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Goal-driven selective attention (GDSA) refers to the brain's function ofprioritizing the activity of a task-relevant subset of its overall network toefficiently process relevant information while inhibiting the effects ofdistractions. Despite decades of research in neuroscience, a comprehensiveunderstanding of GDSA is still lacking. We propose a novel framework usingconcepts and tools from control theory as well as insights and structures fromneuroscience. Central to this framework is an information-processing hierarchywith two main components: selective inhibition of task-irrelevant activity andtop-down recruitment of task-relevant activity. We analyze the internaldynamics of each layer of the hierarchy described as a network withlinear-threshold dynamics and derive conditions on its structure to guaranteeexistence and uniqueness of equilibria, asymptotic stability, and boundednessof trajectories. We also provide mechanisms that enforce selective inhibitionusing the biologically-inspired schemes of feedforward and feedback inhibition.Despite their differences, both lead to the same conclusion: the intrinsicdynamical properties of the (not-inhibited) task-relevant subnetworks are thesole determiner of the dynamical properties that are achievable under selectiveinhibition.

Hierarchical Selective Recruitment in Linear-Threshold Brain Networks, Part I: Single-Layer Dynamics and Selective Inhibition