  Goal-driven selective attention (GDSA) refers to the brain's function of
prioritizing the activity of a task-relevant subset of its overall network to
efficiently process relevant information while inhibiting the effects of
distractions. Despite decades of research in neuroscience, a comprehensive
understanding of GDSA is still lacking. We propose a novel framework using
concepts and tools from control theory as well as insights and structures from
neuroscience. Central to this framework is an information-processing hierarchy
with two main components: selective inhibition of task-irrelevant activity and
top-down recruitment of task-relevant activity. We analyze the internal
dynamics of each layer of the hierarchy described as a network with
linear-threshold dynamics and derive conditions on its structure to guarantee
existence and uniqueness of equilibria, asymptotic stability, and boundedness
of trajectories. We also provide mechanisms that enforce selective inhibition
using the biologically-inspired schemes of feedforward and feedback inhibition.
Despite their differences, both lead to the same conclusion: the intrinsic
dynamical properties of the (not-inhibited) task-relevant subnetworks are the
sole determiner of the dynamical properties that are achievable under selective
inhibition.
