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Abstract Attention has long been thought to enable efficient vision, 1–8 yet it requires additional neural machinery and energy. Whether attention yields net energetic benefits—after accounting for the cost of control—has never been demonstrated. Here we show that attentional control can substantially improve whole-system energy efficiency in a model of primate visual processing. Our model, EAN (“Energy-efficient Attention Network”), implements attention as recurrent top-down multiplicative gain over features, space, and time. EAN is optimized using a joint objective combining task performance and neurobiologically grounded energy costs accounting for action potentials and synaptic transmission across all components, 9–11 including the attentional control circuitry itself. On a visual-category-search task requiring joint identification and localization of a target, EAN learns to focus its energy dynamically on task-relevant locations and features, reducing total energy use by up to 50% at matched accuracy and enabling flexible trial-by-trial trading of accuracy against energy. The model variant combining feature-based and spatial attention is most efficient and best captures human errors and difficulty judgments. EAN generalizes to classical attention tasks, replicating canonical effects of attention on firing rates, variability, and noise correlations, 12 and patterns of V4-to-V1 feedback suppression. 13 Our work connects a cognitive function (attention), a neural mechanism (gain modulation), and a neurobiological constraint (metabolic cost) in a single mechanistic model that explains how selection and recurrence enable flexible, energy-efficient vision.