational complexity theory provides a suitable framework to study the effects of computational hardness on the neural processes associated with solving complex cognitive tasks.
Task-independent metrics of computational hardness predict human cognitive performance
The survival of human organisms depends on our ability to solve complex tasks in the face of limited cognitive resources. However, little is known about the factors that drive the complexity of those tasks. Here, building on insights from computational complexity theory, we quantify the computational hardness of cognitive tasks using a set of task-independent metrics related to the computational resource requirements of individual instances of a task. We then examine the relation between those metrics and human behavior and find that they predict both time spent on a task as well as accuracy in three canonical cognitive tasks. Our findings demonstrate that performance in cognitive tasks can be predicted based on generic metrics of their inherent computational hardness.
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