Harnessing Computational Complexity Theory to Model Human Decision-making and Cognition
A central aim of cognitive science is to understand the fundamental mechanisms that enable humans to navigate and make sense of complex environments. In this letter, we argue that computational complexity theory, a foundational framework for evaluating computational resource requirements, holds significant potential in addressing this challenge. As humans possess limited cognitive resources for processing vast amounts of information, understanding how humans perform complex cognitive tasks requires comprehending the underlying factors that drive information processing demands. Computational complexity theory provides a comprehensive theoretical framework to achieve this goal. By adopting this framework, we can gain new insights into how cognitive systems work and develop a more nuanced understanding of the relation between task complexity and human behaviour. We provide empirical evidence supporting our argument and identify several open research questions and challenges in applying computational complexity theory to human decision-making and cognitive science at large.
Two approaches to incorporate computational complexity into the study of cognition. (a) The set of cognitive functions is refined a priori based on notions of traceability. (b) Human behaviour is modelled based on intrinsic characteristics of the problem. https://doi.org/10.1111/cogs.13304
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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