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Mobile-centric AI applications have high requirements for resource-efficiency of model inference. Input filtering is a promising approach to eliminate the redundancy so as to reduce the cost of inference. Previous efforts have tailored effective solutions for many applications, but left two essential questions unanswered: (1) theoretical filterability of an inference workload to guide the application of input filtering techniques, thereby avoiding the trial-and-error cost for resource-constrained mobile applications; (2) robust discriminability of feature embedding to allow input filtering to be widely effective for diverse inference tasks and input content. To answer them, we first formalize the input filtering problem and theoretically compare the hypothesis complexity of inference models and input filters to understand the optimization potential. Then we propose the first end-to-end learnable input filtering framework that covers most state-of-the-art methods and surpasses them in feature embedding with robust discriminability. We design and implement InFi that supports six input modalities and multiple mobile-centric deployments. Comprehensive evaluations confirm our theoretical results and show that InFi outperforms strong baselines in applicability, accuracy, and efficiency. InFi achieve 8.5x throughput and save 95% bandwidth, while keeping over 90% accuracy, for a video analytics application on mobile platforms.