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With the rise of edge computing, various AI services are expected to be available at a mobile side through the inference based on deep neural network (DNN) operated at the network edge, called edge inference (EI). On the other hand, the resulting AI quality (e.g., mean average precision in objective detection) has been regarded as a given factor, and AI quality control has yet to be explored despite its importance in addressing the diverse demands of different users. This work aims at tackling the issue by proposing a feature hierarchical EI (FHEI), comprising feature network and inference network deployed at an edge server and corresponding mobile, respectively. Specifically, feature network is designed based on feature hierarchy, a one-directional feature dependency with a different scale. A higher scale feature requires more computation and communication loads while it provides a better AI quality. The tradeoff enables FHEI to control AI quality gradually w.r.t. communication and computation loads, leading to deriving a near-to-optimal solution to maximize multi-user AI quality under the constraints of uplink \& downlink transmissions and edge server and mobile computation capabilities. It is verified by extensive simulations that the proposed joint communication-and-computation control on FHEI architecture always outperforms several benchmarks by differentiating each user's AI quality depending on the communication and computation conditions.