Publications

Abstract

In the cognitive, computational, and neuro-sciences, practitioners often reason about what computational models represent or learn, as well as what algorithm is instantiated. The putative goal of such reasoning is to generalize claims about the model in question, to claims about the mind and brain, and the neurocognitive capacities of those systems. Such inference is often based on a model’s performance on a task, and whether that performance approximates human behavior or brain activity. Here we demonstrate how such argumentation problematizes the relationship between models and their targets; we place emphasis on artificial neural networks (ANNs), though any theory-brain relationship that falls into the same schema of reasoning is at risk. In this paper, we model inferences from ANNs to brains and back within a formal framework — metatheoretical calculus — in order to initiate a dialogue on both how models are broadly understood and used, and on how to best formally characterize them and their functions. To these ends, we express claims from the published record about models’ successes and failures in first-order logic. Our proposed formalization describes the decision-making processes enacted by scientists to adjudicate over theories. We demonstrate that formalizing the argumentation in the literature can uncover potential deep issues about how theory is related to phenomena. We discuss what this means broadly for research in cognitive science, neuroscience, and psychology; what it means for models when they lose the ability to mediate between theory and data in a meaningful way; and what this means for the metatheoretical calculus our fields deploy when performing high-level scientific inference.

Abstract

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing objective and open criteria, such as how spatially compact districts are. We formulated one such model that minimised pairwise distance between voters within a district. Using US Census Bureau data, we confirmed our prediction that the difference in compactness between the computed and actual districts would be greatest for states that are large and, therefore, difficult for humans to properly district given their limited capacities. The computed solutions highlighted differences in how humans and machines solve this task with machine solutions more fully optimised and displaying emergent properties not evident in human solutions. These results suggest a division of labour in which humans debate and formulate districting criteria whereas machines optimise the criteria to draw the district boundaries. We discuss how criteria can be expanded beyond notions of compactness to include other factors, such as respecting municipal boundaries, historic communities, and relevant legislation.