As a precursor to the selection of a stimulus for gaze and attention, a midbrain network categorizes stimuli into "strongest" and "others." The categorization tracks flexibly, in real time, the absolute strength of the strongest stimulus. In this study, we take a first-principles approach to computations that are essential for such categorization. We demonstrate that classical feedforward lateral inhibition cannot produce flexible categorization. However, circuits in which the strength of lateral inhibition varies with the relative strength of competing stimuli categorize successfully. One particular implementation--reciprocal inhibition of feedforward lateral inhibition--is structurally the simplest, and it outperforms others in flexibly categorizing rapidly and reliably. Strong predictions of this anatomically supported circuit model are validated by neural responses measured in the owl midbrain. The results demonstrate the extraordinary power of a remarkably simple, neurally grounded circuit motif in producing flexible categorization, a computation fundamental to attention, perception, and decision making.
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