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Deep Neural Networks (DNNs) can achieve state-of-the-art accuracy in many computer vision tasks, such as object counting. Object counting takes two inputs: an image and an object query and reports the number of occurrences of the queried object. To achieve high accuracy on such tasks, DNNs require billions of operations, making them difficult to deploy on resource-constrained, low-power devices. Prior work shows that a significant number of DNN operations are redundant and can be eliminated without affecting the accuracy. To reduce these redundancies, we propose a hierarchical DNN architecture for object counting. This architecture uses a Region Proposal Network (RPN) to propose regions-of-interest (RoIs) that may contain the queried objects. A hierarchical classifier then efficiently finds the RoIs that actually contain the queried objects. The hierarchy contains groups of visually similar object categories. Small DNNs are used at each node of the hierarchy to classify between these groups. The RoIs are incrementally processed by the hierarchical classifier. If the object in an RoI is in the same group as the queried object, then the next DNN in the hierarchy processes the RoI further; otherwise, the RoI is discarded. By using a few small DNNs to process each image, this method reduces the memory requirement, inference time, energy consumption, and number of operations with negligible accuracy loss when compared with the existing object counters.